1.4: Continuous response data

Question 1

Direct testing procedure for comparing two independent group means:

Answer 1

• Students t-test
• 1a: Hypotheses, test statistic, SE of difference estimate
• 1b: Pooled variance estimate

Question 2

Two non-typical approaches to comparing independent group means:

Answer 2

• Non constant variances -> Welch’s (2a)
• Non parametric -> Mann-Whitney test

Question 3

Drawback of hypothesis testing -> further analysis?

Answer 3

• Yields p-values; doesn’t allows for direct assessment / quantification of effect size
• Corresponding confidence interval for D-hat must thus be constructed (3a)

Question 4

Procedure for paired designs (5 steps):

Answer 4

One-sample t-test for within pair differences:
1. Compute mean of within-pair differences
2. Compute standard deviation of the differences
3. Calculate SE of mean of differences (Sd/sqrt(n))
4. Compute test statistic under H0 (mean of differences/SE of mean of differences)
5. Compare to a t-distribution on n-1 degree of freedom OR compute a 100(1-a)% I for the true difference (4a)