pld60.ipynb

{
 "metadata": {
  "name": "",
  "signature": "sha256:b5c5eadb9183d1652489a471889813100eff841ba59a3b97f0c041abbfc13a64"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "pralados60 study"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The subjects were 'randomly' assigned all at once before the training program to one of the two groups, Walk and Run, by the method of minimisation (see [Saguaei (2011)](http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3317766/)) using the factors gender, BMI (below/over 28.3 kg/m$2$), and then $\\dot{V}O_2$ peak (below/over 22.6 ml/kg/min). We also set the assignment with 30% more subjects for the Run group. This assignment was performed using the [Minim software](http://www-users.york.ac.uk/~mb55/guide/minim.htm).\n",
      "\n",
      "We started with **15** subjects in the Walk group and **19** subjects in the Run group.   \n",
      "At the end, we had **12** subjects in the Walk group and **10** subjects in the Run group.\n",
      "\n",
      "Here is the statistical data analysis."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division, print_function\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "import pandas as pd\n",
      "%matplotlib inline\n",
      "from IPython.display import HTML, display, Image\n",
      "from factorplots2 import interaction_plot"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Comparisons for age, mass, height, and BMI"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's test if these two groups of *survivals* are similar about age, mass, height, and BMI.   \n",
      "\n",
      "**The data:**"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# mass before, mass after, height, age\n",
      "r = np.array([[63.1, 62.2, 1.62, 64],\n",
      "             [88.9, 84.7, 1.66, 64],\n",
      "             [64.5, 64.5, 1.52, 71],\n",
      "             [55.0, 54.3, 1.63, 71],\n",
      "             [73.7, 73.9, 1.71, 62],\n",
      "             [89.4, 91.1, 1.77, 66],\n",
      "             [87.9, 88.1, 1.56, 61],\n",
      "             [84.3, 83.5, 1.73, 58],\n",
      "             [79.2, 79.2, 1.52, 66],\n",
      "             [78.2, 78.2, 1.56, 60],\n",
      "             [76.8, 76.8, 1.63, 64],\n",
      "             [64.7, 64.7, 1.64, 60]])\n",
      "# mass before, mass after, height, age\n",
      "w = np.array([[74.5, 74.1, 1.64, 68],\n",
      "             [87.9, 87.5, 1.57, 71],\n",
      "             [71.9, 71.9, 1.62, np.nan],\n",
      "             [68.5, 71.7, 1.68, 62],\n",
      "             [105.4, 105.4, 1.73, 67],\n",
      "             [71.7, 70.5, 1.47, 64],\n",
      "             [60.7, 60.5, 1.52, 64],\n",
      "             [83.1, 82.6, 1.65, 68],\n",
      "             [74.6, 74.6, 1.62, 68],\n",
      "             [61.4, 61.4, 1.49, 57]])\n",
      "data = np.vstack((w, r))\n",
      "# add BMI data\n",
      "bmi = lambda weight, height: weight / height**2\n",
      "data = np.vstack((data[:, :3].T, bmi(data[:, 0], data[:, 2]), \n",
      "                  bmi(data[:, 1], data[:, 2]), data[:, 3].T)).T"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Descriptive statistics:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "columns = ['Mass0', 'Mass1', 'Height', 'BMI0', 'BMI1', 'Age']\n",
      "col_order = np.argsort(columns)\n",
      "df = pd.DataFrame(data, columns=columns)\n",
      "df['Group'] = pd.Series(['Walk']*w.shape[0] + ['Run']*r.shape[0])\n",
      "#display(df.groupby('Group').describe())\n",
      "#axs = df.boxplot(by='Group', figsize=(10, 6))\n",
      "#plt.tight_layout()\n",
      "\n",
      "plt.figure(figsize=(10, 5))\n",
      "plt.subplot(2, 3, 1)\n",
      "interaction_plot(x=df.Group, trace=df.Group, response=df.Mass0, legendloc=None)\n",
      "plt.xlabel(''), plt.tick_params(labelbottom=False)\n",
      "plt.subplot(2, 3, 2)\n",
      "interaction_plot(x=df.Group, trace=df.Group, response=df.Mass1, legendloc=None)\n",
      "plt.xlabel(''), plt.tick_params(labelbottom=False)\n",
      "plt.subplot(2, 3, 3)\n",
      "interaction_plot(x=df.Group, trace=df.Group, response=df.Height, legendloc=None)\n",
      "plt.xlabel(''), plt.tick_params(labelbottom=False)\n",
      "plt.subplot(2, 3, 4)\n",
      "interaction_plot(x=df.Group, trace=df.Group, response=df.BMI0, legendloc=None)\n",
      "plt.subplot(2, 3, 5)\n",
      "interaction_plot(x=df.Group, trace=df.Group, response=df.BMI1, legendloc=None)\n",
      "plt.subplot(2, 3, 6)\n",
      "interaction_plot(x=df.Group, trace=df.Group, response=df.Age, legendloc=None)\n",
      "plt.suptitle('Age, mass, height, and BMI', y=1.04, size=20)\n",
      "plt.tight_layout()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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bdQ6E6LqG8rvCRz7btm2DsbExjIyMsGTJErz11lu4c+eO4tK3DEVFRbC3twcA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\nIiIiIiIrTJKJiIiIiKwwSSYiIiIisvL/z5e8ok4mMLcAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1119b1b00>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "t-tests for the between-group comparisons:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy import stats\n",
      "walk = df[df['Group'] == 'Walk']\n",
      "run  = df[df['Group'] == 'Run']\n",
      "print('Walk versus Run (t-test)')\n",
      "for c in columns:\n",
      "    t, p = stats.ttest_ind(walk[c].dropna(), run[c].dropna())\n",
      "    print('Factor %s: t=%.2f, p=%.2f' %(c, t, p))\n",
      "#stats.ttest_re"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Walk versus Run (t-test)\n",
        "Factor Mass0: t=0.09, p=0.93\n",
        "Factor Mass1: t=0.18, p=0.86\n",
        "Factor Height: t=-0.86, p=0.40\n",
        "Factor BMI0: t=0.60, p=0.55\n",
        "Factor BMI1: t=0.70, p=0.49\n",
        "Factor Age: t=0.83, p=0.41\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**In conclusion, there are no difference between groups with respect to age, mass, height, and BMI.**"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Comparisons for the biomechanical variables"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The plots for all biomechanical variables we are interested are here:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.display import IFrame\n",
      "IFrame('http://demotu.org/x/pld60/pld60xplots.pdf', width=900, height=400)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "\n",
        "        <iframe\n",
        "            width=\"900\"\n",
        "            height=400\"\n",
        "            src=\"http://demotu.org/x/pld60/pld60xplots.pdf\"\n",
        "            frameborder=\"0\"\n",
        "            allowfullscreen\n",
        "        ></iframe>\n",
        "        "
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "<IPython.lib.display.IFrame at 0x11198af98>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Comparisons for spatio-temporal variables during walking"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = pd.read_csv('../X/pld60x/spat_tempo_grf_w.txt', sep='\\t', header=0)\n",
      "data.loc[data.Group==0, 'Group'] = 'walk'\n",
      "data.loc[data.Group==1, 'Group'] = 'run'\n",
      "data.loc[data.Period==0, 'Period'] = 'pre'\n",
      "data.loc[data.Period==1, 'Period'] = 'pos'\n",
      "#data.groupby(['Group','Period']).describe()\n",
      "#data.set_index(['Group', 'Period', 'Subject'], inplace=True)\n",
      "#data.groupby(level=['Group','Period']).describe()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.figure(figsize=(8, 2.5))\n",
      "plt.subplot(1, 2, 1)\n",
      "interaction_plot(x=data.Period, trace=data.Group, response=data.Str_dur)\n",
      "plt.subplot(1, 2, 2)\n",
      "interaction_plot(x=data.Period, trace=data.Group, response=data.Str_len, legendloc=None)\n",
      "plt.suptitle('Stride duration and length during walking', y=1.05, size=20)\n",
      "plt.tight_layout()\n",
      "\n",
      "plt.figure(figsize=(8, 4))\n",
      "plt.subplot(2, 2, 1)\n",
      "interaction_plot(x=data.Period, trace=data.Group, response=data.MIF)\n",
      "plt.xlabel(''), plt.tick_params(labelbottom=False)\n",
      "plt.subplot(2, 2, 2)\n",
      "interaction_plot(x=data.Period, trace=data.Group, response=data.Pks1, legendloc=None)\n",
      "plt.xlabel(''), plt.tick_params(labelbottom=False)\n",
      "plt.subplot(2, 2, 3)\n",
      "interaction_plot(x=data.Period, trace=data.Group, response=data.Pks2, legendloc=None)\n",
      "plt.subplot(2, 2, 4)\n",
      "interaction_plot(x=data.Period, trace=data.Group, response=data.Pks3, legendloc=None)\n",
      "plt.suptitle('GRF variables during walking', y=1.04, size=20)\n",
      "plt.tight_layout()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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av090oxvd6rf5+/tLrd9qNTy2s7ODg4MD0tPT0alTJ5w5cwbdunVDhw4dcPbs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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x111aa63c8>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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VqkMIoe6G6mRkAAkJ7P9+fsCBA40rj4IcPHgQWlpa+OijjwAAn332mUIzcc+c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\niIiISJX+P0YYMia1OyScAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x111a6c860>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# load IPython extension to work with R\n",
      "%load_ext rmagic"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R -i data\n",
      "data$Subject = factor(data$Subject)\n",
      "library(car)\n",
      "library(ez)\n",
      "options(contrasts=c(\"contr.sum\", \"contr.poly\"))\n",
      "print(\"Variable: Str_dur\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Str_dur, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Str_dur), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)\n",
      "print(\"Variable: Str_len\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Str_len, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Str_len), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)\n",
      "print(\"Variable: MIF\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$MIF, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(MIF), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)\n",
      "print(\"Variable: Pks1\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Pks1, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Pks1), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)\n",
      "print(\"Variable: Pks2\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Pks2, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Pks2), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)\n",
      "print(\"Variable: Pks3\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Pks3, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Pks3), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "[1] \"Variable: Str_dur\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value Pr(>F)\n",
        "group  1  0.0035 0.9529\n",
        "      42               \n",
        "Warning: Data is unbalanced (unequal N per group). Make sure you specified a well-considered value for the type argument to ezANOVA().\n",
        "$ANOVA\n",
        "        Effect DFn DFd           F         p p<.05          ges\n",
        "2        Group   1  20 0.333102012 0.5702786       1.416455e-02\n",
        "3       Period   1  20 2.331664783 0.1424268       1.575662e-02\n",
        "4 Group:Period   1  20 0.006458905 0.9367439       4.434393e-05\n",
        "\n",
        "[1] \"Variable: Str_len\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value Pr(>F)\n",
        "group  1  1.6165 0.2106\n",
        "      42               \n",
