Non-Parametric tests (W11)✅

Question 1

What are 3 differences between non-parametric and parametric tests?

Answer 1

1. Non-parametric statistics do not make assumptions about the underlying population distributions
   -> ‘distribution free statistics’
2. Non-parametric tests have less power than their parametric equivalents
   -> e.g. higher risk of Type II error
3. ‘back-up’ options -> should go with parametric analyses if possible

Question 2

When do we use non-parametric tests?

Answer 2

• When population is NOT normally distributed
• Normality assumption can be assessed using Shapiro-Wilk test
• If Shapiro-Wilk test is significant: data is NOT normally distributed
  => Violated normality assumption
  => Use the non-parametric equivalents
• Should use non-parametric if one of the variables is measured on an ordinal scale (intervals between measures are not equivalent)
  => e.g. distance ran between First winner and Second winner might be different from distance ran between Second Winner and Third Winner

Question 3

How is Mann-Whitney U test used?

Answer 3

• 1 IV with 2 levels, between-subject
• Scores are ranked across both IV levels
• Tied scores are given average rank (e.g. 10+11 = 10.5 ~ 11)

Question 4

How is the Wilcoxon T Test used?

Answer 4

• 1 IV with 2 levels, within-subject
• Each participant’s difference score is calculated and those difference scores are ranked
• (IV2 - IV1) -> if score in IV2 is lower then diff score is negative
  -> Difference scores of 0 are ignored
  -> Tied scores are given average rank (e.g. 10+11 = 10.5)

Question 5

How is Kruskal-Wallis one-way ANOVA use?

Answer 5

• 1 IV with >2 levels, between subjects
• Scores are ranked (across all IV levels)
• If significant, need to conduct post-hoc tests to determine which IV level ranks are different
  -> Posthoc tests using Mann Whitney U tests
  -> Adopt Bonferroni corrections for multiple comparisons

Question 5

How is Friedman’s ANOVA test used?

Answer 5

• 1 IV with >2 levels, within subjects
• Based on ranking of difference scores across IV levels
• If significant, need to conduct post-hoc tests to determine which IV level
  ranks are different
• Wilcoxon T tests, corrected for multiple comparisons

Question 6

How is Spearman’s rho/Kendall Tau test used?

Answer 6

• Two variables, both continuous/discrete
• Non-parametric alternatives to Pearson’s r
• Kendall’s Tau reported when N < 20
• Scores are ranked

Question 7

When are Chi-square Tests used?

Answer 7

• Used to analyse data measured on a categorical scale -> NOT continuous
• The ‘data’ are frequency counts (rather than scores)
• The number of cases falling within each category
• 2 types:

1. Goodness-of-Fit test:
   - Single variable
   - Determined difference between observed and expected frequencies
2. Chi-Square Test for Independence:
   - Two variables
   - Example: 22 (rc) - each variable has two category
   - Determines whether there is a relationship/association between the two variables

Question 8

What about regression, hierarchical regression, or two-way ANOVAs?

Answer 8

No non-parametric equivalents :)
-> Better fix or eliminate outliers