Two non-paired continuous variables

TWO NON-PAIRED CONTINUOUS VARIABLES

What does an independent samples t-test evaluate? (t.test() or independentSamplesTTest())

Formal name: Student’s independent samples t-test

It compares the means of two independent groups to see if they are significantly different

• H₀: population means of both groups (samples) are equal

• H₁: population means of both groups (samples) are not equal

What is the test statistic for an independent samples t-test and how are degrees of freedom calculated?

Values further away from zero (i.e., higher absolute values) correspond to a lower probability of H0 being true

Degrees of freedom: df = N−2

• N is the total number of observations across both groups (in the data set)

*exact rejection regions depend on degrees of freedom

What is Cohen’s d and how is it interpreted for independent samples t-tests? (cohensD()) - Effect size

Cohen’s d measures the magnitude of difference between group means:

• 0.20 = small effect

• 0.50 = medium effect

• 0.80 = large effect

What are the 3 assumptions of the independent samples t-test?

• The continuous variable is normally distributed in both groups

  • Check with Shapiro-Wilk test, histogram, Q-Q plot

  • If violated: use Wilcoxon rank sum test (wilcox.test())

• Homoskedasticity: variances are equal between groups (the variance is the same in both groups)

  • Check with Levene’s test (leveneTest())

  • If violated: use Welch’s t-test

• Observations are independent