---
title: "Precept 8"
author: "Emily Nelson"
date: "March 30, 2016"
output: html_document
---

```{r global_options, include=FALSE}
knitr::opts_chunk$set(message=FALSE, cache=TRUE, warning=FALSE)
```


```{r setup}
library(dplyr)
library(ggplot2)
library(knitr)

set.seed(2016)
load("precept8.save")
```

Agenda: Practice selecting and using statistical tests in R.

#Two Samples

##Basics

```{r two_samples, dependson="setup"}
x <- rnorm(10000, 5, 1)
y <- rnorm(10000, -1, 2)

df <- rbind(data.frame(obs = x, label="x"),
           data.frame(obs=y, label="y"))

df %>%
  ggplot(aes(x=obs,fill=label)) + 
  geom_density() +
  theme_bw() +
  scale_fill_manual(values = c("chartreuse3", "darkviolet"))

z = x - y

#expected value
mean(x) - mean(y)
mean(z)
5 - (-1)

#variance
var(x) + var(y)
var(z)
1^2 + 2^2

```


#Pick the test!

##Casino Example

I work security for a casino. I'm suspicious of a certain felow who has been playing roulette all day and winning quite a bit and I want to find out if he is winning at a rate higher than expected. If it's statistically significant then I can kick him out of the casino.


If he is only betting evens, then he should have a 46.37% chance of winning. Below is what I actually observe:

```{r casino}
casino

```

What is my hypothesis? How do I perform this test in R?

Can I kick him out? What if I watch him for a while more and get more data?

```{r casino2}
casino2
```

Can I kick him out now?

##Trial Example

I invented a vaccination for the common cold. I am testing it on some unwitting subjects because being a mad scientist is much more fun than being an ethical one.

I gave one group my vaccine, and the other group some sugar pills, and then counted how many people got a cold over a month-long period.

How can I test to see if the proportions of people who got a cold is equal for the treated and placebo groups?

```{r trial}
head(trial)
```

##Publishing Example

I'm an amazing Nobel prize winning scientist, but my up-start graduate student says that I'm not publishing papers as fast anymore as I used to. I want to prove her wrong, so I looked up the number of papers I published a month for three years randomly sampled from earlier in my career, and then compared that to the number of papers I published a month for three random years later in my career.

How can I show whether or not my publishing rate is the same?

```{r publishing}
head(publishing)

```

##Finals Week

My buddy and I are having a competition to see who can score higher on our finals this year. We're also taking ten classes because we are really smart and we need a sample size that isn't miniscule.

How can we decide if one of us did better (in a statistically significant manner)?

```{r}
my_scores
his_scores

```