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<!DOCTYPE html>
<html>
<head>
<title>Introduction to Statistical Analysis</title>
<meta charset="utf-8">
<link rel="stylesheet" href="slide.css">
</head>
<body>
<textarea id="source">
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<div class="header" style="display:block; text-align: left; color:gray; font-size:1em; position: fixed; top: 0px; left: 0px; height: 30px;vertical-align:middle;margin:7px 0 0 0;width:100%;background: #fcfcfc;
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<p style="display:block;text-align:left;color:gray;font-size:1em; position: fixed; top: 0px; left: 155px; height: 30px;vertical-align:middle;margin:7px 0 0 0; ">Introduction to Statistical Analysis</p>
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<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Introduction to Statistical Analysis</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="http://www.datapolitan.com" property="cc:attributionName" rel="cc:attributionURL">Richard Dunks</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/"><img alt="Creative-Commons-License" style="border-width:0" src="https://i.creativecommons.org/l/by-nc-sa/4.0/80x15.png" /></a>
</p>
</div>
---
class: center, middle
# Introduction to Statistical Analysis
- - -
## Instructors: Mark Yarish & Elizabeth DiLuzio
### Follow along at: http://bit.ly/intro-stats
#### See the code at: http://bit.ly/intro-stats-code
---
class:center,middle
# Welcome
???
+ Facilitators introduce themselves
+ Facilitators (respectfully) assert authority to be teaching material
+ Facilitators begin creating a safe, comfortable container for participants
---
# A Few Ground Rules
--
+ Step up, step back
--
+ Be curious and ask questions!
--
+ Assume noble regard and positive intent
--
+ Respect multiple perspectives
--
+ Listen deeply
--
+ Be present (phone, email, social media, etc.)
---
# Introductions and <a href="http://bit.ly/stats-data" target="_blank">Data Collection</a>
+ Who are you?
+ Where do you work?
+ How many siblings do you have (not including yourself)?
+ How long have you worked for NYC in years?
+ What is your height (in inches)?
???
+ Instructor uses [Google sheet to collect information](http://bit.ly/stats-data) as students introduce themselves
---
# Goals for the Course
--
+ Review descriptive statistics in the context of operational decision making
--
+ Discuss correlation and simple linear regression analysis in the context of operational decision making
--
+ Introduce decision modeling and their use
--
+ Practice calculating descriptive statistics, calculating correlation, and developing predictive models in Excel
---
# Key Takeaways for the Course
--
+ You will be more familiar with basic descriptive statistics
--
+ You will be better able to describe correlation and simple linear regression
--
+ You will better understand the value of decision models in operational decision making
--
+ You will be practiced in calculating descriptive statistics, calculating correlation, and developing predictive models in Excel
---
# Key Assumptions
--
+ You’ve had some previous experience with statistics and probability
--
+ You’re familiar with using Excel to manipulate data and calculate values
--
+ You’re familiar with using formulas in Excel
---
# Disclaimer
--
+ We're not statisticians
--
+ You won’t be a statistician by the end of this course
--
+ WeI often apply statistical tools and understanding in the work we do
--
+ We're assuming you all do the same, which is why you’re here
---
# Housekeeping
???
+ Facilitator sets expectations with the students
+ Establishes the "contract" for the class
--
+ We’ll have one 15 minute break in the morning
--
+ We’ll have an hour for lunch
--
+ We’ll have a 15 minute break in the afternoon
--
+ Class will start promptly after breaks
--
+ Feel free to use the bathroom if you need during class
--
+ Please take any phone conversations into the hall to not disrupt the class
---
# Goals for this Morning
--
+ Review basic statistical measures
--
+ Practice using statistics in real-world applications
--
+ Familiarize you with how to use Excel for statistical analysis
---
class:center,middle
> We are drowning in information and starving for knowledge.
## John Naisbitt
???
+ Facilitator prompts the participants to reflect on the value of statistics for understanding information
+ Helpful to make the distinction between the raw information and intelligence that can be used for decision making
---
# Why Statistics?
???
+ Facilitator emphasizes the utility of statistics for understanding information
--
+ Tools for extracting meaning from data
--
+ Commonly understood ways of communicating meaning to others
???
