Non-parametric Statistics

Question 1

What are the assumptions for ANOVAs?

Answer 1

Between subjects:
Normality
Homogeneity of variance
Independence of scores

Question 2

What is homogeneity of variance?

Answer 2

Checked with Levines test
ANOVA is robust only with equal sample sizes
Large group - higher variance -> conservative f-ratio
Larger group - small variance -> liberal f-ratio

Question 3

What is the importance of distribution?

Answer 3

Check for skewness
Check for kurtosis

Question 4

What are direct tests of normality?

Answer 4

Kolmogorov-Smirnov
Shapiro-Wilk
High false positive rate for larger samples and low power for smaller samples
Rely on visual inspection instead of tests e.g. histogram

Question 5

What are non-parametric alternatives to one-way ANOVAs

Answer 5

One-way between subjects - Kruskal Wallis
One-way repeated measures - Friedman

Question 6

What are non-parametric alternatives?

Answer 6

Can be less powerful than parametric tests
By ranking data we lose info about magnitude of difference between scores

Question 7

What is the procedure for the Krystal Wallis test?

Answer 7

Rank data ignoring membership and sum ranks for groups
Generate H statistic which has known probability distribution

Question 8

What are follow-up tests?

Answer 8

Pairwise comparison with Bonferroni correction (conservative)
Sequential methods (less conservative) - rank p value and adjust alpha by p rank (Holm (smallest p and stop when non-sig)and Hochbergs test (largest p and stop when sig reached))

Question 9

What is the procedure Friedmans test?

Answer 9

Calculate ranks for subject and mean ranks per treatment
If observations >10, follow up with chi-squared distribution
Then follow up with pair wise or sequential procedure

Question 10

What is bootstrapping?

Answer 10

Computationally expensive estimate of properties of sampling distribution from data
Create parameter confidence intervals