Session 2b

Question 1

T-test purpose

Answer 1

To test whether two unknown population means (µ1 and µ2) are different from each other:
- H0 : µ1 = µ2
- H1 : µ1 ̸= µ2
The two samples may be either independent or correlated.

Question 2

Independent samples

Answer 2

Also known as “between-subjects” designs. Example: Each participant only goes through one of two conditions in an experiment, they are randomly assigned. We test the mean preference scores for a brand between treatment (Ad) and control (No ad) groups of subjects

Question 3

Correlated samples

Answer 3

Also known as “dependent-subjects”, “paired-samples”,“repeated-measures”, etc.
Example: Each participant goes through both conditions in an experiment. We test the mean preference scores for a brand for before seeing an Ad and after seeing an Ad for the same subjects

Question 4

Independent Samples t-test assumptions

Answer 4

• The dependent variable is normally distributed in both populations
• The standard deviations (σ1 and σ2) of the populations are the same (homogeneity of variance)
• Each subject is independent (simple random sample from population)

Question 5

Effect sizes for t-tests (Cohen’s d)

Answer 5

The observed mean difference D = X1 − X2 is in the units of the original variable X. Mean differences are not comparable across studies that used different measurement instruments (e.g., 2 dollars versus 2 points on a Likert scale). The standardized mean difference between groups (Cohen’s d) expresses the mean difference in terms of standard deviation of the DV.