Non-parametric ANOVA

Question 1

What is a parameter?

Answer 1

A parameter is a thing we are estimating from the data such as a mean, a mean difference, correlation, etc

Question 2

What is bootstrapping?

Answer 2

Bootstrapping is resampling technique that resamples with replacement from the original data to make a new population drawn from the sample.

It is done when the sample is not normal

Question 3

What can you do to your data if it is not normal?

Answer 3

Do a transformation of the data (logarithmic, square root, etc) to see if it is normal after a transformation

Question 4

What is the purpose of a non-parametric test?

Answer 4

To be used when the data does not meet the assumptions of a test - like normality

Question 5

How does a non-parametric test work?

Answer 5

It works by replacing raw scores with a rank order (like the HSC). This also gets rid of uncertainty if we’re not sure if data is ratio or interval, since it only requires that data be ordinal

Question 6

What happens in a non-parametric test when two scores are the same? How are they ranked?

Answer 6

They are given the average of the ranks that they would occupy. For example two scores of 15 which would be 6th and 7th in the rank order are both given the 6.5th rank

Question 7

What non-parametric test do you use when comparing two independent groups? (t-test equivalent for non-normal data)

Answer 7

Mann-Whitney U test (sometimes called Wilcoxon test)

Question 8

What non-parametric test do you use when comparing more than two independent groups (influenced by one IV)? (one-way ANOVA equivalent for non-normal data)

Answer 8

Kruskal-Wallis test

Question 9

How does the Mann-Whitney U test work?

Answer 9

You get the rank order of each of the groups (A and B) and sum them up. Then do you do math stuff to get the Mann-Whitney U which is the smaller of the two U values (either group A or B).

It measures the number of times observations in one group precede those in another group when ranked. You see if the rank order differs significantly between the groups and get a p value. If significant, the groups are significantly different

Question 10

What is the null hypothesis for the Mann-Whitney U test?

Answer 10

The sum of the ranks in group A are no different to the sum of the ranks in group B

Question 11

What descriptive statistics do you report for non-parametric tests?

Answer 11

Since means are often skewed, it is better to report the median and IQR. You can report the effect size (eta^2) for the Kruskal-Wallis test

Question 12

What non-parametric test do you use when you have two IVs? (equivalent of two-way ANOVA)

Answer 12

Aligned Rank Transform (ART)

Used very rarely. You align the data by removing the influence of other effects, then rank them

Question 13

What are the drawbacks of non-parametric tests? (2)

Answer 13

1. Can’t do contrasts (must do pair-wise analyses)
2. Less powerful