        "Warning: Data is unbalanced (unequal N per group). Make sure you specified a well-considered value for the type argument to ezANOVA().\n",
        "$ANOVA\n",
        "        Effect DFn DFd        F          p p<.05        ges\n",
        "2        Group   1  20 2.637027 0.12005548       0.11105024\n",
        "3       Period   1  20 3.561369 0.07373957       0.00927024\n",
        "4 Group:Period   1  20 4.519490 0.04615625     * 0.01173496\n",
        "\n",
        "[1] \"Variable: MIF\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value Pr(>F)\n",
        "group  1  0.0772 0.7825\n",
        "      42               \n",
        "Warning: Data is unbalanced (unequal N per group). Make sure you specified a well-considered value for the type argument to ezANOVA().\n",
        "$ANOVA\n",
        "        Effect DFn DFd         F         p p<.05          ges\n",
        "2        Group   1  20 1.4268988 0.2462459       0.0601418545\n",
        "3       Period   1  20 0.1407576 0.7114782       0.0007249735\n",
        "4 Group:Period   1  20 0.8944023 0.3555738       0.0045888151\n",
        "\n",
        "[1] \"Variable: Pks1\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value Pr(>F)\n",
        "group  1  0.9131 0.3448\n",
        "      42               \n",
        "Warning: Data is unbalanced (unequal N per group). Make sure you specified a well-considered value for the type argument to ezANOVA().\n",
        "$ANOVA\n",
        "        Effect DFn DFd         F         p p<.05         ges\n",
        "2        Group   1  20 1.2027252 0.2858075       0.047684275\n",
        "3       Period   1  20 0.2708095 0.6085025       0.002260997\n",
        "4 Group:Period   1  20 1.0207324 0.3244130       0.008469098\n",
        "\n",
        "[1] \"Variable: Pks2\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value Pr(>F)\n",
        "group  1  0.4109  0.525\n",
        "      42               \n",
        "Warning: Data is unbalanced (unequal N per group). Make sure you specified a well-considered value for the type argument to ezANOVA().\n",
        "$ANOVA\n",
        "        Effect DFn DFd            F           p p<.05          ges\n",
        "2        Group   1  20 3.149868e-05 0.995577606       1.481375e-06\n",
        "3       Period   1  20 5.969936e-01 0.448762781       1.770041e-03\n",
        "4 Group:Period   1  20 8.283310e+00 0.009297708     * 2.401217e-02\n",
        "\n",
        "[1] \"Variable: Pks3\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value  Pr(>F)  \n",
        "group  1   4.564 0.03852 *\n",
        "      42                  \n",
        "---\n",
        "Signif. codes:  0 \u2018***\u2019 0.001 \u2018**\u2019 0.01 \u2018*\u2019 0.05 \u2018.\u2019 0.1 \u2018 \u2019 1\n",
        "Warning: Data is unbalanced (unequal N per group). Make sure you specified a well-considered value for the type argument to ezANOVA().\n",
        "$ANOVA\n",
        "        Effect DFn DFd          F         p p<.05          ges\n",
        "2        Group   1  20 0.13506773 0.7170948       0.0062961397\n",
        "3       Period   1  20 0.04308681 0.8376609       0.0001331189\n",
        "4 Group:Period   1  20 0.93190916 0.3458960       0.0028712961\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**Post-hoc analysis**   \n",
      "In our 2x2 design, we are interested in only four comparisons for the interaction effect: Pre:G1/G2; Pos:G1/G2; G1:Pre/Pos; G2:Pre/Pos and two comparisons for each of the main effects.   \n",
      "So, as post hoc, let's use t-tests with Bonferroni correction (the p value will be multiplied by 4 for the interaction effects and by 2 for the main effects)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R -i data\n",
      "print(t.test(subset(data$Str_len, data$Group==\"walk\" & data$Period==\"pre\"),\n",
      "             subset(data$Str_len, data$Group==\"run\"  & data$Period==\"pre\")))\n",
      "print(t.test(subset(data$Str_len, data$Group==\"walk\" & data$Period==\"pos\"), \n",
      "             subset(data$Str_len, data$Group==\"run\"  & data$Period==\"pos\")))\n",
      "print(t.test(subset(data$Str_len, data$Group==\"walk\" & data$Period==\"pre\"), \n",
      "             subset(data$Str_len, data$Group==\"walk\" & data$Period==\"pos\"), paired=T))\n",
      "print(t.test(subset(data$Str_len, data$Group==\"run\"  & data$Period==\"pre\"), \n",
      "             subset(data$Str_len, data$Group==\"run\"  & data$Period==\"pos\"), paired=T))\n",
      "print(\"effect size\")\n",
      "library(lsr)\n",
      "A = data$Str_len[data$Group==\"run\"]\n",
      "B = data$Period[data$Group==\"run\"]\n",
      "print(cohensD(A ~ B), paired=T)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "\n",
        "\tWelch Two Sample t-test\n",
        "\n",
        "data:  subset(data$Str_len, data$Group == \"walk\" & data$Period == \"pre\") and subset(data$Str_len, data$Group == \"run\" & data$Period == \"pre\")\n",
        "t = 1.07, df = 17.065, p-value = 0.2995\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -1.498191  4.583478\n",
        "sample estimates:\n",
        "mean of x mean of y \n",
        " 86.72097  85.17833 \n",
        "\n",
        "\n",
        "\tWelch Two Sample t-test\n",
        "\n",
        "data:  subset(data$Str_len, data$Group == \"walk\" & data$Period == \"pos\") and subset(data$Str_len, data$Group == \"run\" & data$Period == \"pos\")\n",
        "t = 1.9805, df = 14.426, p-value = 0.06704\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -0.233264  6.068946\n",
        "sample estimates:\n",
        "mean of x mean of y \n",
        " 86.79819  83.88035 \n",
        "\n",
        "\n",
        "\tPaired t-test\n",
        "\n",
        "data:  subset(data$Str_len, data$Group == \"walk\" & data$Period == \"pre\") and subset(data$Str_len, data$Group == \"walk\" & data$Period == \"pos\")\n",
        "t = -0.1609, df = 11, p-value = 0.8751\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -1.1335329  0.9790914\n",
        "sample estimates:\n",
        "mean of the differences \n",
        "            -0.07722075 \n",
        "\n",
        "\n",
        "\tPaired t-test\n",
        "\n",
        "data:  subset(data$Str_len, data$Group == \"run\" & data$Period == \"pre\") and subset(data$Str_len, data$Group == \"run\" & data$Period == \"pos\")\n",
        "t = 3.1537, df = 9, p-value = 0.01167\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " 0.3669361 2.2290171\n",
        "sample estimates:\n",
        "mean of the differences \n",
        "               1.297977 \n",
        "\n",
        "[1] \"effect size\"\n",
        "[1] 0.3344627\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R -i data\n",
      "print(t.test(subset(data$Pks2, data$Group==\"walk\" & data$Period==\"pre\"),\n",
      "             subset(data$Pks2, data$Group==\"run\"  & data$Period==\"pre\")))\n",
      "print(t.test(subset(data$Pks2, data$Group==\"walk\" & data$Period==\"pos\"), \n",
      "             subset(data$Pks2, data$Group==\"run\"  & data$Period==\"pos\")))\n",
      "print(t.test(subset(data$Pks2, data$Group==\"walk\" & data$Period==\"pre\"), \n",
      "             subset(data$Pks2, data$Group==\"walk\" & data$Period==\"pos\"), paired=T))\n",
      "print(t.test(subset(data$Pks2, data$Group==\"run\"  & data$Period==\"pre\"), \n",
      "             subset(data$Pks2, data$Group==\"run\"  & data$Period==\"pos\"), paired=T))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "\n",
        "\tWelch Two Sample t-test\n",
        "\n",
        "data:  subset(data$Pks2, data$Group == \"walk\" & data$Period == \"pre\") and subset(data$Pks2, data$Group == \"run\" & data$Period == \"pre\")\n",
        "t = 0.7765, df = 19.994, p-value = 0.4466\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -3.896763  8.517633\n",
        "sample estimates:\n",
        "mean of x mean of y \n",
        " 117.1347  114.8242 \n",
        "\n",
        "\n",
        "\tWelch Two Sample t-test\n",
        "\n",
        "data:  subset(data$Pks2, data$Group == \"walk\" & data$Period == \"pos\") and subset(data$Pks2, data$Group == \"run\" & data$Period == \"pos\")\n",
        "t = -0.6511, df = 19.314, p-value = 0.5226\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -9.579326  5.029616\n",
        "sample estimates:\n",
        "mean of x mean of y \n",
        " 114.2265  116.5014 \n",
        "\n",
        "\n",
        "\tPaired t-test\n",
        "\n",
        "data:  subset(data$Pks2, data$Group == \"walk\" & data$Period == \"pre\") and subset(data$Pks2, data$Group == \"walk\" & data$Period == \"pos\")\n",
        "t = 2.866, df = 11, p-value = 0.01535\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " 0.6748009 5.1414659\n",
        "sample estimates:\n",
        "mean of the differences \n",
        "               2.908133 \n",
        "\n",
        "\n",
        "\tPaired t-test\n",
        "\n",
        "data:  subset(data$Pks2, data$Group == \"run\" & data$Period == \"pre\") and subset(data$Pks2, data$Group == \"run\" & data$Period == \"pos\")\n",
        "t = -1.34, df = 9, p-value = 0.2131\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -4.508507  1.154193\n",
        "sample estimates:\n",
        "mean of the differences \n",
        "              -1.677157 \n",
        "\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**In conclusion, during walking there were statistically significant interactions between factors Group and Period for the variables stride length (p=0.046, $\\mathbf{\\eta2=0.01}$) and the first active peak of the vertical ground reaction force (p=0.009, $\\mathbf{\\eta2=0.02}$). The post-hoc analysis revealed that only the variable stride length for the group 'run' increased after training (p=0.047, d=0.33). See the corresponding interaction plots above. **"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Comparisons for spatio-temporal variables during running"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = pd.read_csv('../X/pld60x/spat_tempo_grf_r.txt', sep='\\t', header=0)\n",
      "data.loc[data.Group==0, 'Group'] = 'walk'\n",
      "data.loc[data.Group==1, 'Group'] = 'run'\n",
      "data.loc[data.Period==0, 'Period'] = 'pre'\n",
      "data.loc[data.Period==1, 'Period'] = 'pos'\n",
      "#data.groupby(['Group','Period']).describe()\n",
      "#data.set_index(['Group', 'Period', 'Subject'], inplace=True)\n",
      "#data.groupby(level=['Group','Period']).describe()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.figure(figsize=(9, 2.5))\n",
      "plt.subplot(1, 2, 1)\n",
      "interaction_plot(x=data.Period, trace=data.Group, response=data.Str_dur)\n",
      "plt.subplot(1, 2, 2)\n",
      "interaction_plot(x=data.Period, trace=data.Group, response=data.Str_len, legendloc=None)\n",
      "plt.suptitle('Stride duration and length during running', y=1.05, size=20)\n",
      "plt.tight_layout()\n",
      "\n",
      "plt.figure(figsize=(9, 4))\n",
      "plt.subplot(2, 2, 1)\n",
      "interaction_plot(x=data.Period, trace=data.Group, response=data.MIF)\n",
      "plt.xlabel(''), plt.tick_params(labelbottom=False)\n",
      "plt.subplot(2, 2, 2)\n",
      "interaction_plot(x=data.Period, trace=data.Group, response=data.Pks1, legendloc=None)\n",
      "plt.xlabel(''), plt.tick_params(labelbottom=False)\n",
      "plt.subplot(2, 2, 3)\n",
      "interaction_plot(x=data.Period, trace=data.Group, response=data.Pks2, legendloc=None)\n",
      "#plt.subplot(2, 2, 4)\n",
      "#interaction_plot(x=data.Period, trace=data.Group, response=data.Pks3, legendloc=None)\n",
      "plt.suptitle('GRF variables during running', y=1.04, size=20)\n",
