Unit 12: non-parametric statistics

Beyond Parametric statistics

what are some assumptions of parametric stats?

1. each of your observations MUST be obtained independently from one another

2. data SHOULD BE measured on interval or ratio scale

3. Sampling distribution of the mean must be normally distributed (Null population should be normally distributed, OR you must have 30 or more participants in your groups

in a t-test/ANOVA how does the variance look?

variance within each group (or condition) should be approximately the same (homogeneity of variance)

what test are normally robust to violations of normality?

• t-test and F-test are normally robust to violations of normality and homogeneity of variances

  • large sample size (CLT)

  • if sample is small, corrections can be made to adjust the statistics appropriately.

what is the reality of violating the assumption of independence? what will it cause?

no statistic can mitigate violating the assumption of independence in b/t groups design

• this will systematically under-estimate variance in the population

why is it a problem to have a violation of assumptions in t-test/ANOVAs?

• conclusions are based on hypothetical curved derived from probability theory (remember the t and f curves are theoretical not actual)

• if violated, the math may still “work” but we lose the guarantee that our data follows the probability structure of these curves

• we should be less confident of our conclusions based on the statistical inferences

when do we consider a non-parametric test?

• gross violations of normality and homogeneity of variance, particularly when groups are small

• nominal or ordinal data

what are non-parametric options?

Mann-Whitney U test

Wilcoxin ranked sum test

kruskal-wallace test

what do non-parametric options generally tend to do?

generally, these tests take the scores in each group, rank order them, and put them back into the groups (ranks are summed for each group)

what can the null hypothesis not be expressed as in these non-parametric options?

they cannot be expressed as a function of mean difference between groups

(if the null is true, then the distribution of scores for group 1 is the same as group 2)

when is there an effect when we use the wilcoxin rank sum test?

when the summed ranks are different

so what is thought of non-parametric stats? why?

its an excellent alternative to parametric tests, especially with small sample sizes and non-normal distributions

• less restrictive in terms of assumptions

• less restrictive in terms of types of data/distributions

• do NOT require estimating population parameters

however, what is a con of non-parametric tests?

they’re generally less powerful… so they should be used when parametric statistics cannot be used