+ Facilitator makes point about being able to compare using statistics
+ I often use the example of comparing one class with the other -> if mean years of service is higher than this class, what might that imply about the
---
class:center,middle
# Let’s run the statistics on our class today
## Download <a href="http://bit.ly/stats-data" target="_blank">the data for the class</a>
???
+ Facilitator leads the participants through applying basic descriptive stats to the data collected at the introductions
+ Facilitator reviews each concept with participants then leads them through calculating it in the appropriate place on the spreadsheet
---
# Mean
--
+ A representative value for the data
--
+ Usually what people mean by “average”
--
+ Calculate by adding all the values together and dividing by the number instances
--
+ Sensitive to extremes
--
## .dp-orange[Calculate the means (number of siblings, years of service, and height) for our class today]
---
# Median
--
+ The “middle” value of a data set
--
+ Center value of a data set with an odd number of values
--
+ Sum of two middle values divided by 2 if the number of items in a data set is even
--
+ Resistant to extreme values
--
--
## .dp-orange[Calculate the medians for our class today]
---
exclude:true
# Median vs Mean
---
# Mode
--
+ The most frequent value in a dataset
--
+ Often used for categorical data
--
####
<br>
## .dp-orange[Calculate the mode for our class today]
---
# Median vs Mean vs Mode
By Cmglee (Own work) <a href="http://creativecommons.org/licenses/by-sa/3.0">CC BY-SA 3.0</a> or <a href="http://www.gnu.org/copyleft/fdl.html">GFDL</a>, <a href="https://commons.wikimedia.org/wiki/File%3AComparison_mean_median_mode.svg">via Wikimedia Commons</a>
???
+ Facilitator describes the difference between mean, median, and mode, emphasizing when you would use one over the other
---
# When Do We Use Median rather than Mean (Average)?
???
+ Facilitator reflects with participants when they recall using median rather than mean in their work or in the media
+ Establishes key learning point of when these measure should be used (depends on the shape of the data)
--
+ House Prices
--
+ Household Income
--
+ What else?
--
+ Why?
---
# Anscombe's Quartet
???
+ Facilitator uses example of Anscombe's Quartet to demonstrate the need to visually inspect data
+ For more information, see [this article](https://heap.io/blog/data-stories/anscombes-quartet-and-why-summary-statistics-dont-tell-the-whole-story)
---
# Histogram
--
+ Charts the frequency of instances in the data
--
+ Shows the frequency distribution
--
+ Values are grouped into class intervals
--
+ Best to have a consistent size to class intervals
--
<br>
<br>
.caption[http://mathematica.stackexchange.com/questions/59520/histogram-with-variable-bin-size]
---
class:center,middle
# Creating a Histogram for Height in Post-Its
???
+Have participants write their height, in inches, on a post-it
+Collect and graph post-its on poster paper
+Point out that there are a lot of bars that are quite small
+Not very helpful in understanding trends in our data
+What happens when we group the bars together? Group evenly to be sure we can draw conclusions.
+Can you see a trend better now?
---
class:center,middle
# Creating a Histogram for Height in Excel
---
# Installing Data Analysis ToolPak
+ File
+ Options
+ Add-ins
+ Manage
+ “Go…”
---
# Installing Data Analysis ToolPak
---
# Setup Your Bins
???
+ Starting with arbitrarily determining bin size by range helps to introduce the topic
+ Later introduce equal interval based on either range of the data or the limits of the lower and upper bounds to eliminate outlines
+ Key learning point is that we control how to tell the story of the data with the bin size we select
+ Easily to obscure or manufacture a pattern to the data by picking the wrong bin size
--
+ Use an empty column and label it “Bins”
--
+ Start with the max of the first bin
--
+ Create an entry for each bin you want
--
+ Use a formula to save time
---
# Creating a Histogram (Height)
## .center[Under the Data Ribbon]
---
# Creating a Histogram (Height)
---
# Creating a Histogram (Height)
---
# Creating a Histogram (Height)
---
class:center,middle
# Distributions of Data
---
# Normal(-ish) Distribution
---
# Long-tail Distribution
---
# Bi-Modal Distribution
---
# Measures of Central Tendency
--
+ Quantitative data tends to cluster around some central value
--
+ Contrasts with the spread of data around that center (i.e. the variability in the data)
--
+ Mean is a more precise measure and more often used
--
+ Median is better when there are extreme outliers
--
+ Mode is used when the data is categorical (as opposed to numeric)
---
class:center,middle
# Measuring Variability
---
# Range
--
+ The gap between the minimum value and the maximum value
--
+ Calculated by subtracting the minimum from the maximum
--
+ Use the [`MAX`](https://support.office.com/en-us/article/MAX-function-e0012414-9ac8-4b34-9a47-73e662c08098) and [`MIN`](https://support.office.com/en-us/article/MIN-function-61635d12-920f-4ce2-a70f-96f202dcc152) functions in Excel to calculate this for our data
---
# Quartiles
???