      "plt.tight_layout()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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5eTnKy8sRHx8Pe3t7rReSEEL05dmzZ/jvv//w33//4dmzZ5J/4mmivtRUvq/W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\nAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x111b733c8>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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rV+zZs0esDz9RsYN51DaPobGDKRQZR85fzEKVwA4dOgidQmQYhtsdJ4ywsDCB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\nkQwxCCQiIiKSof8HwEuf6aQvdG8AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x111bbe0b8>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R -i data\n",
      "data$Subject = factor(data$Subject)\n",
      "library(car)\n",
      "library(ez)\n",
      "options(contrasts=c(\"contr.sum\", \"contr.poly\"))\n",
      "print(\"Variable: Str_dur\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Str_dur, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Str_dur), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)\n",
      "print(\"Variable: Str_len\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Str_len, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Str_len), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)\n",
      "print(\"Variable: MIF\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$MIF, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(MIF), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)\n",
      "print(\"Variable: Pks1\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Pks1, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Pks1), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)\n",
      "print(\"Variable: Pks2\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Pks2, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Pks2), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "[1] \"Variable: Str_dur\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value Pr(>F)\n",
        "group  1  0.0041 0.9492\n",
        "      34               \n",
        "$ANOVA\n",
        "        Effect DFn DFd          F         p p<.05          ges\n",
        "2        Group   1  16 1.02617801 0.3261329       0.0430622010\n",
        "3       Period   1  16 0.04924761 0.8271854       0.0009175247\n",
        "4 Group:Period   1  16 1.97537620 0.1789986       0.0355279992\n",
        "\n",
        "[1] \"Variable: Str_len\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value Pr(>F)\n",
        "group  1  1.5454 0.2223\n",
        "      34               \n",
        "$ANOVA\n",
        "        Effect DFn DFd          F          p p<.05          ges\n",
        "2        Group   1  16 0.14194370 0.71130607       8.255986e-03\n",
        "3       Period   1  16 3.39767386 0.08389207       1.291875e-02\n",
        "4 Group:Period   1  16 0.02047813 0.88799645       7.887549e-05\n",
        "\n",
        "[1] \"Variable: MIF\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value Pr(>F)\n",
        "group  1  0.3899 0.5365\n",
        "      34               \n",
        "$ANOVA\n",
        "        Effect DFn DFd         F          p p<.05        ges\n",
        "2        Group   1  16 3.4125951 0.08327605       0.12357853\n",
        "3       Period   1  16 0.8921302 0.35894661       0.01854614\n",
        "4 Group:Period   1  16 1.1306676 0.30341885       0.02338901\n",
        "\n",
        "[1] \"Variable: Pks1\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value Pr(>F)\n",
        "group  1  0.1923 0.6638\n",
        "      34               \n",
        "$ANOVA\n",
        "        Effect DFn DFd         F          p p<.05        ges\n",
        "2        Group   1  16 4.7042213 0.04550187     * 0.10038812\n",
        "3       Period   1  16 0.5015004 0.48903078       0.01907652\n",
        "4 Group:Period   1  16 0.2591190 0.61767386       0.00994832\n",
        "\n",
        "[1] \"Variable: Pks2\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value Pr(>F)\n",
        "group  1  1.2782 0.2661\n",
        "      34               \n",
        "$ANOVA\n",
        "        Effect DFn DFd           F         p p<.05          ges\n",
        "2        Group   1  16 2.128303832 0.1639531       0.0433989533\n",
        "3       Period   1  16 0.410225088 0.5309219       0.0166138444\n",
        "4 Group:Period   1  16 0.009750893 0.9225660       0.0004014153\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R -i data\n",
      "print(t.test(subset(data$Pks1, data$Group==\"walk\" & data$Period==\"pre\"),\n",
      "             subset(data$Pks1, data$Group==\"run\"  & data$Period==\"pre\")))\n",
      "print(t.test(subset(data$Pks1, data$Group==\"walk\" & data$Period==\"pos\"), \n",
      "             subset(data$Pks1, data$Group==\"run\"  & data$Period==\"pos\")))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "\n",
        "\tWelch Two Sample t-test\n",
        "\n",
        "data:  subset(data$Pks1, data$Group == \"walk\" & data$Period == \"pre\") and subset(data$Pks1, data$Group == \"run\" & data$Period == \"pre\")\n",
        "t = -0.9428, df = 13.96, p-value = 0.3618\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -46.09537  17.94990\n",
        "sample estimates:\n",
        "mean of x mean of y \n",
        " 152.3357  166.4084 \n",
        "\n",
        "\n",
        "\tWelch Two Sample t-test\n",
        "\n",
        "data:  subset(data$Pks1, data$Group == \"walk\" & data$Period == \"pos\") and subset(data$Pks1, data$Group == \"run\" & data$Period == \"pos\")\n",
        "t = -1.7235, df = 15.997, p-value = 0.1041\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -58.292483   6.013508\n",
        "sample estimates:\n",
        "mean of x mean of y \n",
        " 154.6959  180.8354 \n",
        "\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**In conclusion, during running there was no statistically significant difference for the stride length, stride period and the ground-reaction-force peaks.**"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Flexion/Extension ROM during walking"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# this ploting function will be used for all variable from now on\n",
      "\n",
      "def plot(x, title):\n",
      "    plt.figure(figsize=(9, 5))\n",
      "    plt.subplot(2, 2, 1)\n",
      "    interaction_plot(x=x.Period, trace=x.Group, response=x.Pelvis)\n",
      "    plt.xlabel(''), plt.tick_params(labelbottom=False)\n",
      "    plt.subplot(2, 2, 2)\n",
      "    interaction_plot(x=x.Period, trace=x.Group, response=x.Hip, legendloc=None)\n",
      "    plt.xlabel(''), plt.tick_params(labelbottom=False)\n",
      "    plt.subplot(2, 2, 3)\n",
      "    interaction_plot(x=x.Period, trace=x.Group, response=x.Knee, legendloc=None)\n",
      "    plt.subplot(2, 2, 4)\n",
      "    interaction_plot(x=x.Period, trace=x.Group, response=x.Ankle, legendloc=None)\n",
      "    plt.suptitle(title, y=1.04, size=16)\n",
      "    plt.tight_layout()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = pd.read_csv('../X/pld60x/FlexROM_w.txt', sep='\\t', header=0)\n",
      "data.loc[data.Group==0, 'Group'] = 'walk'\n",
      "data.loc[data.Group==1, 'Group'] = 'run'\n",
      "data.loc[data.Period==0, 'Period'] = 'pre'\n",
      "data.loc[data.Period==1, 'Period'] = 'pos'\n",
      "\n",
      "plot(data, 'Flexion/Extension ROM during walking')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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a6N5d8/+kVVVVdJ4StbVo0QK2traSZVtbW7Ro0UKHERkm+gImRH/xmiImKSkJ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\nTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x111c17eb8>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R -i data\n",
      "data$Subject = factor(data$Subject)\n",
      "library(car)\n",
      "library(ez)\n",
      "options(contrasts=c(\"contr.sum\", \"contr.poly\"))\n",
      "print(\"Variable: Pelvis Flexion/Extension ROM\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Pelvis, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Pelvis), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)\n",
      "print(\"Variable: Hip Flexion/Extension ROM\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Hip, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Hip), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)\n",
      "print(\"Variable: Knee Flexion/Extension ROM\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Knee, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Knee), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)\n",
      "print(\"Variable: Ankle Flexion/Extension ROM\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Ankle, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Ankle), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "[1] \"Variable: Pelvis Flexion/Extension ROM\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value Pr(>F)\n",
        "group  1   3e-04 0.9853\n",
        "      42               \n",
        "Warning: Data is unbalanced (unequal N per group). Make sure you specified a well-considered value for the type argument to ezANOVA().\n",
        "$ANOVA\n",
        "        Effect DFn DFd         F         p p<.05         ges\n",
        "2        Group   1  20 0.3361967 0.5685079       0.014485201\n",
        "3       Period   1  20 0.8847742 0.3581205       0.005526753\n",
        "4 Group:Period   1  20 1.2386120 0.2789369       0.007719943\n",
        "\n",
        "[1] \"Variable: Hip Flexion/Extension ROM\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value Pr(>F)\n",
        "group  1  1.3634 0.2495\n",
        "      42               \n",
        "Warning: Data is unbalanced (unequal N per group). Make sure you specified a well-considered value for the type argument to ezANOVA().\n",
        "$ANOVA\n",
        "        Effect DFn DFd         F          p p<.05          ges\n",
        "2        Group   1  20 0.3940106 0.53730049       0.0177944084\n",
        "3       Period   1  20 0.2488968 0.62329591       0.0009994533\n",
        "4 Group:Period   1  20 3.4778421 0.07693784       0.0137866340\n",
        "\n",
        "[1] \"Variable: Knee Flexion/Extension ROM\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value Pr(>F)\n",
        "group  1  0.1591  0.692\n",
        "      42               \n",
        "Warning: Data is unbalanced (unequal N per group). Make sure you specified a well-considered value for the type argument to ezANOVA().\n",
        "$ANOVA\n",
        "        Effect DFn DFd          F          p p<.05          ges\n",
        "2        Group   1  20 1.61364754 0.21855951       0.0653092990\n",
        "3       Period   1  20 0.01742621 0.89629668       0.0001167237\n",
        "4 Group:Period   1  20 4.25829670 0.05227956       0.0277349497\n",
        "\n",
        "[1] \"Variable: Ankle Flexion/Extension ROM\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value Pr(>F)\n",
        "group  1  0.0083 0.9277\n",
        "      42               \n",
        "Warning: Data is unbalanced (unequal N per group). Make sure you specified a well-considered value for the type argument to ezANOVA().\n",
        "$ANOVA\n",
        "        Effect DFn DFd         F         p p<.05          ges\n",
        "2        Group   1  20 0.2641752 0.6128985       1.279573e-02\n",
        "3       Period   1  20 0.0118068 0.9145557       1.104687e-05\n",
        "4 Group:Period   1  20 1.0957211 0.3076936       1.024158e-03\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Flexion/Extension ROM during running"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = pd.read_csv('../X/pld60x/FlexROM_r.txt', sep='\\t', header=0)\n",
