Session 7 - Comparison of variables between two groups using distribution free methods

Question 1

What are other names for Non-paraametric tests?

Answer 1

-Distribution free
-Rank based

Question 2

What does the sign test check?

What is the main assumption?

What is its parametric equivalent?

Answer 2

1. Median
2. Continuous outcome
3. one-sample t-test

Question 3

Wilcoxon signed-rank test

Checks?

Main assumptions?

Equivalent?

Answer 3

Median

Symmetric variable

one-sample t-test

Question 4

Wilcoxon signed-rank test

-Hypothesis checks?

-Assumptions?

-Parametric equivalent?

Answer 4

• Mean rank difference
• The difference has a symmetric distribution
• two-sample paired t-test

Question 5

Kruskal-Wallis

Hypothesis?

Assumptions?

Parametric equivalent?

Answer 5

H0: Identical populations (in terms of ranks)
H1: At least one is different

• As a rank-based method, the null and alternate hypotheses are in terms of ranks (not means, can be in terms of medians if additionally assume equal shape)
• One-way analysis of variance (ANOVA)

Question 6

Cuzick non-parametric test for trend

-Hypothesis?

-Assumptions?

-Parametric equivalent?

Answer 6

-Hypothesis
H0: θ1 =θ2 =···=θk
H1: θ1 <θ2 <···<θk

-Assumptions
Assumes same shape and scale (to test for trend)

-Parametric equivalent
Chi-squared test for trend