Exercise on the t-test (difficult)

Scenario:
You collect data from people in three groups (e.g., professional fields) on their interest in technology using three items. Examine whether Group 1 and Group 2 differ significantly in their scale mean. Group 3 should not be taken into account.

Download data

Items:

  • item1: Interest in technology in everyday life
  • item2: Enjoyment of using technological devices
  • item3: Desire to learn more about technology

Solution in R

1. Read in the data and calculate the scale mean

daten <- read.table("Schwer_Technikinteresse.dat", header = TRUE, sep = "\t")

# Compare only Groups 1 and 2
daten12 <- subset(daten, gruppe %in% c("Gruppe1", "Gruppe2"))

# Calculate the scale mean
daten12$interesse <- rowMeans(daten12[, c("item1", "item2", "item3")])

2. Check the assumptions

# Shapiro test for each group
shapiro.test(daten12$interesse[daten12$gruppe == "Gruppe1"])
shapiro.test(daten12$interesse[daten12$gruppe == "Gruppe2"])

# Levene's test for equality of variances
install.packages("car") # if necessary
library(car)
leveneTest(interesse ~ gruppe, data = daten12)

3. t-test

t.test(interesse ~ gruppe, data = daten12, var.equal = TRUE)

4. Nonparametric alternative (if assumptions are violated)

wilcox.test(interesse ~ gruppe, data = daten12)

Solution in SPSS

1. Import the CSV file

  • Open SPSS → File → Open → Schwer_Technikinteresse.csv

2. Compute a new variable

  • Menu: Transform → Compute Variable
  • Target name: interesse
  • Formula: (item1 + item2 + item3) / 3

3. Compare only Groups 1 and 2

  • Menu: Data → Select Cases
  • Condition: gruppe = "Gruppe1" OR gruppe = "Gruppe2"

4. Check the assumptions

  • Analyze → Descriptive Statistics → Explore
  • Dependent variable: interesse, grouping variable: gruppe
  • Charts → Activate normality tests

5. t-test

  • Analyze → Compare Means → Independent-Samples T Test
  • Test variable: interesse, grouping variable: gruppe
  • Define groups: "Gruppe1" and "Gruppe2"

6. Nonparametric test

Test: Mann-Whitney U test

Analyze → Nonparametric Tests → Independent Samples

Test variable: interesse, grouping variable: gruppe

Looking for a bigger challenge?

If you would like to make the task a little more challenging (in terms of data management), complete it using this dataset.

Download messy data

Example solution in R

 
df <- read.table("Komplexe_Spaltenstruktur_gruppiert.dat", header = TRUE, sep = "\t", na.strings = "NA")

# Calculate group means (for valid cases only)
g1 <- rowMeans(df[, c("Gruppe1_Item1", "Gruppe1_Item2", "Gruppe1_Item3")], na.rm = TRUE)
g2 <- rowMeans(df[, c("Gruppe2_Item1", "Gruppe2_Item2", "Gruppe2_Item3")], na.rm = TRUE)

# Extract and compare non-NA values
g1 <- g1[!is.na(g1)]
g2 <- g2[!is.na(g2)]
t.test(g1, g2)