11: NON-PARAMETRIC STATISTICS Flashcards
What basic features distinguish non-parametric statistics from parametric?
- they do not draw assumptions about the underlying population distributions (distribution free statistics)
- have less power (more likely to make type II error)
What is the non-parametric equivalent of the independent t test?
Mann-Whitney U test
What is the non-parametric equivalent of the paired t test?
Wilcoxon T test
What is the non-parametric equivalent of the 1-way independent ANOVA?
kruskal wallis test
What is the non-parametric equivalent of the 1-way RM ANOVA?
Friedman test
How do we assess the normality assumption?
- the Shapiro-Wilk test
- can also use the results to decide whether to use parametric or non-parametric test
What is the non-parametric equivalent of Pearson’s correlation coefficient?
- Spearman’s Rho: used when N>20
- Kendall’s Tau: used where N<20
What are the non-parametric equivalents for partial correlation and regression?
There are none
When should you use a non-parametric test of relationships?
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)
What are the non-parametric tests to analyse categorical data?
- 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
Mann-Whitney U test
- 1 IV, 2 levels, between subjects
- scores are ranked across both levels
- H0: mean ranks across the 2 IV levels are equivalent
How do you check the normality assumption in independent designs?
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
Calculate effect size (Mann Whitney U, and Wilcoxon)
r = z / -/N
- using z score reported with spss output
- > .1=small, >.4=medium, >.7=large
Wilcoxon T test
- 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
checking the normality assumption in repeated measures designs
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
Kruskal-Wallis one way ANOVA
- 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)
Calculate effect size - Kruskal-Wallis One way ANOVA
partial n squared = H / (N-1)
H value given in SPSS output
>.01 = small, >.0.6=medium, >.14 = large
Friedman’s ANOVA
-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)
-
Spearman’s rho/Kendall’s Tau
- 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
Spearman’s rho/Kendall’s Tau df
df = N-2
What are Chi-square tests used for?
- to analyse data measured on a categorical scale
- the ‘data’ are frequency counts (not scores)
One -variable chi-square
- 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
chi-square test for independence
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)
chi square test for independence (2x2): assumptions
-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
How do you measure effect size in a chi square test for independence?
Cramer’s V
