Week 10 - non-parametric tests

what are parametric statistics?

make assumptions about the population from which the sample has been drawn

• a common assumption being that the distribution of scores in the population is normal

what are non-parametric statistics?

do not make assumptions about the underlying population distributions → distribution free statistics

• non-parametric tests have less power than their parametric equivalents (higher risk of type II error)

what’s the non-parametric equivalent of an independent t-test (between ps)

Mann-Whitney U test

what’s the non-parametric equivalent of a paired t-test (within)

Wilcoxon T test

what’s the non-parametric equivalent of a 1-way Independent ANOVA (between)

Kruskal Wallis Test

what’s the non-parametric equivalent of 1-way repeated measures ANOVA (within)

Friedman Test

what’s the non-parametric equivalent of factorial designs

there is no non-parametric equivalents

how can normality be tested in t-tests and ANOVAs?

• shapiro-wilk test shows if its normal or not

when do you use a non-parametric test?

• if either variable is measured on an ordinal scale

• if data is not normally distributed according to Shapiro-wilk

when do you use asymptotic p-value vs exact p-value?

• asymptotic → ok for large samples

• exact → more conservative (better when sample size is small, sample size differs across IV levels, or where distributions aren’t normal)

what measure of central tendency do you use for non-parametric measures?

median & min and max range

what is the format of a Mann Whitney U writeup?

U= , p= .__ , r = .__

how do you write up a wilcoxon T test

z = , p = .__ r= ._

what would you report after a significant Kruskal-wallis result

post-hoc (Mann-whitney U)

what would you report after a significant Freidman’s ANOVA

Wilcoxon T tests, corrected for multiple comparisons

How do you report Freidman’s ANOVA?

X² (2, N=24) =27.58, p <.001, with a Kendall’s coefficient of concordance (W = .575) reflecting a strong effect

what are the non-parametric tests of relationships?

• Spearman’s rho

• Kendall’s tau

When do you use Spearman’s rho/Kendall’s tau

use Spearman’s rho when N>20, Kendall’s Tau when N<20

How do you report Spearman’s Rho?

rs(23) = .580, p = .003

how do you report Kendall’s Tau?

rt(23) = .580, p = .003

what are non-parametric tests for categorical data?

• one variable chi-square

• chi-square test of independence

the ‘data’ are frequency counts rather than scores

How would you write up chi - square?

X² (1, N=35) = 1.61, p = .240 and then a table reporting observed frequency and expected frequency

What does the Chi-square test for independence measure>

measures the association between 2 variables:

• each variable measured on a categorical scale, 2×2, r*c (row, colomn)

What is Cramer’s V?

Chi-squared equivalent of a r value → percentage of shared variance = V²