7_More_ANOVAs.qmd

---
title: "More ANOVAs"
---

<!-- COMMENT NOT SHOW IN ANY OUTPUT: Code chunk below sets overall defaults for .qmd file; these inlcude showing output by default and looking for files relative to .Rpoj file, not .qmd file, which makes putting filesin different folders easier  -->

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
knitr::opts_knit$set(root.dir = rprojroot::find_rstudio_root_file())
```

Remember you should

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    or by pressing *Ctrl+Alt+I* to answer the questions!
-   **render** your file to produce a markdown version that you can see!
-   save your work often
    -   **commit** it via git!
    -   **push** updates to github

## Overview

This practice reviews the [More ANOVAs
lecuture](https://jsgosnell.github.io/cuny_biostats_book/content/chapters/More_ANOVAs.html){target="_blank"}.

## Examples

### If interaction is significant

Following the memory example from class, read in and check data

```{r}
memory <- read.table("http://www.statsci.org/data/general/eysenck.txt", header = T,
                     stringsAsFactors = T)
str(memory)
```

Let's put younger level first

```{r}
library(plyr)
memory$Age <- relevel(memory$Age, "Younger")
```

and graph

```{r}
library(Rmisc)
function_output <- summarySE(memory, measurevar="Words", groupvars =
                               c("Age", "Process"), na.rm = T)
library(ggplot2)
ggplot(function_output, aes(x=Age, y=Words,color=Process, 
                                   shape = Process)) +
  geom_line(aes(group=Process, linetype = Process), size=2) +
    geom_point(size = 5) +
  ylab("Words remembered")+ 
  xlab("Age") + 
  ggtitle("Process type interacts with age to impact memory")+
  theme(axis.title.x = element_text(face="bold", size=28), 
        axis.title.y = element_text(face="bold", size=28), 
        axis.text.y  = element_text(size=20),
        axis.text.x  = element_text(size=20), 
        legend.text =element_text(size=20),
        legend.title = element_text(size=20, face="bold"),
        plot.title = element_text(hjust = 0.5, face="bold", size=32))
```

There appears to be some interactions. Let' build a model

```{r}
memory_interactions <- lm(Words ~ Age * Process, memory)
```

and check assumptions.

```{r}
par(mfrow=c(2,2))
plot(memory_interactions)
```

These appear to be met, so look at output

```{r}
library(car)
Anova(memory_interactions, type = "III")
```

Since interaction is significant, analyze subsets. For example,

```{r}
memory_interactions_young <- lm(Words ~ Process, memory[memory$Age == "Younger",])
plot(memory_interactions_young)
Anova(memory_interactions_young, type = "III")
```

There is a significant difference in words recalled based on process,
but why? Investigate with post-hoc tests.

```{r}
library(multcomp)
comp_young <- glht(memory_interactions_young, linfct = mcp(Process = "Tukey"))
summary(comp_young)
```

### Blocking example

Following feather color example from class:

```{r}
# more than 2? ####
feather <-  read.csv("https://raw.githubusercontent.com/jsgosnell/CUNY-BioStats/master/datasets/wiebe_2002_example.csv", stringsAsFactors = T)
str(feather)
set.seed(25)
special <- data.frame(Bird = LETTERS[1:16], Feather = "Special", 
                      Color_index= feather[feather$Feather == "Typical", "Color_index"] +
                        .3 +runif(16,1,1)*.01)
feather <- merge(feather, special, all = T)


Anova(lm(Color_index ~ Feather + Bird, data=feather), type= "III")

library(multcomp)
compare <- glht(lm(Color_index ~ Feather + Bird, data=feather), linfct = mcp("Feather" = "Tukey"))
summary(compare)
```

```{r, error=T}
#note comparison doesn't work
Anova(lm(Color_index ~ Feather * Bird, data=feather), type= "III")
```

## Practice

### 1

A survey was conducted to see if athletes and non-athletes deal with
anger in the same way. Data is \@

angry \<-
read.csv("<https://docs.google.com/spreadsheets/d/e/2PACX-1vSaawG37o1ZUEs1B4keIJpZAY2c5tuljf29dWnzqQ0tHNCzfbz85AlWobYzBQ3nPPXJBLP-FWe4BNZB/pub?gid=1784556512&single=true&output=csv>",
stringsAsFactors = T)

and more information is at

<http://onlinestatbook.com/case_studies/angry_moods.html>.

Focus on the following variables:

Sports 1 = athletes, 2 = non-athletes Gender 1 = males, 2 = females
Expression (AE) index of general anger expression: (Anger-Out) +
(Anger-In) - (Control-Out) - (Control-In) + 48

Is there any evidence that gender or athlete status impact how anger is
expressed?

### 2

A professor carried out a long-term study to see how various factors
impacted pulse rate before and after exercise. Data can be found at
<http://www.statsci.org/data/oz/ms212.txt> With more info at
<http://www.statsci.org/data/oz/ms212.html>. Is there evidence that
frequency of exercise (Exercise column) and gender impact change in
pulse rate for students who ran (Ran column = 1)?

### 3

Data from Valdez et al 2023 is available \@
<https://docs.google.com/spreadsheets/d/e/2PACX-1vT2gaLu6pyRMlcbzarn3ej4bFmT_iHvrlNWJYSdrsLdUWIjcJi7rU11-ipvYpGnqD9qLDnbhNd2sDUW/pub?gid=1707080634&single=true&output=csv>.

Import it into to R and

-   determine how the snail grazing and nitrogen levels impact number of
    flowering shoots ( Shoot.density..m2)
-   construct a plot to showcase your analysis

### 4

Find an example of a factorial ANOVA from a paper that is related to
your research or a field of interest.  Make sure you understand the connections between the methods,
results, and graphs. Briefly answer the following questions

-   What was the dependent variable?
-   What were the independent variables?
-   Was the interaction significant?
    -   If so, how did they interpret findings
    -   If not, were the main effects significant?