Statistical_Inference_2.Rmd

---
title: "Statistical Inference - Project Part 2"
author: "Rafael Mejia"
date: "19 de noviembre de 2017"
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

## Project Part 2 -  Analysis

First we will load the necessary libraries.

```{r}
library(ggplot2)
```

In next step we will load the data and provide a quick summary.

```{r}
# Load ToothGrowth data
data("ToothGrowth")

# Display a summary of the data
summary(ToothGrowth)

# Dicplay the first few rows of data
head(ToothGrowth)

# Unique values
unique(ToothGrowth$len)

unique(ToothGrowth$supp)

unique(ToothGrowth$dose)

```

Now we will create some plots to explore the data.

```{r}
# Convert dose to a factor
ToothGrowth$dose <- as.factor(ToothGrowth$dose)

# Plot tooth length ('len') versus the dose a mount ('dose'), broken out by supplement delivery method ('supp')
ggplot(aes(x = dose, y = len), data = ToothGrowth) + geom_boxplot(aes(fill = dose)) + xlab("Dose Amount") + ylab("Tooth Length") + facet_grid(~supp) + ggtitle("Tooth Length vs Dose Amount by Delivery method") + theme(plot.title = element_text(lineheight = 7, face = "bold"))

# Plot tooth length ('len') versus supplement delivery method ('supp'), broken out by the dose amount ('dose')
ggplot(aes(x = supp, y = len), data = ToothGrowth) + geom_boxplot(aes(fill = supp)) + xlab("Supplement Delivery") + ylab("Tooth Length") + facet_grid(~dose) + ggtitle("Tooth Length vs Delivery method by Dose Amount") + theme(plot.title = element_text(lineheight = 7, face = "bold"))

```

Now we will compare the tooth growth by supplement using a t-test.

```{r}
# Run t-test
t.test(len~supp, data = ToothGrowth)
```

The p-value of this test was 0.06 Since the p-value is greater than 0.05 and the confidence interval if the test contains zero we can say that supplement types seems to have no impact on Tooth growt based on this test.

Now we will compare tooth growth by dose, looking at the different pais if dose values.

```{r}
# Run t-test using dose amounts 0.5 and 1.0

ToothGrowth_sub <- subset(ToothGrowth, ToothGrowth$dose %in% c(1.0, 0.5))
t.test(len~dose, data = ToothGrowth_sub)

# Run t-test using dose amount s 0.5 and 2.0
ToothGrowth_sub <- subset(ToothGrowth, ToothGrowth$dose %in% c(2.0, 0.5))
t.test(len~dose, data = ToothGrowth_sub)

# Run t-test using dose amount s 1.0 and 2.0
ToothGrowth_sub <- subset(ToothGrowth, ToothGrowth$dose %in% c(1.0, 2.0))
t.test(len~dose, data = ToothGrowth_sub)

```

We can see that the p-value of each test was essentially zero and the confidence interval of each test does not cross over zero (0).

Based on this result we can asssume that the average tooth lenght increases with an inceasing dose, and therefore the null hypothesis can be rejected.

## Conclusions

Given the following assumptions:

1. The sample is representative of the population
2. The distribution of the sample means follows the Central Limit Theorem

In reviewing our t-test analysis from above, we can conclude that supplement delivery method has no effect on tooth growth/length, however increased dosages do result in increased tooth length.