---
title: "Piglets Data Two-Way Factorial"
author: "Randi Garcia"
---

```{r global-options, include=FALSE}
knitr::opts_chunk$set(eval = FALSE)
library(tidyverse)
library(Stat2Data)
```

# Explore the Data

```{r}
data("PigFeed")
```

First we get the cell counts.

```{r}
PigFeed %>%
  group_by(Antibiotic, B12) %>%
  count()
```

Then we look at it visually with boxplots.

```{r}
ggplot(PigFeed, aes(x = interaction(B12, Antibiotic), y = WgtGain)) + 
  geom_boxplot()
```

Or with `fill`.

```{r}
ggplot(PigFeed, aes(x = B12, y = WgtGain, fill = Antibiotic)) +
  geom_boxplot()
```

Create a parallel dot plot for `PigFeed` data

```{r}
ggplot(PigFeed, aes(x = B12, y = WgtGain, color = Antibiotic)) +
  geom_point()
```

# Check for Equal Variances

```{r}
ds <- PigFeed %>%
  group_by(Antibiotic, B12) %>%
  summarise(n = n(),
            mean = mean(WgtGain),
            sd = sd(WgtGain))
ds

ds %>% 
  ungroup() %>%
  summarise(max(sd)/min(sd))
```

Note variances unequal. Try log transformation.

```{r}
PigFeed <- PigFeed %>%
  mutate(logWgtGain = log(WgtGain + 1)) 

ggplot(PigFeed, aes(x = interaction(B12, Antibiotic), y = logWgtGain)) + 
  geom_boxplot()
```

Doesn't help much!

```{r}
PigFeed %>%
  group_by(Antibiotic, B12) %>%
  summarise(n = n(),
            mean = mean(logWgtGain),
            sd = sd(logWgtGain)) %>% 
  ungroup() %>%
  summarise(max(sd)/min(sd))
```

# Formal Analysis

Run two-way ANOVA without the interaction term using the original data.

```{r}
mod1 <- lm(WgtGain ~ Antibiotic + B12, data = PigFeed)

anova(mod1)
```

## Interactions

Check for interactions: Create an interaction plot.

```{r}
ggplot(PigFeed, aes(x = B12, y = WgtGain, 
                    group = Antibiotic, 
                    color = Antibiotic)) +
  geom_point() +
  geom_smooth(method = "lm", se = 0)
```

Conduct a two-way ANOVA

```{r}
mod2 <- lm(WgtGain ~ Antibiotic * B12, data = PigFeed)

anova(mod2)
```
There was no evidence of a main effect of antibiotics on average daily weight gain (at the 5% level), F(1,8) = 5.30, p = .050. There was a statistically significant main effect of B12 on average daily weight gain such that bigs who got 5mg B12 gained more weight on averaged than pigs that got no B12, F(1, 8) = 60.33, p < .001. There was a statistically significant interaction of antibiotics and B12 on average daily weight gain, F(1,8) = 47.67, p < .001. The nature of this interaction is such that B12 increases weight pig weight gain when the pigs have been given antibiotics, CI95% = [], however there is no significant effect of B12 when teh pigs have not gotten any antibiotics, Ci95% = [-8.34, 14.34].     


# Residual Analysis

Check conditions on the residuals

```{r}
qplot(x = mod2$residuals, bins = 6)
plot(mod2, which = 2)
plot(mod2, which = 1)
```

# Confidence intervals and effect sizes

```{r}
SD = sqrt(36.25) 
t = qt(.975, 8)

#Conditional averages
mean_B12_antiNO <- 22 - 19

mean_B12_antiYES <- 54 - 3

LL_B12_antiNO = mean_B12_antiNO - SD*t*sqrt(1/3+1/3)
UL_B12_antiNO = mean_B12_antiNO + SD*t*sqrt(1/3+1/3)

LL_B12_antiYES = mean_B12_antiYES - SD*t*sqrt(1/3+1/3)
UL_B12_antiYES = mean_B12_antiYES + SD*t*sqrt(1/3+1/3)

LL_B12_antiNO
UL_B12_antiNO

LL_B12_antiYES
UL_B12_antiYES
```

```{r}
mean_B12_antiNO/SD
mean_B12_antiYES/SD
```