+ Facilitator introduces concept by discussing percentiles
+ Prompts participants with the scenario: "Your child comes home and says they scored on the 98th percentile on the SAT. What does that mean?"
+ The answer is that they scored at or above 98% of the students who took the SAT
+ This introduces the idea important to understanding Quartiles as breaking up the data into 4 equal portions of the data
--
.caption-small[[Image](https://commons.wikimedia.org/wiki/File:Iqr.png) credit Ark0n [CC BY-SA 3.0](http://creativecommons.org/licenses/by-sa/3.0/)]
--
+ Quartiles split the data into four equal groups
--
+ First quartile is 0-25% of the data
--
+ Second quartile is 25-50% of the data
--
+ Third quartile is 50-75% of the data
--
+ Fourth quartile is 75-100% of the data
--
+ Use the [`QUARTILE`](https://support.office.com/en-us/article/QUARTILE-function-93cf8f62-60cd-4fdb-8a92-8451041e1a2a) function in Excel to calculate this
---
# Interquartile Range
--
+ “Middle” 50% of data (between 1st Quartile and 3rd Quartile)
--
.caption[[Image source](https://community.qlik.com/t5/Qlik-Design-Blog/Recipe-for-a-Box-Plot/ba-p/1471745?)]
---
# Outliers
--
+ Any data points less than 1.5x the IQR or greater than 1.5x the IQR are considered outliers
--
+ Helps identify data points that may skew the analysis
--
+ Focus on the “meat” of the data
--
#
.caption-right[[Image source FlowingData.com](http://flowingdata.com/2008/02/15/how-to-read-and-use-a-box-and-whisker-plot/)]
---
name:calc-iqr
class:center,middle
# Do We Have Any Outliers in Our Data?
???
+ First calculate the Upper Limit -> participants will usually calculate the formula as `=1.5 * IQR + Q3`
+ In calculating the Lower Limit -> participants will use the same order to get `=1.5 * IQR - Q1`, which leads to an incorrect result. Make sure to point this out to them
+ Reflect on any outliers with the class
---
# Standard Deviation
--
+ The average distance of each data point from the mean
--
--
+ Larger the standard deviation, the greater the spread
--
---
# Standard Deviation
???
+ Facilitator discusses the idea of standard deviations and the amount of data at each deviation
+ For more information, see: https://simple.wikipedia.org/wiki/Standard_deviation
+ For the breakdowns of standard deviations, see https://www.robertniles.com/stats/stdev.shtml
---
# Measures of Variability
--
+ Describe the distribution of our data
--
+ Range (Maximum – Minimum)
--
+ Inter-quartile Range
--
+ Standard Deviation
--
+ Identification of outliers (1.5 x IQR)
---
# Descriptive Statistics
--
+ Quantitatively describe the main features of a dataset
--
+ Help distinguish distributions and make them comparable
--
+ 5 number summary
--
<br> - Minimum
--
<br> - 1st Quartile
--
<br> - Median
--
<br> - 3rd Quartile
--
<br> - Maximum
---
# Exploratory Data Analysis
--
+ Goal -> Discover patterns in the data
--
+ Understand the context
--
+ Summarize fields
--
+ Use graphical representations of the data
--
+ Explore outliers
--
### Tukey, J.W. (1977). Exploratory data analysis. Reading, MA: Addison-Wesley.
---
class:center,middle
# 15 MIN BREAK
Source: https://xkcd.com/539/
---
class:center,middle
# Let's Try That Again
# [Vehicle Collisions in NYC](data/20160401_0630_NYPD_Motor_Vehicle_Collisions.xlsx)
---
class:center,middle
# But before we get too deep into data...
???
