workshop-notebook.Rmd

---
title: "T-Tests & Linear Regression"
output: pdf_document
---

# T-Tests and ANOVAs

Today we're going to dive into some statistical capabilities using R....specifically t-tests and ANOVAs. We're going to practice using some code to generate these statistical measures, and use ggplot to create corresponding visualizations. 


## t-tests

A t-test is used to  determine if there is a significant difference between the means of two groups, assuming normal distribution in both groups. 

Let's start off by loading the tidyverse, and loading/viewing our penguin data:



```{r}
library(tidyverse)
library(palmerpenguins)

penguins

```


Let's say we want to run a t-test comparing flipper length of Adelie vs Chinstrap penguins. First, we'll use the 'filter' and 'select' functions to limit our data to Adelie & Chinstrap, and only include the species and flipper_length_mm columns:

```{r}

flippers<-penguins %>% filter(species=="Adelie" | species=="Chinstrap") %>% select(species, flipper_length_mm)



flippers

```


Now we can plug this dataset into the t.test function:


```{r}

t.test(flipper_length_mm ~ species, data=flippers)


```


Based upon the output, the p-value is way below 0.05, which is often the threshold for statistical significance. It can be interpreted as: "there is a <p-value> probability that the differences in the mean are due to random chance".


YOUR TURN:

Run a t-test comparing the bill length between Gentoo and Adelie penguins. Are the means significantly different?


```{r}




```



## Plots for t-test 

We can use ggplot to generate plots to visualize our data. First, we can try a boxplot:



```{r}
ggplot(data=flippers, mapping = aes(species, flipper_length_mm))+geom_boxplot()


```



We can also create a bar plot, though first let's use group_by/summarize to generate the mean valaues for both groups. This is important because normally the geom_bar() function will generate the bar plot based upon the count of each group. But, we can provide explicit y-values to it (in our case, the mean), as long as we use the attribute stat="identity":


```{r}

flipper_summary<-flippers%>%na.omit()%>%group_by(species)%>%summarize(avg_flipper_length_mm=mean(flipper_length_mm))

ggplot(data=flipper_summary, mapping = aes(x=species,y=avg_flipper_length_mm, fill=species ))+geom_bar(stat="identity")


```



YOUR TURN:

Generate a box plot and bar plot for your comparison of bill length between Gentoo and Adelie penguins.

```{r}




```



## ANOVAs

An ANOVA, or Analysis of Variance, compares the means of two or more groups, and provides p-values similar to a t-test. 

Let's run an ANOVA to compare mean bill lenghts among the three species of penguins:

```{r}

bills_aov<-aov(bill_length_mm ~ species, data=penguins)



summary(bills_aov)

#TukeyHSD(bills_aov)

```


The summary statement indicates that there is some statistical significance identified, given the 3 asterisks next to the Pr(>F) value. Of course, the question is "significant between which groups?". We can now use the "TukeyHSD" function to yield that information:

```{r}
TukeyHSD(bills_aov)
```

If we run the boxplot command below, it sort of visually confirms the p adj values listed above.


```{r}
ggplot(data=penguins, mapping = aes(species, bill_length_mm))+geom_boxplot()
```


YOUR TURN:

* Use the ANOVA test to check for differences in bill depth among the three species. 
* Create a bar plot to show the results.


```{r}







```