      "data.loc[data.Group==0, 'Group'] = 'walk'\n",
      "data.loc[data.Group==1, 'Group'] = 'run'\n",
      "data.loc[data.Period==0, 'Period'] = 'pre'\n",
      "data.loc[data.Period==1, 'Period'] = 'pos'\n",
      "\n",
      "plot(data, 'Flexion/Extension ROM during running')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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OLi4uOoxI/8nrd0VztBF9YuoTR6uVBCYkJOD27dsYO3Ysdu3ahTZt2tCdMVHK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       "text": [
        "<matplotlib.figure.Figure at 0x111ee4550>"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R -i data\n",
      "data$Subject = factor(data$Subject)\n",
      "library(car)\n",
      "library(ez)\n",
      "options(contrasts=c(\"contr.sum\", \"contr.poly\"))\n",
      "print(\"Variable: Pelvis Flexion/Extension ROM\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Pelvis, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Pelvis), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)\n",
      "print(\"Variable: Hip Flexion/Extension ROM\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Hip, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Hip), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)\n",
      "print(\"Variable: Knee Flexion/Extension ROM\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Knee, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Knee), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)\n",
      "print(\"Variable: Ankle Flexion/Extension ROM\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Ankle, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Ankle), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "[1] \"Variable: Pelvis Flexion/Extension ROM\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value Pr(>F)\n",
        "group  1   1.876 0.1798\n",
        "      34               \n",
        "$ANOVA\n",
        "        Effect DFn DFd         F         p p<.05         ges\n",
        "2        Group   1  16 0.8646010 0.3662718       0.038770270\n",
        "3       Period   1  16 0.1539046 0.7000081       0.002433383\n",
        "4 Group:Period   1  16 1.2662648 0.2770661       0.019674852\n",
        "\n",
        "[1] \"Variable: Hip Flexion/Extension ROM\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value   Pr(>F)   \n",
        "group  1  9.2725 0.004471 **\n",
        "      34                    \n",
        "---\n",
        "Signif. codes:  0 \u2018***\u2019 0.001 \u2018**\u2019 0.01 \u2018*\u2019 0.05 \u2018.\u2019 0.1 \u2018 \u2019 1\n",
        "$ANOVA\n",
        "        Effect DFn DFd         F         p p<.05         ges\n",
        "2        Group   1  16 2.1080459 0.1658532       0.103874859\n",
        "3       Period   1  16 2.3110820 0.1479688       0.017066345\n",
        "4 Group:Period   1  16 0.8638446 0.3664762       0.006448031\n",
        "\n",
        "[1] \"Variable: Knee Flexion/Extension ROM\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value  Pr(>F)  \n",
        "group  1  5.3338 0.02712 *\n",
        "      34                  \n",
        "---\n",
        "Signif. codes:  0 \u2018***\u2019 0.001 \u2018**\u2019 0.01 \u2018*\u2019 0.05 \u2018.\u2019 0.1 \u2018 \u2019 1\n",
        "$ANOVA\n",
        "        Effect DFn DFd         F         p p<.05        ges\n",
        "2        Group   1  16 0.4043257 0.5338541       0.02289713\n",
        "3       Period   1  16 2.3201752 0.1472248       0.01042959\n",
        "4 Group:Period   1  16 4.8933842 0.0418519     * 0.02174508\n",
        "\n",
        "[1] \"Variable: Ankle Flexion/Extension ROM\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value  Pr(>F)  \n",
        "group  1  4.8627 0.03431 *\n",
        "      34                  \n",
        "---\n",
        "Signif. codes:  0 \u2018***\u2019 0.001 \u2018**\u2019 0.01 \u2018*\u2019 0.05 \u2018.\u2019 0.1 \u2018 \u2019 1\n",
        "$ANOVA\n",
        "        Effect DFn DFd           F         p p<.05          ges\n",
        "2        Group   1  16 0.271946739 0.6091723       1.613076e-02\n",
        "3       Period   1  16 0.008388129 0.9281633       1.855095e-05\n",
        "4 Group:Period   1  16 1.006735277 0.3306202       2.221562e-03\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R -i data\n",
      "print(t.test(subset(data$Knee, data$Group==\"walk\" & data$Period==\"pre\"),\n",
      "             subset(data$Knee, data$Group==\"run\"  & data$Period==\"pre\")))\n",
      "print(t.test(subset(data$Knee, data$Group==\"walk\" & data$Period==\"pos\"), \n",
      "             subset(data$Knee, data$Group==\"run\"  & data$Period==\"pos\")))\n",
      "print(t.test(subset(data$Knee, data$Group==\"walk\" & data$Period==\"pre\"), \n",
      "             subset(data$Knee, data$Group==\"walk\" & data$Period==\"pos\"), paired=T))\n",
      "print(t.test(subset(data$Knee, data$Group==\"run\"  & data$Period==\"pre\"), \n",
      "             subset(data$Knee, data$Group==\"run\"  & data$Period==\"pos\"), paired=T))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "\n",
        "\tWelch Two Sample t-test\n",
        "\n",
        "data:  subset(data$Knee, data$Group == \"walk\" & data$Period == \"pre\") and subset(data$Knee, data$Group == \"run\" & data$Period == \"pre\")\n",
        "t = -1.0883, df = 10.687, p-value = 0.3004\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -15.758794   5.355829\n",
        "sample estimates:\n",
        "mean of x mean of y \n",
        " 62.36230  67.56379 \n",
        "\n",
        "\n",
        "\tWelch Two Sample t-test\n",
        "\n",
        "data:  subset(data$Knee, data$Group == \"walk\" & data$Period == \"pos\") and subset(data$Knee, data$Group == \"run\" & data$Period == \"pos\")\n",
        "t = -0.0182, df = 9.435, p-value = 0.9858\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -8.532119  8.394803\n",
        "sample estimates:\n",
        "mean of x mean of y \n",
        " 63.16153  63.23019 \n",
        "\n",
        "\n",
        "\tPaired t-test\n",
        "\n",
        "data:  subset(data$Knee, data$Group == \"walk\" & data$Period == \"pre\") and subset(data$Knee, data$Group == \"walk\" & data$Period == \"pos\")\n",
        "t = -0.442, df = 8, p-value = 0.6702\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -4.968509  3.370056\n",
        "sample estimates:\n",
        "mean of the differences \n",
        "             -0.7992267 \n",
        "\n",
        "\n",
        "\tPaired t-test\n",
        "\n",
        "data:  subset(data$Knee, data$Group == \"run\" & data$Period == \"pre\") and subset(data$Knee, data$Group == \"run\" & data$Period == \"pos\")\n",
        "t = 2.9798, df = 8, p-value = 0.01761\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " 0.9799077 7.6872874\n",
        "sample estimates:\n",
        "mean of the differences \n",
        "               4.333598 \n",
        "\n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**In conclusion, during walking and running there was no statistically significant difference for the Flexion/Extension ROM of the pelvis, hip, knee and ankle.**"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Flexion/Extension minimum during walking"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = pd.read_csv('../X/pld60x/FlexMin_w.txt', sep='\\t', header=0)\n",
      "data.loc[data.Group==0, 'Group'] = 'walk'\n",
      "data.loc[data.Group==1, 'Group'] = 'run'\n",
      "data.loc[data.Period==0, 'Period'] = 'pre'\n",
      "data.loc[data.Period==1, 'Period'] = 'pos'\n",
      "\n",
      "plot(data, 'Flexion/Extension minimum during walking')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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bMHXqVL0lqKKiAtOnT8ehQ4fg6+uLrl27YvDgwWjXrp3ejkkIIVLvvPOOLODz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\nbDA+LEGjabiAucyxF8R2VVVCAlhS0nTf3bvC+7W1wudMxj7tUBj9wfc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AhUIBM8UmImrC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\n/wf0ZjIy1XwChAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10f19e860>"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R -i data\n",
      "data$Subject = factor(data$Subject)\n",
      "library(car)\n",
      "library(ez)\n",
      "options(contrasts=c(\"contr.sum\", \"contr.poly\"))\n",
      "print(\"Variable: Pelvis Flexion/Extension minimum\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Pelvis, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Pelvis), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)\n",
      "print(\"Variable: Hip Flexion/Extension minimum\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Hip, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Hip), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)\n",
      "print(\"Variable: Knee Flexion/Extension minimum\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Knee, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Knee), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)\n",
      "print(\"Variable: Ankle Flexion/Extension minimum\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Ankle, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Ankle), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "[1] \"Variable: Pelvis Flexion/Extension minimum\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value Pr(>F)\n",
        "group  1   1.351 0.2517\n",
        "      42               \n",
        "Warning: Data is unbalanced (unequal N per group). Make sure you specified a well-considered value for the type argument to ezANOVA().\n",
        "$ANOVA\n",
        "        Effect DFn DFd         F          p p<.05        ges\n",
        "2        Group   1  20 5.8587120 0.02513972     * 0.16616000\n",
        "3       Period   1  20 0.6475562 0.43045047       0.01024657\n",
        "4 Group:Period   1  20 2.0456084 0.16808390       0.03166801\n",
        "\n",
        "[1] \"Variable: Hip Flexion/Extension minimum\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value Pr(>F)\n",
        "group  1  2.8162 0.1007\n",
        "      42               \n",
        "Warning: Data is unbalanced (unequal N per group). Make sure you specified a well-considered value for the type argument to ezANOVA().\n",
        "$ANOVA\n",
        "        Effect DFn DFd          F         p p<.05          ges\n",
        "2        Group   1  20 0.16766529 0.6865473       0.0040614105\n",
        "3       Period   1  20 0.01486855 0.9041661       0.0003816473\n",
        "4 Group:Period   1  20 2.65392487 0.1189449       0.0637994497\n",
        "\n",
        "[1] \"Variable: Knee Flexion/Extension minimum\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value Pr(>F)\n",
        "group  1   9e-04 0.9764\n",
        "      42               \n",
        "Warning: Data is unbalanced (unequal N per group). Make sure you specified a well-considered value for the type argument to ezANOVA().\n",
        "$ANOVA\n",
        "        Effect DFn DFd         F         p p<.05         ges\n",
        "2        Group   1  20 0.6631622 0.4250364       0.025342213\n",
        "3       Period   1  20 0.1901217 0.6674856       0.002047628\n",
        "4 Group:Period   1  20 0.9949144 0.3304601       0.010623238\n",
        "\n",
        "[1] \"Variable: Ankle Flexion/Extension minimum\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value Pr(>F)\n",
        "group  1  0.0654 0.7993\n",
        "      42               \n",
        "Warning: Data is unbalanced (unequal N per group). Make sure you specified a well-considered value for the type argument to ezANOVA().\n",
        "$ANOVA\n",
        "        Effect DFn DFd         F         p p<.05          ges\n",