+ Facilitator demonstrates the concepts of a pivot table by doing a human pivot table
+ Facilitator asks participants to move to the front of the room
+ Facilitator leads them through exercises to show sort, filter, and aggregate
---
class:center,middle
---
# PivotTables
???
+ Facilitator introduces concept and usage of pivottables to the class
+ Best to introduce by having someone describe how they use a pivottable in their work (connects to the day-to-day concretely)
--
+ A data summarization tool
--
+ Useful to quickly understand data
--
+ Can use to graph data totals
--
---
# Creating a PivotTable
???
+ Facilitator describes the steps to creating a pivottable in Excel
+ Please don't model selecting all data before selecting "Insert Pivottable" -> creates `(blank)` field in pivottable
+ Just allow to select all data by itself
--
+ Should default to all your data .red[unless you have any cells selected]
???
+ Remind participants not to have any data selected when inserting a pivottable. When this comes up in class (because someone did it), use it as a teachable moment
--
+ Should default to a new worksheet
---
# Creating a PivotTable
## Drag and drop fields to visualize
--
+ Row labels
--
+ Values
--
+ Filter
--
+ Column Labels
---
# Creating a PivotTable of Dates
---
exclude:true
# Creating a PivotTable
---
# Calculating Descriptive Statistics
---
# Calculating Descriptive Statistics
---
# Calculating Descriptive Statistics
---
# Calculating Descriptive Statistics
---
# Questions of the Data
--
+ What is the mean number of accidents per day?
--
+ Is mean or median the best way to describe this data?
--
+ Are there any outliers in this data?
---
# Wrap-Up
???
+ Facilitator reviews the concepts introduced in the morning and ensures all questions are answered
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+ Reviewed basic descriptive statistics
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+ Calculated basic descriptive statistics in Excel
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+ Discussed histograms
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+ Created histograms in Excel
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+ Analyzed NYC motor vehicle collision data
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# Lunch
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# Welcome Back!
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# Let's Get Back to the Data
## What is the mean (average) time a [311 noise-related service request](data/20140601_20140901_311_noise.csv) remains open? The median?
???
+ Facilitator allows participants to apply learning in a release exercise
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# Preparing the Data - Insert Column
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# Preparing the Data - Calculate Days Open
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# Preparing the Data - Format Result
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# Preparing the Data - Calculate Hours Open
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# Now Let's Calculate the Descriptive Statistics
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# Calculating Descriptive Statistics
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# Calculating Descriptive Statistics
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# Calculating Descriptive Statistics
--
+ What's missing?
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+ Q1
--
+ Q3
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+ IQR
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+ Upper Bound
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+ Lower Bound
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## .dp-orange[Calculate those now<br>(trust us, it'll be useful)]
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# Creating a Histogram
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# Creating a Histogram
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# Creating a Histogram - Bin Size 100
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# Creating a Histogram - Bin Size 100
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# Creating a Histogram - Bin Size 50
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# Creating a Histogram - Bin Size 50
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# Creating a Histogram - Formatting Histogram
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# Creating a Histogram
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# Do these tell a true and compelling story?
#
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# Do these tell a true and compelling story?
# What do we do about that?
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# Things to Think About
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+ Do we need to display all of the data?
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+ What data do we keep?
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+ How do we determine what to show?
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+ How do we be clear about what we're not showing?
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# Removing Outliers (Using 1.5 x IQR)
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# Removing Outliers (Using 1.5 x IQR)
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+ Creating 10 equal bins (IQR of 9.275 divided by 10)
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+ Alternative strategy for determining bins
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# Removing Outliers (Using 1.5 x IQR)
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+ Only 3,659 service requests greater than 9.275 hours (upper bound)
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+ Represents less than 10% (~9.73%) of 37,615 total service requests
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# What Do We Know?
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+ The median time a noise complaint is open is 2 hours
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+ 50% of the noise complaints are closed between 1-4 hours (median is 2 hours, IQR is 3 hours)
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+ There is a long tail of complaints that take longer to close (range of 1158 hours, standard deviation of 36 hours)
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# 15 Min Break
[Source](https://xkcd.com/523/)
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# Correlations
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+ Values tend to have a relationship
--