Conducting a t-test in R (exercise)

You are checking whether the average stress level differs statistically significantly between male and female participants. Using a t-test (and, if necessary, a Mann–Whitney U test), you will learn how to turn a research question into a testable hypothesis—and how to test it in R or SPSS.

Task

Dataset: Einfach_Stressvergleich

Research question:
Does the average stress level of male and female participants in your sample differ statistically significantly?

Hypotheses:
$H_0$: $\mu_{\text{male}} = \mu_{\text{female}}$
$H_1$: $\mu_{\text{male}} e \mu_{\text{female}}$

Solution in R

# t-test
# Import data
df <- read.csv("Data/Einfach_Stressvergleich.csv")

# Data management
group1 <- df[df$gruppe == "männlich", "stress"]
group2 <- df[df$gruppe == "weiblich", "stress"]

# Assumptions
## Homogeneity of variances
library(car)
car::leveneTest(df$stress, group = as.factor(df$gruppe))

## Normal distribution
shapiro.test(group1) #not normally distributed
shapiro.test(group2) #normally distributed

hist(group1)
hist(group2)

# t-test
group1 <- df[df$gruppe == "männlich", "stress"]
group2 <- df[df$gruppe == "weiblich", "stress"]

t.test(x = group1, y = group2) #Welch t-test (as an alternative)
t.test(x = group1, y = group2, var.equal = TRUE) #classic t-test

# U test
wilcox.test(x = group1, y = group2)

Solution in SPSS or PSPP

1. Import data

• Open SPSS
• File → Open → select Einfach_Stressvergleich.csv

2. Check the prerequisites

a) Check normality (for each group)

• Menu: Analyze → Descriptive Statistics → Explore
• Dependent variable: stress
• Grouping variable: gruppe
• In the Plots window, activate “Normality plots with tests”
• Click OK
  → You will receive Shapiro-Wilk tests for each group

b) Check the equality of variances

This test is automatically included with the t-test (Levene’s test).

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3. Independent-samples t-test

• Menu: Analyze → Compare Means → Independent-Samples T Test
• Test variable: stress
• Grouping variable: gruppe → click “Define Groups” (e.g., männlich, weiblich)
• Click OK
  → You will receive the t-value, p-value, mean difference, confidence interval, and Levene’s test

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4. Nonparametric test (Mann-Whitney U)

If the normality assumption is not met:

• Menu: Analyze → Nonparametric Tests → Two Independent Samples
• Test variable: stress
• Grouping variable: gruppe
• Test: Mann-Whitney U
• Click OK