        "2        Group   1  20 0.2202342 0.6439372       0.0095721661\n",
        "3       Period   1  20 0.1241048 0.7283095       0.0007584951\n",
        "4 Group:Period   1  20 0.6931894 0.4149135       0.0042219013\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R -i data\n",
      "print(t.test(subset(data$Pelvis, data$Group==\"walk\" & data$Period==\"pre\"),\n",
      "             subset(data$Pelvis, data$Group==\"run\"  & data$Period==\"pre\")))\n",
      "print(t.test(subset(data$Pelvis, data$Group==\"walk\" & data$Period==\"pos\"), \n",
      "             subset(data$Pelvis, data$Group==\"run\"  & data$Period==\"pos\")))\n",
      "print(\"effect size\")\n",
      "library(lsr)\n",
      "A = data$Pelvis[data$Period==\"pre\"]\n",
      "B = data$Group[data$Period==\"pre\"]\n",
      "print(cohensD(A ~ B))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "\n",
        "\tWelch Two Sample t-test\n",
        "\n",
        "data:  subset(data$Pelvis, data$Group == \"walk\" & data$Period == \"pre\") and subset(data$Pelvis, data$Group == \"run\" & data$Period == \"pre\")\n",
        "t = -2.9434, df = 19.674, p-value = 0.008132\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -4.5586213 -0.7747956\n",
        "sample estimates:\n",
        " mean of x  mean of y \n",
        "-3.4571266 -0.7904181 \n",
        "\n",
        "\n",
        "\tWelch Two Sample t-test\n",
        "\n",
        "data:  subset(data$Pelvis, data$Group == \"walk\" & data$Period == \"pos\") and subset(data$Pelvis, data$Group == \"run\" & data$Period == \"pos\")\n",
        "t = -1.0998, df = 15.049, p-value = 0.2887\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -3.316402  1.058378\n",
        "sample estimates:\n",
        "mean of x mean of y \n",
        "-3.120860 -1.991848 \n",
        "\n",
        "[1] \"effect size\"\n",
        "[1] 1.252707\n"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**In conclusion, during walking there was a statistically significant main effect of Group on the Felexion/Extension minimum angle for the Pelvis (p=0.025, $\\mathbf{\\eta2=0.017}$). The post-hoc analysis revealed that the Felexion/Extension minimum angle for the Pelvis was higher for the 'run' group than for the 'walk' group (p=0.016, d=1.25). See the corresponding interaction plots above. **"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Flexion/Extension minimum during running"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = pd.read_csv('../X/pld60x/FlexMin_r.txt', sep='\\t', header=0)\n",
      "data.loc[data.Group==0, 'Group'] = 'walk'\n",
      "data.loc[data.Group==1, 'Group'] = 'run'\n",
      "data.loc[data.Period==0, 'Period'] = 'pre'\n",
      "data.loc[data.Period==1, 'Period'] = 'pos'\n",
      "\n",
      "plot(data, 'Flexion/Extension minimum during running')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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RKpXIz8/H6tWrNdavWLEC7u7uaN++faljMIWlE6rSUv1NTpw4oV53586dYuejJbRv3x5b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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x111ab4a90>"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R -i data\n",
      "data$Subject = factor(data$Subject)\n",
      "library(car)\n",
      "library(ez)\n",
      "options(contrasts=c(\"contr.sum\", \"contr.poly\"))\n",
      "print(\"Variable: Pelvis Flexion/Extension minimum\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Pelvis, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Pelvis), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)\n",
      "print(\"Variable: Hip Flexion/Extension minimum\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Hip, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Hip), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)\n",
      "print(\"Variable: Knee Flexion/Extension minimum\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Knee, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Knee), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)\n",
      "print(\"Variable: Ankle Flexion/Extension minimum\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Ankle, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Ankle), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "[1] \"Variable: Pelvis Flexion/Extension minimum\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value Pr(>F)\n",
        "group  1   0.163 0.6889\n",
        "      34               \n",
        "$ANOVA\n",
        "        Effect DFn DFd            F          p p<.05          ges\n",
        "2        Group   1  16 7.0354625234 0.01738228     * 2.057914e-01\n",
        "3       Period   1  16 0.5190609831 0.48163656       1.314917e-02\n",
        "4 Group:Period   1  16 0.0008934031 0.97652457       2.293327e-05\n",
        "\n",
        "[1] \"Variable: Hip Flexion/Extension minimum\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value Pr(>F)\n",
        "group  1  1.3198 0.2587\n",
        "      34               \n",
        "$ANOVA\n",
        "        Effect DFn DFd         F          p p<.05         ges\n",
        "2        Group   1  16 0.2173707 0.64733510       0.007313695\n",
        "3       Period   1  16 0.1074866 0.74727492       0.003065329\n",
        "4 Group:Period   1  16 4.5839044 0.04801578     * 0.115925861\n",
        "\n",
        "[1] \"Variable: Knee Flexion/Extension minimum\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value Pr(>F)\n",
        "group  1  0.2202 0.6419\n",
        "      34               \n",
        "$ANOVA\n",
        "        Effect DFn DFd         F         p p<.05        ges\n",
        "2        Group   1  16 0.6773330 0.4226040       0.02292098\n",
        "3       Period   1  16 0.5128852 0.4842149       0.01409073\n",
        "4 Group:Period   1  16 0.5813515 0.4568772       0.01594175\n",
        "\n",
        "[1] \"Variable: Ankle Flexion/Extension minimum\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value  Pr(>F)  \n",
        "group  1  4.3783 0.04394 *\n",
        "      34                  \n",
        "---\n",
        "Signif. codes:  0 \u2018***\u2019 0.001 \u2018**\u2019 0.01 \u2018*\u2019 0.05 \u2018.\u2019 0.1 \u2018 \u2019 1\n",
        "$ANOVA\n",
        "        Effect DFn DFd         F         p p<.05          ges\n",
        "2        Group   1  16 0.5482276 0.4697697       0.0306186454\n",
        "3       Period   1  16 1.1943503 0.2906360       0.0058013670\n",
        "4 Group:Period   1  16 0.2040207 0.6575575       0.0009957884\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R -i data\n",
      "print(t.test(subset(data$Pelvis, data$Group==\"walk\" & data$Period==\"pre\"),\n",
      "             subset(data$Pelvis, data$Group==\"run\"  & data$Period==\"pre\")))\n",
      "print(t.test(subset(data$Pelvis, data$Group==\"walk\" & data$Period==\"pos\"), \n",
      "             subset(data$Pelvis, data$Group==\"run\"  & data$Period==\"pos\")))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "\n",
        "\tWelch Two Sample t-test\n",
        "\n",
        "data:  subset(data$Pelvis, data$Group == \"walk\" & data$Period == \"pre\") and subset(data$Pelvis, data$Group == \"run\" & data$Period == \"pre\")\n",
        "t = -2.0445, df = 14.48, p-value = 0.05953\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -3.37673716  0.07560983\n",
        "sample estimates:\n",
        " mean of x  mean of y \n",
        "-2.3465949 -0.6960312 \n",
        "\n",
        "\n",
        "\tWelch Two Sample t-test\n",
        "\n",
        "data:  subset(data$Pelvis, data$Group == \"walk\" & data$Period == \"pos\") and subset(data$Pelvis, data$Group == \"run\" & data$Period == \"pos\")\n",
        "t = -2.0284, df = 15.997, p-value = 0.05951\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -3.43975705  0.07592661\n",
        "sample estimates:\n",
        "mean of x mean of y \n",
        "-2.740116 -1.058201 \n",
        "\n"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R -i data\n",
      "print(t.test(subset(data$Hip, data$Group==\"walk\" & data$Period==\"pre\"),\n",
      "             subset(data$Hip, data$Group==\"run\"  & data$Period==\"pre\")))\n",
      "print(t.test(subset(data$Hip, data$Group==\"walk\" & data$Period==\"pos\"), \n",
      "             subset(data$Hip, data$Group==\"run\"  & data$Period==\"pos\")))\n",
      "print(t.test(subset(data$Hip, data$Group==\"walk\" & data$Period==\"pre\"), \n",
      "             subset(data$Hip, data$Group==\"walk\" & data$Period==\"pos\"), paired=T))\n",
      "print(t.test(subset(data$Hip, data$Group==\"run\"  & data$Period==\"pre\"), \n",
      "             subset(data$Hip, data$Group==\"run\"  & data$Period==\"pos\"), paired=T))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "\n",
        "\tWelch Two Sample t-test\n",
        "\n",
        "data:  subset(data$Hip, data$Group == \"walk\" & data$Period == \"pre\") and subset(data$Hip, data$Group == \"run\" & data$Period == \"pre\")\n",
        "t = -1.0572, df = 15.759, p-value = 0.3064\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -10.956025   3.670759\n",
        "sample estimates:\n",
        "mean of x mean of y \n",
        "-0.395722  3.246911 \n",
        "\n",
        "\n",
        "\tWelch Two Sample t-test\n",
        "\n",
        "data:  subset(data$Hip, data$Group == \"walk\" & data$Period == \"pos\") and subset(data$Hip, data$Group == \"run\" & data$Period == \"pos\")\n",
        "t = 1.8811, df = 10.428, p-value = 0.08814\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -1.050747 12.862785\n",
        "sample estimates:\n",
        "mean of x mean of y \n",
        " 5.109695 -0.796324 \n",
        "\n",
        "\n",
        "\tPaired t-test\n",
        "\n",
        "data:  subset(data$Hip, data$Group == \"walk\" & data$Period == \"pre\") and subset(data$Hip, data$Group == \"walk\" & data$Period == \"pos\")\n",
        "t = -1.4049, df = 8, p-value = 0.1977\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -14.541988   3.531154\n",
        "sample estimates:\n",
        "mean of the differences \n",
        "              -5.505417 \n",
        "\n",
        "\n",
        "\tPaired t-test\n",
        "\n",
        "data:  subset(data$Hip, data$Group == \"run\" & data$Period == \"pre\") and subset(data$Hip, data$Group == \"run\" & data$Period == \"pos\")\n",
        "t = 1.8988, df = 8, p-value = 0.09415\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -0.8671521  8.9536221\n",
        "sample estimates:\n",
        "mean of the differences \n",
        "               4.043235 \n",
        "\n"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**In conclusion, during running there was no statistically significant difference for the Flexion/Extension ROM of the pelvis, hip, knee and ankle.**"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Flexion/Extension maximum during walking"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = pd.read_csv('../X/pld60x/FlexMax_w.txt', sep='\\t', header=0)\n",
      "data.loc[data.Group==0, 'Group'] = 'walk'\n",
      "data.loc[data.Group==1, 'Group'] = 'run'\n",
      "data.loc[data.Period==0, 'Period'] = 'pre'\n",
      "data.loc[data.Period==1, 'Period'] = 'pos'\n",
      "\n",
      "plot(data, 'Flexion/Extension maximum during walking')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Vd+/evQgKCoKHh4fc/cpSUVGBt956C35+fjh9+jRGjx6Nt99+W3TFD9S1BpSXl4utO2jQ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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1130e3a90>"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R -i data\n",
      "data$Subject = factor(data$Subject)\n",
