Project 2 Anova

# One-way Anova from Introduction to R:Anova youtube 2/22/2022

```{r}
set.seed(12)

# Generate some sample Demographic data

voter_race <- sample(c("white", "hispanic", "black", "asian", "other"),
                       prob = c(0.5, 0.25, 0.15, 0.1, 0.1),
                       size = 1000,
                       replace = TRUE)

#Generate some age data (equal means)

voter_age <- rnorm(1000, 50, 20)
voter_age <- ifelse(voter_age<18, 18, voter_age)

#Conduct anova

av_model <- aov(voter_age ~ voter_race)

summary(av_model)
```
0.515 > 0.05, therefore there is no difference in the means between the two variables

```{r}
str(voter_race)
```


```{r}
plot(voter_age)
```



```{r}
#Draw ages from a different distribution for white voters

white_dist <- rnorm(1000, 55, 20)
white_dist <- ifelse(voter_age<18, 18, white_dist)

new_voter_ages <- ifelse(voter_race == "white", white_dist, voter_age)

av_model2 <-  aov(new_voter_ages ~ voter_race)

summary(av_model2)
```
The F statistic is higher, so we can see there is a difference from the first model. Also P-value is less than 0.05 therefore there is a differen in the means.

```{r}
pairwise.t.test(new_voter_ages,
                voter_race,
                p.adj = "none")
```
```{r}
pairwise.t.test(new_voter_ages,
                voter_race,
                p.adj = "bonferroni") # conservative way of adjusting p-value
```
```{r}
TukeyHSD(av_model2)
```

# Two-way ANOVA

A two-way ANOVA extends the analysis of variance to cases where you have 2 categorical variables of interest.

```{r}
set.seed(10)

voter_gender <- sample(c("male", "female"),
                       size=1000,
                       prob=c(0.5,0.5),
                       replace = TRUE)

voter_age_2 <- ifelse(voter_gender=="male", voter_age-1.5, voter_age+1.5)
voter_age_2 <- ifelse(voter_age_2<18,18, voter_age_2)

av_model3 <- aov(voter_age_2 ~ voter_race + voter_gender)
summary(av_model3)

```
```{r}
#check for interaction

av_model4 <- aov(voter_age_2 ~ voter_race + voter_gender +
                   (voter_race * voter_gender))
summary(av_model4)

```
```{r}
plot(av_model4)
```