inference-project-toothgrowth.Rmd

---
title: "ToothGrowth Dataset Analysis"
author: "Gabe Rudy"
date: "April 20, 2015"
output: html_document
---

The response is the length of odontoblasts (teeth) in each of 10 guinea pigs at each of three dose levels of Vitamin C (0.5, 1, and 2 mg) with each of two delivery methods (orange juice or ascorbic acid).

```{r, results='hold'}
library(datasets)
summary(ToothGrowth$len)
```

```{r, results='hold'}
#Create a list by supplement type
by_supp <- split(ToothGrowth$len, ToothGrowth$supp)
summary(by_supp$OJ)
summary(by_supp$VC)
```

```{r, results='hold'}
#Create a list by dosage levels
by_dose <- split(ToothGrowth$len, ToothGrowth$dose)
summary(by_dose$`0.5`)
summary(by_dose$`1`)
summary(by_dose$`2`)
```

We can see by the summary information that that *OJ* has a greater mean than *VC* (absorbic acid) delivery. Also, the mean length increases with dosage.

```{r, fig.width=8, fig.height=6, echo=FALSE}
require(graphics)
par(mfrow=c(1,2))
plot(len ~ dose, main="OJ (Orange Juice)", data=subset(ToothGrowth, supp == "OJ"))
plot(len ~ dose, main="VC (Ascorbic Acid)", data=subset(ToothGrowth, supp == "VC"))
```

Plot of the data from the two supplement types. Length appears to increase with dosage and absorbic acid VC) has a greater max and min values than OJ (which we also saw in the summary statistics).

##Confidence Interval and Tests for Supplement Type

Lets compare the observations in group OJ and VC. 

We will use a Student's t-Test to compare the two groups with `0.95` confidence level.

```{r}
t.test(by_supp$OJ, by_supp$VC, paired=FALSE, var.equal = TRUE)
```

Our T test statistic is `1.9`, meaning we estimate our difference of means is `1.9` standard error from the hypothosized mean. The P-value is `0.06`, meaning there is `0.06` probability of obtaining differences of means greather than the observed if the truely where no difference based on supplement type.

We are makeing the assumption that *the variance of the two groups is equal*. We are also making a two-sided test, saying the difference of the means could be either greater than or less than, not just strictly greater than or less than.

##Confidence Interval and Tests for Dose

Lets compare the observations in dosage group `0.5` and `2`.

We will use a Student's t-Test to compare the two groups with a `0.95` confidence level.

```{r}
t.test(by_dose$`0.5`, by_dose$`2`, paired=FALSE, var.equal = TRUE)
```

Our T test statistic is `11.8`, meaning we estimate our difference of means is `11.8` standard error from the hypothosized mean. The P-value is `2.8e-14`, meaning there is `2.8e-14` probability of obtaining differences of means greather than the observed if the truely where no difference based on supplement type. We are makeing the assumption that *the variance of the two groups is equal*. We are also making a two-sided test, saying the difference of the means could be either greater than or less than, not just strictly greater than or less than.