Nonparametric testing

Question 1

When to use nonparametric tests

Answer 1

• Data is not normally distributed and/or
• Data is measured at the ordinal level

Question 2

Nonparametric test assumptions

Answer 2

• Random and independent data
• Continuous measure

Question 3

Nonparametric test advantages/disadvantages

Answer 3

• Advantages:
  
  • Make fewer assumptions
  • Can use very small databases
  • Easy to calculate and interpret
• Disadvantages:
  
  • Typically have lower power than parametric tests → increased chances of Type II error
  • Not always an easy alternative for all parametric tests

Question 4

Common nonparametric tests

Answer 4

• Wilcoxon signed ranks test
• Mann-Whitney U test
• Spearman’s rho correlation
• Kruskal-Wallis test
• Friedman’s test
• Chi-square

Question 5

Wilcoxon test

Answer 5

• Equivalent of dependent t-test
• Within-subject IV with two levels
• Each participant gives scores in both conditions
• Calculate by hand:
  
  1. Calculate difference between the scores
  2. Rank order the difference scores
     
     • Ignore sign while ranking
     • Exclude any differences that are zero
     • When two or more scores are the same, sum the ranks and divide by no of scores (mean rank)
  3. Sum negative ranks
  4. Sum positive ranks
  5. T (or W) = smaller of the 2 sums of ranks
  6. Look up in significance table

Question 6

Nonparametric test descriptive statistics

Answer 6

• Median
• IQR

Question 7

Wilcoxon test output in SPSS

Answer 7

Question 8

Effect size for Mann-Whitney test

Answer 8

• r = z/√N
• Report r as positive, ignore minus sign
• N: total number of observations not number of participants

Question 9

Mann-Whitney U test

Answer 9

• Equivalent of independent t-test
• Comparing 2 groups in between-groups design
• Each participant gives a score in only one of the conditions
• By hand:
  
  1. Rank all scores (together) from lowest to highest
  2. Sum ranks for largest group (or either if they are the same) = R1
  3. Calculate value of U
  4. Look up significance on table

Question 10

Mann-Whitney test output in SPSS

Answer 10

Question 11

Effect size for Wilcoxon test

Answer 11

• r = z/√N
• Report r as positive, ignore minus sign
• N: total number of observations not number of participants