      "library(car)\n",
      "library(ez)\n",
      "options(contrasts=c(\"contr.sum\", \"contr.poly\"))\n",
      "print(\"Variable: Pelvis Flexion/Extension maximum\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Pelvis, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Pelvis), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)\n",
      "print(\"Variable: Hip Flexion/Extension maximum\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Hip, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Hip), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)\n",
      "print(\"Variable: Knee Flexion/Extension maximum\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Knee, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Knee), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)\n",
      "print(\"Variable: Ankle Flexion/Extension maximum\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Ankle, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Ankle), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "[1] \"Variable: Pelvis Flexion/Extension maximum\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value Pr(>F)\n",
        "group  1  0.5193 0.4751\n",
        "      42               \n",
        "Warning: Data is unbalanced (unequal N per group). Make sure you specified a well-considered value for the type argument to ezANOVA().\n",
        "$ANOVA\n",
        "        Effect DFn DFd            F         p p<.05          ges\n",
        "2        Group   1  20 1.548198e+00 0.2277869       6.432994e-02\n",
        "3       Period   1  20 2.439622e-06 0.9987692       1.364172e-08\n",
        "4 Group:Period   1  20 5.674433e-01 0.4600530       3.162956e-03\n",
        "\n",
        "[1] \"Variable: Hip Flexion/Extension maximum\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value Pr(>F)\n",
        "group  1   0.179 0.6744\n",
        "      42               \n",
        "Warning: Data is unbalanced (unequal N per group). Make sure you specified a well-considered value for the type argument to ezANOVA().\n",
        "$ANOVA\n",
        "        Effect DFn DFd          F          p p<.05         ges\n",
        "2        Group   1  20 0.79720832 0.38254719       0.021770356\n",
        "3       Period   1  20 0.06919058 0.79520973       0.001525675\n",
        "4 Group:Period   1  20 4.44742303 0.04775986     * 0.089433127\n",
        "\n",
        "[1] \"Variable: Knee Flexion/Extension maximum\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value Pr(>F)  \n",
        "group  1  5.3414 0.0258 *\n",
        "      42                 \n",
        "---\n",
        "Signif. codes:  0 \u2018***\u2019 0.001 \u2018**\u2019 0.01 \u2018*\u2019 0.05 \u2018.\u2019 0.1 \u2018 \u2019 1\n",
        "Warning: Data is unbalanced (unequal N per group). Make sure you specified a well-considered value for the type argument to ezANOVA().\n",
        "$ANOVA\n",
        "        Effect DFn DFd          F          p p<.05          ges\n",
        "2        Group   1  20 0.33788130 0.56754864       0.0128463791\n",
        "3       Period   1  20 0.08278128 0.77652331       0.0009498259\n",
        "4 Group:Period   1  20 5.99544365 0.02368952     * 0.0644208431\n",
        "\n",
        "[1] \"Variable: Ankle Flexion/Extension maximum\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value Pr(>F)\n",
        "group  1  1.1133 0.2974\n",
        "      42               \n",
        "Warning: Data is unbalanced (unequal N per group). Make sure you specified a well-considered value for the type argument to ezANOVA().\n",
        "$ANOVA\n",
        "        Effect DFn DFd         F         p p<.05          ges\n",
        "2        Group   1  20 1.4426935 0.2437359       0.0579601841\n",
        "3       Period   1  20 0.1054310 0.7487789       0.0007746549\n",
        "4 Group:Period   1  20 0.1884231 0.6688790       0.0013835958\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R -i data\n",
      "print(t.test(subset(data$Hip, data$Group==\"walk\" & data$Period==\"pre\"),\n",
      "             subset(data$Hip, data$Group==\"run\"  & data$Period==\"pre\")))\n",
      "print(t.test(subset(data$Hip, data$Group==\"walk\" & data$Period==\"pos\"), \n",
      "             subset(data$Hip, data$Group==\"run\"  & data$Period==\"pos\")))\n",
      "print(t.test(subset(data$Hip, data$Group==\"walk\" & data$Period==\"pre\"), \n",
      "             subset(data$Hip, data$Group==\"walk\" & data$Period==\"pos\"), paired=T))\n",
      "print(t.test(subset(data$Hip, data$Group==\"run\"  & data$Period==\"pre\"), \n",
      "             subset(data$Hip, data$Group==\"run\"  & data$Period==\"pos\"), paired=T))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "\n",
        "\tWelch Two Sample t-test\n",
        "\n",
        "data:  subset(data$Hip, data$Group == \"walk\" & data$Period == \"pre\") and subset(data$Hip, data$Group == \"run\" & data$Period == \"pre\")\n",
        "t = -2.3, df = 19.924, p-value = 0.03239\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -13.2411847  -0.6444608\n",
        "sample estimates:\n",
        "mean of x mean of y \n",
        " 37.83755  44.78038 \n",
        "\n",
        "\n",
        "\tWelch Two Sample t-test\n",
        "\n",
        "data:  subset(data$Hip, data$Group == \"walk\" & data$Period == \"pos\") and subset(data$Hip, data$Group == \"run\" & data$Period == \"pos\")\n",
        "t = 0.6883, df = 19.962, p-value = 0.4992\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -5.006094  9.935517\n",
        "sample estimates:\n",
        "mean of x mean of y \n",
        " 41.95462  39.48991 \n",
        "\n",
        "\n",
        "\tPaired t-test\n",
        "\n",
        "data:  subset(data$Hip, data$Group == \"walk\" & data$Period == \"pre\") and subset(data$Hip, data$Group == \"walk\" & data$Period == \"pos\")\n",
        "t = -1.2065, df = 11, p-value = 0.2529\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -11.627951   3.393814\n",
        "sample estimates:\n",
        "mean of the differences \n",
        "              -4.117069 \n",
        "\n",
        "\n",
        "\tPaired t-test\n",
        "\n",
        "data:  subset(data$Hip, data$Group == \"run\" & data$Period == \"pre\") and subset(data$Hip, data$Group == \"run\" & data$Period == \"pos\")\n",
        "t = 1.9938, df = 9, p-value = 0.07732\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -0.7121441 11.2930757\n",
        "sample estimates:\n",
        "mean of the differences \n",
        "               5.290466 \n",
        "\n"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R -i data\n",
      "print(t.test(subset(data$Knee, data$Group==\"walk\" & data$Period==\"pre\"),\n",
      "             subset(data$Knee, data$Group==\"run\"  & data$Period==\"pre\")))\n",
      "print(t.test(subset(data$Knee, data$Group==\"walk\" & data$Period==\"pos\"), \n",
      "             subset(data$Knee, data$Group==\"run\"  & data$Period==\"pos\")))\n",
      "print(t.test(subset(data$Knee, data$Group==\"walk\" & data$Period==\"pre\"), \n",
      "             subset(data$Knee, data$Group==\"walk\" & data$Period==\"pos\"), paired=T))\n",
      "print(t.test(subset(data$Knee, data$Group==\"run\"  & data$Period==\"pre\"), \n",
      "             subset(data$Knee, data$Group==\"run\"  & data$Period==\"pos\"), paired=T))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "\n",
        "\tWelch Two Sample t-test\n",
        "\n",
        "data:  subset(data$Knee, data$Group == \"walk\" & data$Period == \"pre\") and subset(data$Knee, data$Group == \"run\" & data$Period == \"pre\")\n",
        "t = -1.8048, df = 14.752, p-value = 0.09155\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -8.5254625  0.7135921\n",
        "sample estimates:\n",
        "mean of x mean of y \n",
        " 62.51076  66.41670 \n",
        "\n",
        "\n",
        "\tWelch Two Sample t-test\n",
        "\n",
        "data:  subset(data$Knee, data$Group == \"walk\" & data$Period == \"pos\") and subset(data$Knee, data$Group == \"run\" & data$Period == \"pos\")\n",
        "t = 0.575, df = 13.212, p-value = 0.575\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -4.233708  7.311469\n",
        "sample estimates:\n",
        "mean of x mean of y \n",
        " 64.91328  63.37439 \n",
        "\n",
        "\n",
        "\tPaired t-test\n",
        "\n",
        "data:  subset(data$Knee, data$Group == \"walk\" & data$Period == \"pre\") and subset(data$Knee, data$Group == \"walk\" & data$Period == \"pos\")\n",
        "t = -2.0314, df = 11, p-value = 0.06709\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -5.005625  0.200601\n",
        "sample estimates:\n",
        "mean of the differences \n",
        "              -2.402512 \n",
        "\n",
        "\n",
        "\tPaired t-test\n",
        "\n",
        "data:  subset(data$Knee, data$Group == \"run\" & data$Period == \"pre\") and subset(data$Knee, data$Group == \"run\" & data$Period == \"pos\")\n",
        "t = 1.5323, df = 9, p-value = 0.1598\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -1.449141  7.533749\n",
        "sample estimates:\n",
        "mean of the differences \n",
        "               3.042304 \n",
        "\n"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Flexion/Extension maximum during running"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = pd.read_csv('../X/pld60x/FlexMax_r.txt', sep='\\t', header=0)\n",
      "data.loc[data.Group==0, 'Group'] = 'walk'\n",
      "data.loc[data.Group==1, 'Group'] = 'run'\n",
      "data.loc[data.Period==0, 'Period'] = 'pre'\n",
      "data.loc[data.Period==1, 'Period'] = 'pos'\n",
      "\n",
      "plot(data, 'Flexion/Extension maximum during running')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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GB4asXLkS9+7dw+HDh/H5559j8+bNmDBhAubOnVuvQK9evYrp06ejoqIC7dq1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       "text": [
        "<matplotlib.figure.Figure at 0x111a5d4a8>"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R -i data\n",
      "data$Subject = factor(data$Subject)\n",
      "library(car)\n",
      "library(ez)\n",
      "options(contrasts=c(\"contr.sum\", \"contr.poly\"))\n",
      "print(\"Variable: Pelvis Flexion/Extension maximum\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Pelvis, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Pelvis), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)\n",
      "print(\"Variable: Hip Flexion/Extension maximum\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Hip, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Hip), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)\n",
      "print(\"Variable: Knee Flexion/Extension maximum\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Knee, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Knee), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)\n",
      "print(\"Variable: Ankle Flexion/Extension maximum\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Ankle, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Ankle), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "[1] \"Variable: Pelvis Flexion/Extension maximum\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value Pr(>F)\n",
        "group  1  2.0772 0.1587\n",
        "      34               \n",
        "$ANOVA\n",
        "        Effect DFn DFd         F         p p<.05         ges\n",
        "2        Group   1  16 1.1499546 0.2994674       0.054359121\n",
        "3       Period   1  16 0.2095924 0.6532429       0.002615568\n",
        "4 Group:Period   1  16 1.0119108 0.3294172       0.012502761\n",
