Non-Parametric Alternatives to ANOVA & Statistical Power

Question 1

What are the parametric test assumptions?

Answer 1

Interval/ratio data.
Independence.
Normally distributed data.
Homogeneity of variance (for between-subjects).

Question 2

What are 3 advantages of non-parametric tests?

Answer 2

Fewer assumptions.
Can use small datasets.
Easy to calculate + interpret by hand.

Question 3

What is a disadvantage of non-parametric tests?

Answer 3

They have a lower power than parametric tests (increase in Type II error).

Question 4

When is Friedman’s ANOVA used?

Answer 4

For repeated measures where the IV has 3 or more levels.

Question 5

When is Kruskal-Wallis used?

Answer 5

For independent measures where the IV has 3 or more levels.

Question 6

What is the main statistic for Friedman’s ANOVA named in SPSS?

Answer 6

Chi-squared statistic.

Question 7

What is the asymptotic sig./adj.sig. in SPSS?

Answer 7

The p-value.

Question 8

What is the z-value named in SPSS?

Answer 8

The std. test statistic.

Question 9

What does R stand for in both tests’ formula?

Answer 9

R is the sum of ranks for each condition.

Question 10

How do you calculate H in Kruskal-Wallis?

Answer 10

You rank all scores ignoring the group they belong too (as it’s independent conditions).
Add up ranks for each condition and put these into the main formula.

Question 11

How do you calculate Fr in Friedman’s ANOVA?

Answer 11

You rank scores within each participant (as it’s repeated conditions).
Calculate the sum and mean of ranks in each condition and put these into the main formula.

Question 12

What are the two options when normality assumptions aren’t met (therefore a mixed ANOVA can’t be used)?

Answer 12

Transforming data.

Using several non-parametric tests.

Question 13

Why do we transform data?

Answer 13

If we have skewness or kurtosis then transforming data could potentially stop this (e.g. log transformation) and we can then use a mixed ANOVA.

Question 14

What non-parametric test is used for within-subject conditions?

Answer 14

Wilcoxon.

Question 15

What non-parametric test is used for between-subject conditions?

Answer 15

Mann-Whitney.

Question 16

What are the two choices when looking at the interaction of variables in several non-parametric tests?

Answer 16

1. Calculate the change of score and compare changes across groups using an Independent T-Test or Mann-Whitney.
2. Calculate difference between groups’ scores using a Dependent T-Test or Wilcoxon.

Question 17

How do you complete a Bonferroni adjustment for the number of tests used?

Answer 17

Bonferroni alpha = alpha / number of comparisons.

Question 18

What is a Type I error?

Answer 18

Incorrectly rejecting the null hypothesis. Probability of this is alpha (.05).

Question 19

What is a Type II error?

Answer 19

Incorrectly accepting the null hypothesis. Probability of this is beta.

Question 20

What is the definition of power?

Answer 20

The ability to detect an effect if there is one.

Question 21

What value should power usually be?

Answer 21

.80.

Question 22

What are the three influences on power?

Answer 22

Effect size (the larger the effect, the easier it is to detect). 
Alpha level (usually p < .05). 
Sample size (larger samples are more representative = less error, more power).

Question 23

Power, effect size, alpha level and sample size are all linked. Which one is useful to be able to calculate?

Answer 23

The estimated sample size needed to achieve adequate power.

Question 24

Which program can be used to calculate power?

Answer 24

G*Power.