R Workshop: T-test

An Introduction to T-tests

Assumptions of T-tests

Normality of Residuals

library(tidyverse)

data <- starwars %>% 
  filter(sex == "male" | sex == "female")

model <- lm(height ~ sex, data = data)

residuals <- data.frame(res = residuals(model))

problem <- residuals %>% filter(res > 2.5 | res < -2.5)

nrow(problem)/nrow(data) 

1

Filtering for male the female using the filter() function

2

Running a linear regression (that is a t-test here) to get residuals

3

Calculate residuals for the observations

4

Find potentially problematic observations

[1] 0.8157895

Graphical Depiction of Normality of Residuals

residual_graph <- ggplot(residuals,aes(x = res)) +
  geom_histogram(aes(y=after_stat(density))) +
  stat_function(fun = dnorm,
                args = list(mean = mean(residuals$res),
                            sd = sd(residuals$res)),
                col = "blue",
                linewidth = 1) +
  theme_classic()

print(residual_graph)

1

We are plotting the residuals here. We give ggplot a geom (i.e., histogram)

2

We also give some other arguments like a density distribution.

3

Here we are basically providing what is needed to draw a normal distribution given the data using the stat_function() function. The col and linewidth arguments simply change the colr and size of the normal curve. The theme_classic() just changes some aesthetic things. I personally prefer this theme for all ggplot2 graphs

4

print will show us the graph output

Statistical Depiction of Normality of Residuals

We can also test the assumption statistically using the shapiro.test() function here

shapiro.test(residuals$res)

    Shapiro-Wilk normality test

data:  residuals$res
W = 0.84515, p-value = 3.515e-07

Homogeneity of Variance

Homogeneity of variance is important even for a basic t-test. Below is how we might go about testing this assumption.

Graphical Depiction of Homogeneity of Variance

variance_boxplot <- ggplot(data,aes(x = sex,
                               y = height)) +
  geom_boxplot() +
  theme_classic()

print(variance_boxplot)

1

Graphically we can represent this as a boxplot with the group variable as the x and the outcome as the y. We see this here

2

We again provide a geom for ggplot2 to use and provide a theme() choice here

Statistical Depiction of Homogeneity of Variance

We can also test the assumption using the Bartlett test. This can be shown below

bartlett.test(height ~ sex,data)

    Bartlett test of homogeneity of variances

data:  height by sex
Bartlett's K-squared = 11.126, df = 1, p-value = 0.0008511

Running a T-test

t.test(height ~ sex, data = data)

1

The t.test() function will take a DV and IV argument as well as the dataframe used. We can see this here

    Welch Two Sample t-test

data:  height by sex
t = -1.5876, df = 55.148, p-value = 0.1181
alternative hypothesis: true difference in means between group female and group male is not equal to 0
95 percent confidence interval:
 -22.256861   2.579668
sample estimates:
mean in group female   mean in group male 
            169.2667             179.1053