Hypothesis testing using the t-test

First, we’ll read in the Finches data

finches <- case0201

We first visualize the data

finches$Year <- as.character(finches$Year)
ggplot(finches) + geom_bar(mapping = aes(x = Depth, y = ..prop..,fill = Year), alpha = 0.5, position = "dodge") 

ggplot(finches) + geom_density(mapping = aes(x = Depth,fill = Year), alpha = 0.5)

ggplot(finches) + geom_boxplot(mapping = aes(x = Year, y = Depth))

Since we are satisfied that the model assumptions (that the two distributions in 1976 and 1978 are close to normal) are satisfied, we can proceed to compute the p-value

a <- t.test(filter(finches, Year == "1976")$Depth, filter(finches, Year == "1978")$Depth, alternative = "two.sided", var.equal = FALSE)
a$p.value
## [1] 8.739145e-06

If we set alternative to "one.sided", the p-value would be computed by only considering values that are more extreme and positive (if the difference is positive in the first place).

Note that we could have used the formula we saw before and pt in order to compute this value.