11: NON-PARAMETRIC STATISTICS

Question 1

What basic features distinguish non-parametric statistics from parametric?

Answer 1

• they do not draw assumptions about the underlying population distributions (distribution free statistics)
• have less power (more likely to make type II error)

Question 2

What is the non-parametric equivalent of the independent t test?

Answer 2

Mann-Whitney U test

Question 3

What is the non-parametric equivalent of the paired t test?

Answer 3

Wilcoxon T test

Question 4

What is the non-parametric equivalent of the 1-way independent ANOVA?

Answer 4

kruskal wallis test

Question 5

What is the non-parametric equivalent of the 1-way RM ANOVA?

Answer 5

Friedman test

Question 6

How do we assess the normality assumption?

Answer 6

• the Shapiro-Wilk test
• can also use the results to decide whether to use parametric or non-parametric test

Question 7

What is the non-parametric equivalent of Pearson’s correlation coefficient?

Answer 7

• Spearman’s Rho: used when N>20
• Kendall’s Tau: used where N<20

Question 8

What are the non-parametric equivalents for partial correlation and regression?

Answer 8

There are none

Question 9

When should you use a non-parametric test of relationships?

Answer 9

Best to use non-parametric if either variable is measured on a nordinal scale (especially if you are concerned that the intervals betwen mesures are not equivalent)

Question 10

What are the non-parametric tests to analyse categorical data?

Answer 10

• one-variable Chi-Square (aka goodness of fit test)
• chi-square test of independence (two variables)

Note: no parametric equivalents, if the DV is measured on a categorical scalew, non-parametric tests are the only option

Question 11

Mann-Whitney U test

Answer 11

• 1 IV, 2 levels, between subjects
• scores are ranked across both levels
• H0: mean ranks across the 2 IV levels are equivalent

Question 12

How do you check the normality assumption in independent designs?

Answer 12

Shapiro wilk:
- assess the p of obtaining a distribution of scores like the distribution we see inthe sample if in fact the population were normally distributed
- significant result (p<.05) suggests less than 5% chance that we could have obtained this dist. if the population was normally distributes
- means we have to reject the null (that pop. is normally distributed)

Points:
- test is a ‘blunt’ instrument, particularly when sample size small
- should be used in conjunction with visual inspection of histograms

Question 13

Calculate effect size (Mann Whitney U, and Wilcoxon)

Answer 13

r = z / -/N

• using z score reported with spss output
• > .1=small, >.4=medium, >.7=large

Question 14

Wilcoxon T test

Answer 14

• 1 IV, 2 levels, within subjects
• equivalent to paired t test
• each participant’s difference score is calculated and those difference scores are ranked
• H0: median difference score is equivalent to 0

Question 15

checking the normality assumption in repeated measures designs

Answer 15

shapiro-wilk: tests the null hypothesis that the sampled difference scores, are drawn from a normally distributed population of difference scrores
- significant result (p<.05) means we need to reject the null hypothesis and conclude that the distribution of difference scores in the population is unlikley to be normal

Shapiro-Walk provides an objective, but rather insensitive, measure of normality - also need visual inspection of histrograms

Question 16

Kruskal-Wallis one way ANOVA

Answer 16

• 1 IV, >2 levels, between subjects
• equivalent to independent 1 way ANOVA
• scores are ranked across all IV levels
• H0: mean ranks across IV levels are equivalent
• if significant (H0 not true), need to conduct post-hoc tests to determine which IV level ranks are different (Mann-Whitney U, corrected for multiple comparisons)

Question 17

Calculate effect size - Kruskal-Wallis One way ANOVA

Answer 17

partial n squared = H / (N-1)

H value given in SPSS output
>.01 = small, >.0.6=medium, >.14 = large

Question 18

Friedman’s ANOVA

Answer 18

-1 IV, >2 levels, within subjects
- non parametric equivalent - repeated measures one way ANOVA
- based on ranking of difference scores across IV levels
- H0: mean ranks across IV levels are equivalent (significant result - mean ranks not equivalent)
- if significant, conduct post hoc tests (Wilcoxon T tests, corrected for multiple comparisons)
-

Question 19

Spearman’s rho/Kendall’s Tau

Answer 19

• 2 variables, continuous/ discrete
• alternative to pearson’s r
• Tau reported when N < 20
• scores are ranked
• H0: no relationships between the ranks of the 2 variables
• significant result - ranks are related

Question 20

Spearman’s rho/Kendall’s Tau df

Answer 20

df = N-2

Question 21

What are Chi-square tests used for?

Answer 21

• to analyse data measured on a categorical scale
• the ‘data’ are frequency counts (not scores)

Question 22

One -variable chi-square

Answer 22

• also known as goodness of fit test
• used where there is a single variable, measured on categorical scale
• determines whether there is a difference between observed and expected frequencies

2 options:
-observed frequencies are compared to equal distribution of expected frequencies
-observed frequencies are compared to unequal distribution of expected frequencies

Question 23

chi-square test for independence

Answer 23

measures the association between two variables
-each variable measured on a categorical scale
-r*c first variable has “r” categories, second has “c”
-determines whether there is a relationship/association between the two variables (difference between expected and obtained frequencies)

Question 24

chi square test for independence (2x2): assumptions

Answer 24

-in 2x2 tables, expected frequencies should be >5
-fisher’s exact probability test can be used if this assumption is broken - it’s less sensitive to small expected frequencies

Question 25

How do you measure effect size in a chi square test for independence?

Answer 25

Cramer’s V