PSYC3016 Week 7 Comparing Two Means

Paired T test assumptions

1. dependent variable is at least interval scale

2. normality

How does a paired t test differ from an independent t test?

A paired t test compares the means of the same group under two separate scenarios, while an independent t test compares the means of two independent or unrelated groups

Nonparametric test: Wilcoxon Signed-Rank test

can be used when the normality and/or homogeneity of variance assumptions of the t-test are violated, based on ranked rather than raw scores

Drawbacks of Wilcoxon Signed-Rank test

• can only say which condition tended to have higher or lower scores, not by how much

• not as much statistical power as t test

What is the effect size measure for the wilcoxon signed-rank test?

Probability of Superiority for Paired designs (PSpaired)

PSpaired

If one were to randomly sample one participant, the PSpaired is the probability of their first score being greater than their second score

Benchmarks for interpreting PSpaired

small: .56, medium: .64, large: .71

Rank-Biserial Correlation

Note the sum of positive, negative and total ranks from wilcoxon signed-rank test

Interpreting Rank-Biserial correlations

0: no difference between conditions. positive values: scores in first condition tend to be larger than scores in second condition. negative values: scores in first condition tend to be smaller than scores in second condition

Benchmarks for Rank-Biseral correlation

small: .13, medium: .30, large: .47

Do within-subjects (paired designs) have more statistical power than between-subjects (independent)?

Yes, thus we require fewer participants to achieve 80 percent statistical power in within-subjects designs