        "\n",
        "[1] \"Variable: Hip Flexion/Extension maximum\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value Pr(>F)\n",
        "group  1   5e-04 0.9831\n",
        "      34               \n",
        "$ANOVA\n",
        "        Effect DFn DFd         F          p p<.05         ges\n",
        "2        Group   1  16 0.6507952 0.43165727       0.025289030\n",
        "3       Period   1  16 0.0805921 0.78013744       0.001820731\n",
        "4 Group:Period   1  16 6.2403527 0.02376633     * 0.123759200\n",
        "\n",
        "[1] \"Variable: Knee Flexion/Extension maximum\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value Pr(>F)  \n",
        "group  1  5.1502 0.0297 *\n",
        "      34                 \n",
        "---\n",
        "Signif. codes:  0 \u2018***\u2019 0.001 \u2018**\u2019 0.01 \u2018*\u2019 0.05 \u2018.\u2019 0.1 \u2018 \u2019 1\n",
        "$ANOVA\n",
        "        Effect DFn DFd         F          p p<.05        ges\n",
        "2        Group   1  16 0.6193272 0.44279905       0.03392388\n",
        "3       Period   1  16 3.0319402 0.10083031       0.01728481\n",
        "4 Group:Period   1  16 5.1870186 0.03683699     * 0.02921181\n",
        "\n",
        "[1] \"Variable: Ankle Flexion/Extension maximum\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value Pr(>F)\n",
        "group  1  0.9858 0.3278\n",
        "      34               \n",
        "$ANOVA\n",
        "        Effect DFn DFd         F         p p<.05         ges\n",
        "2        Group   1  16 0.1447383 0.7086186       0.007983565\n",
        "3       Period   1  16 2.1684875 0.1602630       0.014736676\n",
        "4 Group:Period   1  16 0.0863679 0.7726245       0.000595366\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R -i data\n",
      "print(t.test(subset(data$Hip, data$Group==\"walk\" & data$Period==\"pre\"),\n",
      "             subset(data$Hip, data$Group==\"run\"  & data$Period==\"pre\")))\n",
      "print(t.test(subset(data$Hip, data$Group==\"walk\" & data$Period==\"pos\"), \n",
      "             subset(data$Hip, data$Group==\"run\"  & data$Period==\"pos\")))\n",
      "print(t.test(subset(data$Hip, data$Group==\"walk\" & data$Period==\"pre\"), \n",
      "             subset(data$Hip, data$Group==\"walk\" & data$Period==\"pos\"), paired=T))\n",
      "print(t.test(subset(data$Hip, data$Group==\"run\"  & data$Period==\"pre\"), \n",
      "             subset(data$Hip, data$Group==\"run\"  & data$Period==\"pos\"), paired=T))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "\n",
        "\tWelch Two Sample t-test\n",
        "\n",
        "data:  subset(data$Hip, data$Group == \"walk\" & data$Period == \"pre\") and subset(data$Hip, data$Group == \"run\" & data$Period == \"pre\")\n",
        "t = -2.6799, df = 15.997, p-value = 0.01644\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -14.357263  -1.674918\n",
        "sample estimates:\n",
        "mean of x mean of y \n",
        " 41.48012  49.49621 \n",
        "\n",
        "\n",
        "\tWelch Two Sample t-test\n",
        "\n",
        "data:  subset(data$Hip, data$Group == \"walk\" & data$Period == \"pos\") and subset(data$Hip, data$Group == \"run\" & data$Period == \"pos\")\n",
        "t = 0.7372, df = 15.288, p-value = 0.4722\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -6.049251 12.461690\n",
        "sample estimates:\n",
        "mean of x mean of y \n",
        " 46.45360  43.24739 \n",
        "\n",
        "\n",
        "\tPaired t-test\n",
        "\n",
        "data:  subset(data$Hip, data$Group == \"walk\" & data$Period == \"pre\") and subset(data$Hip, data$Group == \"walk\" & data$Period == \"pos\")\n",
        "t = -1.3571, df = 8, p-value = 0.2118\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -13.424215   3.477239\n",
        "sample estimates:\n",
        "mean of the differences \n",
        "              -4.973488 \n",
        "\n",
        "\n",
        "\tPaired t-test\n",
        "\n",
        "data:  subset(data$Hip, data$Group == \"run\" & data$Period == \"pre\") and subset(data$Hip, data$Group == \"run\" & data$Period == \"pos\")\n",
        "t = 2.4048, df = 8, p-value = 0.04285\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        "  0.2568317 12.2408125\n",
        "sample estimates:\n",
        "mean of the differences \n",
        "               6.248822 \n",
        "\n"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**In conclusion, during running there was no statistically significant difference between factors Group and Period for the Flexion/Extension maximum of the pelvis, hip, knee and ankle.**"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Flexion/Extension angle at heel strike during walking"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = pd.read_csv('../X/pld60x/FlexHS_w.txt', sep='\\t', header=0)\n",
      "data.loc[data.Group==0, 'Group'] = 'walk'\n",
      "data.loc[data.Group==1, 'Group'] = 'run'\n",
      "data.loc[data.Period==0, 'Period'] = 'pre'\n",
      "data.loc[data.Period==1, 'Period'] = 'pos'\n",
      "\n",
      "plot(data, 'Flexion/Extension angle at heel strike walking')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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SG8P69evRunVrue1OTk4yyzNmzEBpaSmaNWuG6dOn4/jx43KZW0X16tVT+BSekZEh3a6J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\nI7vevgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10f19eda0>"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R -i data\n",
      "data$Subject = factor(data$Subject)\n",
      "library(car)\n",
      "library(ez)\n",
      "options(contrasts=c(\"contr.sum\", \"contr.poly\"))\n",
      "print(\"Variable: Pelvis Flexion/Extension angle at heel strike\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Pelvis, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Pelvis), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)\n",
      "print(\"Variable: Hip Flexion/Extension angle at heel strike\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Hip, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Hip), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)\n",
      "print(\"Variable: Knee Flexion/Extension angle at heel strike\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Knee, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Knee), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)\n",
      "print(\"Variable: Ankle Flexion/Extension angle at heel strike\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Ankle, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Ankle), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "[1] \"Variable: Pelvis Flexion/Extension angle at heel strike\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value Pr(>F)\n",
        "group  1  0.2093 0.6497\n",
        "      42               \n",
        "Warning: Data is unbalanced (unequal N per group). Make sure you specified a well-considered value for the type argument to ezANOVA().\n",
        "$ANOVA\n",
        "        Effect DFn DFd         F          p p<.05         ges\n",
        "2        Group   1  20 5.7195422 0.02671932     * 0.188609891\n",
        "3       Period   1  20 0.1073325 0.74660637       0.001003426\n",
        "4 Group:Period   1  20 1.7389818 0.20216967       0.016013059\n",
        "\n",
        "[1] \"Variable: Hip Flexion/Extension angle at heel strike\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value Pr(>F)\n",
        "group  1  0.2309 0.6334\n",
        "      42               \n",
        "Warning: Data is unbalanced (unequal N per group). Make sure you specified a well-considered value for the type argument to ezANOVA().\n",
        "$ANOVA\n",
        "        Effect DFn DFd            F          p p<.05          ges\n",
        "2        Group   1  20 0.0002499089 0.98754380       6.950602e-06\n",
        "3       Period   1  20 0.0149909281 0.90377454       3.324970e-04\n",
        "4 Group:Period   1  20 5.1615583664 0.03428228     * 1.027534e-01\n",
        "\n",
        "[1] \"Variable: Knee Flexion/Extension angle at heel strike\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value Pr(>F)\n",
        "group  1  0.1339 0.7163\n",
        "      42               \n",
        "Warning: Data is unbalanced (unequal N per group). Make sure you specified a well-considered value for the type argument to ezANOVA().\n",
        "$ANOVA\n",
        "        Effect DFn DFd          F         p p<.05          ges\n",
        "2        Group   1  20 0.25366031 0.6200119       0.0109279620\n",
        "3       Period   1  20 0.06832338 0.7964666       0.0004400086\n",
        "4 Group:Period   1  20 1.96167793 0.1766582       0.0124811913\n",
        "\n",
        "[1] \"Variable: Ankle Flexion/Extension angle at heel strike\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value Pr(>F)\n",
        "group  1  0.3491 0.5578\n",
        "      42               \n",
        "Warning: Data is unbalanced (unequal N per group). Make sure you specified a well-considered value for the type argument to ezANOVA().\n",
        "$ANOVA\n",
        "        Effect DFn DFd           F         p p<.05          ges\n",
        "2        Group   1  20 0.004874994 0.9450294       0.0001989515\n",
        "3       Period   1  20 0.758165106 0.3942349       0.0069127990\n",
        "4 Group:Period   1  20 0.325448736 0.5747054       0.0029791309\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R -i data\n",
      "print(t.test(subset(data$Pelvis, data$Group==\"walk\" & data$Period==\"pre\"),\n",
      "             subset(data$Pelvis, data$Group==\"run\"  & data$Period==\"pre\")))\n",
      "print(t.test(subset(data$Pelvis, data$Group==\"walk\" & data$Period==\"pos\"), \n",
      "             subset(data$Pelvis, data$Group==\"run\"  & data$Period==\"pos\")))\n",
      "print(\"effect size\")\n",
      "library(lsr)\n",
      "A = data$Pelvis[data$Period==\"pre\"]\n",
      "B = data$Group[data$Period==\"pre\"]\n",
      "print(cohensD(A ~ B))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "\n",
        "\tWelch Two Sample t-test\n",
        "\n",
        "data:  subset(data$Pelvis, data$Group == \"walk\" & data$Period == \"pre\") and subset(data$Pelvis, data$Group == \"run\" & data$Period == \"pre\")\n",
        "t = -2.6594, df = 19.109, p-value = 0.01544\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -3.8945070 -0.4648503\n",
        "sample estimates:\n",
        " mean of x  mean of y \n",
        "-0.1649288  2.0147498 \n",
        "\n",
        "\n",
        "\tWelch Two Sample t-test\n",
        "\n",
        "data:  subset(data$Pelvis, data$Group == \"walk\" & data$Period == \"pos\") and subset(data$Pelvis, data$Group == \"run\" & data$Period == \"pos\")\n",
        "t = -1.6812, df = 18.073, p-value = 0.1099\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -2.8511431  0.3160069\n",
        "sample estimates:\n",
        "mean of x mean of y \n",
        "0.4044279 1.6719960 \n",
        "\n",
        "[1] \"effect size\"\n",
        "[1] 1.096651\n"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R -i data\n",
      "print(t.test(subset(data$Hip, data$Group==\"walk\" & data$Period==\"pre\"),\n",
      "             subset(data$Hip, data$Group==\"run\"  & data$Period==\"pre\")))\n",
      "print(t.test(subset(data$Hip, data$Group==\"walk\" & data$Period==\"pos\"), \n",
      "             subset(data$Hip, data$Group==\"run\"  & data$Period==\"pos\")))\n",
      "print(t.test(subset(data$Hip, data$Group==\"walk\" & data$Period==\"pre\"), \n",
      "             subset(data$Hip, data$Group==\"walk\" & data$Period==\"pos\"), paired=T))\n",
