How to look at interactions when using a Mann Whitney U test

[Phil Davies]

Hi,

I am currently doing my third year dissertation project and need some advice.  Before I ask any questions, it may be best to give some information about my study.

* Its a 2x2x2 independent groups design:

 Profession: Laypeople vs. Police Officer

Sexuality of Victim: Gay vs. Straight

Violence: Verbal vs.  Physical

My D.V’s are

Decision to charge a perpetrator (using a 6 point Likert scale [one question]).

Male Rape Myth Acceptance (using a 6 point Likert scale [22 question]).

Basically I have given lay people and police officers a fictitious scenario depicting rape and have altered the sexuality of the victim and the type of violence used.

1) I ran descriptive stats, on both DV’s to check normality, outliers, skewness etc.  Both DV’s had extreme outliers and the skewness was awful.

2.  Any how I decided to transform the data and re-run descriptives. The Decision to charge variable remained skewed and non normally distributed while the Rape Myth variable had a normal distribution.

3. The origninal plan was to run a MANOVA however due to decision to charge D.V not meeting any parametric assumptions I decided to run a two way ANOVA and three Mann Whitney U tests.

This is where I am stuck:  The Anova test is not an issue, My issues are with the Mann Whitney U tests.

I have hypothesised that police officers are more likely to charge a perpetrator when physical violence is used and when the victim is homosexual, compared with laypeople

However:

Q1) the mann whitney u test only compares groups. So looking at the main effects is ok.  However, how do I look at any interaction effects? (Some advice I have been given is to run a chi square test. I have tried a chi square but the output does not look right. May be I am inputting the data incorrectly)

Q2) My supervisor has said because I am running 4 tests I need to do a Bonferroni significant level of .05/4, Im not sure this is the case.  I am running two separate tests, surely the bonferroni should only apply to the 3 x Mann Whitney U tests and not include the Anova?

Any help would be really helpful.

Cheers

Phil

[Nicolas Stefaniak]

Hi Phil,

concerning you first question, I think that I would try to perform ANOVA with bootstrap in order to explore all the interaction effects. You can get the codes in the Book (discovering statistics with R)

Concerning the second question : many researchers do not apply any correction. This is probably an error. The application of the correction for the three U would be correct. But the best is to correct for all the study.

Howell explains the difference the familywise error by analysis and by experiment.

My advice is to use Holm’s correction which is generally preferred to Bonferroni. R provides this correction.

Note that Wilcox’s robust method should be the best choice in your situation (and it is possible to compute the in R)

Good luck. Hope that it helps!

[Phil Davies]

Hi Nicolas,

Thanks for the quick reply. I have never used R only SPSS (I am still an undergraduate and R has never been taught to me).  Would you use ANOVA with bootstrap even though the data does not meet parametric assumptions?

Are you suggesting I use Wilcox’s method instead of Mann Whitney You?

Sorry i’m a little confused ha!

[Nicolas Stefaniak]

Wilcox’s method allow you to perform non parametric ANOVA, but I do not think that SPSS provides these statistics.

The role of the bootstrap is to create an artificial population with the same shapes as your sample. Thus, it is quite robust if you have a sample large enough (large enough is subjective … but I think that at least 30 participants by groups are needed).

If you’re interested by interactions and you are not using R, bootstrap seems to be the best choice from my view.

I think that SPSS provides bootstrap for ANOVAs.

[Rafael Garcia]

Phil,
It is a common misconception that you’re variables need to be normaly distributed.The residuals of your model must be normal not the raw variables.

That being said, unless normality is egregiously violated, you can still use MANOVA (though I never suggest MANOVA). The generalizability of your results will be questionable, but (as we almost never have true random samples) when aren’t they? Normality is really only critical when trying to predict individual data points (and much smarter people than I agree http://andrewgelman.com/2013/08/04/19470/).

If you have a hypothesized causal order of your DVs, you should consider something like path analysis, sequential canonical analysis, or “cascade” modeling in regression.

That may or may not help.
Raf

[Phil Davies]

Raf,

Thanks for the help! How do I test if my residuals are normal?  Do I test the residuals before transformation?

[Anonymous]

Hi

You can use a three dimension qi square and see total relation and all of  2*2 relations between your variables

[Author]

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