      "print(t.test(subset(data$Hip, data$Group==\"run\"  & data$Period==\"pre\"), \n",
      "             subset(data$Hip, data$Group==\"run\"  & data$Period==\"pos\"), paired=T))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "\n",
        "\tWelch Two Sample t-test\n",
        "\n",
        "data:  subset(data$Hip, data$Group == \"walk\" & data$Period == \"pre\") and subset(data$Hip, data$Group == \"run\" & data$Period == \"pre\")\n",
        "t = -1.7633, df = 19.992, p-value = 0.09314\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -10.7825281   0.9040978\n",
        "sample estimates:\n",
        "mean of x mean of y \n",
        " 34.50583  39.44505 \n",
        "\n",
        "\n",
        "\tWelch Two Sample t-test\n",
        "\n",
        "data:  subset(data$Hip, data$Group == \"walk\" & data$Period == \"pos\") and subset(data$Hip, data$Group == \"run\" & data$Period == \"pos\")\n",
        "t = 1.3715, df = 19.829, p-value = 0.1855\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -2.537313 12.263015\n",
        "sample estimates:\n",
        "mean of x mean of y \n",
        " 39.14274  34.27989 \n",
        "\n",
        "\n",
        "\tPaired t-test\n",
        "\n",
        "data:  subset(data$Hip, data$Group == \"walk\" & data$Period == \"pre\") and subset(data$Hip, data$Group == \"walk\" & data$Period == \"pos\")\n",
        "t = -1.389, df = 11, p-value = 0.1923\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -11.984622   2.710808\n",
        "sample estimates:\n",
        "mean of the differences \n",
        "              -4.636907 \n",
        "\n",
        "\n",
        "\tPaired t-test\n",
        "\n",
        "data:  subset(data$Hip, data$Group == \"run\" & data$Period == \"pre\") and subset(data$Hip, data$Group == \"run\" & data$Period == \"pos\")\n",
        "t = 2.0714, df = 9, p-value = 0.0682\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -0.4755342 10.8058530\n",
        "sample estimates:\n",
        "mean of the differences \n",
        "               5.165159 \n",
        "\n"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**In conclusion, during running there was a statistically significant main effect for the factor 'group' the Felexion/Extension angle at heel strike for the Pelvis (p=0.012, $\\mathbf{\\eta2=0.017}$). The post-hoc analysis revealed that the Felexion/Extension angle at heel strike for the Pelvis was higher for the 'run' group than for the 'walk' group (p=0.031, d=1.1) before training. See the corresponding interaction plots above. **"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Flexion/Extension angle at heel strike during running"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = pd.read_csv('../X/pld60x/FlexHS_r.txt', sep='\\t', header=0)\n",
      "data.loc[data.Group==0, 'Group'] = 'walk'\n",
      "data.loc[data.Group==1, 'Group'] = 'run'\n",
      "data.loc[data.Period==0, 'Period'] = 'pre'\n",
      "data.loc[data.Period==1, 'Period'] = 'pos'\n",
      "\n",
      "plot(data, 'Flexion/Extension angle at heel strike running')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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WYfz48SgrK4O/vz82bNig8TYJIaQ++Pv7w9/fXzwmevDgweDxeHj+/LmOa0YI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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x111ecc198>"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R -i data\n",
      "data$Subject = factor(data$Subject)\n",
      "library(car)\n",
      "library(ez)\n",
      "options(contrasts=c(\"contr.sum\", \"contr.poly\"))\n",
      "print(\"Variable: Pelvis Flexion/Extension angle at heel strike\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Pelvis, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Pelvis), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)\n",
      "print(\"Variable: Hip Flexion/Extension angle at heel strike\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Hip, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Hip), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)\n",
      "print(\"Variable: Knee Flexion/Extension angle at heel strike\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Knee, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Knee), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)\n",
      "print(\"Variable: Ankle Flexion/Extension angle at heel strike\")\n",
      "# test homogeneity of variance between groups\n",
      "r = leveneTest(data$Ankle, data$Group, center=\"mean\")\n",
      "print(r)\n",
      "r = ezANOVA(data=data, dv=.(Ankle), wid=.(Subject), within=.(Period), between=.(Group), type=3)\n",
      "print(r)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "[1] \"Variable: Pelvis Flexion/Extension angle at heel strike\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value Pr(>F)\n",
        "group  1   0.037 0.8486\n",
        "      34               \n",
        "$ANOVA\n",
        "        Effect DFn DFd         F         p p<.05         ges\n",
        "2        Group   1  16 4.9148761 0.0414591     * 0.175890651\n",
        "3       Period   1  16 0.5867266 0.4548404       0.011067624\n",
        "4 Group:Period   1  16 0.1493461 0.7042520       0.002840602\n",
        "\n",
        "[1] \"Variable: Hip Flexion/Extension angle at heel strike\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value Pr(>F)\n",
        "group  1  0.0705 0.7922\n",
        "      34               \n",
        "$ANOVA\n",
        "        Effect DFn DFd           F          p p<.05          ges\n",
        "2        Group   1  16 0.005393445 0.94236622       0.0001920408\n",
        "3       Period   1  16 0.009517028 0.92349708       0.0002558172\n",
        "4 Group:Period   1  16 6.693613321 0.01984987     * 0.1525208067\n",
        "\n",
        "[1] \"Variable: Knee Flexion/Extension angle at heel strike\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value Pr(>F)\n",
        "group  1   1.551 0.2215\n",
        "      34               \n",
        "$ANOVA\n",
        "        Effect DFn DFd         F         p p<.05        ges\n",
        "2        Group   1  16 1.5773303 0.2271762       0.05979308\n",
        "3       Period   1  16 0.9638435 0.3408336       0.02093194\n",
        "4 Group:Period   1  16 1.5057944 0.2375323       0.03232117\n",
        "\n",
        "[1] \"Variable: Ankle Flexion/Extension angle at heel strike\"\n",
        "Levene's Test for Homogeneity of Variance (center = \"mean\")\n",
        "      Df F value  Pr(>F)  \n",
        "group  1  3.4478 0.07202 .\n",
        "      34                  \n",
        "---\n",
        "Signif. codes:  0 \u2018***\u2019 0.001 \u2018**\u2019 0.01 \u2018*\u2019 0.05 \u2018.\u2019 0.1 \u2018 \u2019 1\n",
        "$ANOVA\n",
        "        Effect DFn DFd           F         p p<.05          ges\n",
        "2        Group   1  16 0.459603244 0.5074958       0.0222308488\n",
        "3       Period   1  16 0.230527982 0.6376308       0.0029949218\n",
        "4 Group:Period   1  16 0.008382897 0.9281856       0.0001092223\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 41
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R -i data\n",
      "print(t.test(subset(data$Pelvis, data$Group==\"walk\" & data$Period==\"pre\"),\n",
      "             subset(data$Pelvis, data$Group==\"run\"  & data$Period==\"pre\")))\n",
      "print(t.test(subset(data$Pelvis, data$Group==\"walk\" & data$Period==\"pos\"), \n",
      "             subset(data$Pelvis, data$Group==\"run\"  & data$Period==\"pos\")))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "\n",
        "\tWelch Two Sample t-test\n",
        "\n",
        "data:  subset(data$Pelvis, data$Group == \"walk\" & data$Period == \"pre\") and subset(data$Pelvis, data$Group == \"run\" & data$Period == \"pre\")\n",
        "t = -1.9699, df = 15.945, p-value = 0.06648\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -4.2404716  0.1561605\n",
        "sample estimates:\n",
        " mean of x  mean of y \n",
        "0.06441656 2.10657211 \n",
        "\n",
        "\n",
        "\tWelch Two Sample t-test\n",
        "\n",
        "data:  subset(data$Pelvis, data$Group == \"walk\" & data$Period == \"pos\") and subset(data$Pelvis, data$Group == \"run\" & data$Period == \"pos\")\n",
        "t = -1.7182, df = 15.942, p-value = 0.1051\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -3.6174480  0.3791198\n",
        "sample estimates:\n",
        "mean of x mean of y \n",
        "-0.143289  1.475875 \n",
        "\n"
       ]
      }
     ],
     "prompt_number": 43
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R -i data\n",
      "print(t.test(subset(data$Hip, data$Group==\"walk\" & data$Period==\"pre\"),\n",
      "             subset(data$Hip, data$Group==\"run\"  & data$Period==\"pre\")))\n",
      "print(t.test(subset(data$Hip, data$Group==\"walk\" & data$Period==\"pos\"), \n",
      "             subset(data$Hip, data$Group==\"run\"  & data$Period==\"pos\")))\n",
      "print(t.test(subset(data$Hip, data$Group==\"walk\" & data$Period==\"pre\"), \n",
      "             subset(data$Hip, data$Group==\"walk\" & data$Period==\"pos\"), paired=T))\n",
      "print(t.test(subset(data$Hip, data$Group==\"run\"  & data$Period==\"pre\"), \n",
      "             subset(data$Hip, data$Group==\"run\"  & data$Period==\"pos\"), paired=T))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "\n",
        "\tWelch Two Sample t-test\n",
        "\n",
        "data:  subset(data$Hip, data$Group == \"walk\" & data$Period == \"pre\") and subset(data$Hip, data$Group == \"run\" & data$Period == \"pre\")\n",
        "t = -2.1438, df = 15.967, p-value = 0.04779\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -12.23479855  -0.06759523\n",
        "sample estimates:\n",
        "mean of x mean of y \n",
        " 30.81397  36.96516 \n",
        "\n",
        "\n",
        "\tWelch Two Sample t-test\n",
        "\n",
        "data:  subset(data$Hip, data$Group == \"walk\" & data$Period == \"pos\") and subset(data$Hip, data$Group == \"run\" & data$Period == \"pos\")\n",
        "t = 1.4223, df = 14.573, p-value = 0.176\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -2.894674 14.418679\n",
        "sample estimates:\n",
        "mean of x mean of y \n",
        " 36.99517  31.23317 \n",
        "\n",
        "\n",
        "\tPaired t-test\n",
        "\n",
        "data:  subset(data$Hip, data$Group == \"walk\" & data$Period == \"pre\") and subset(data$Hip, data$Group == \"walk\" & data$Period == \"pos\")\n",
        "t = -1.5766, df = 8, p-value = 0.1535\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        " -15.221967   2.859559\n",
        "sample estimates:\n",
        "mean of the differences \n",
        "              -6.181204 \n",
        "\n",
        "\n",
        "\tPaired t-test\n",
        "\n",
        "data:  subset(data$Hip, data$Group == \"run\" & data$Period == \"pre\") and subset(data$Hip, data$Group == \"run\" & data$Period == \"pos\")\n",
        "t = 2.3735, df = 8, p-value = 0.045\n",
        "alternative hypothesis: true difference in means is not equal to 0\n",
        "95 percent confidence interval:\n",
        "  0.1629237 11.3010661\n",
        "sample estimates:\n",
        "mean of the differences \n",
        "               5.731995 \n",
        "\n"
       ]
      }
     ],
     "prompt_number": 44
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**In conclusion, during running there was no statistically significant difference for the Flexion/Extension angle at heel strike of the pelvis, hip, knee and ankle.**"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}