Significance test with four categorical predictors?

I'm analysing the following data:

I'm interested in the difference between the "CONT" control group, and PPS/PWS (which I'll collapse to one group), on the Normal/Abnormal measurements. I'm not interested in sex or age differences.

I thought I might be able to analyse this with a factorial ANOVA, or by using multiple regression.

What would be the best way to proceed? Are there any guides I could follow? I can use R or SPSS.

• Just to clarify, you are interested in knowing if the "CONT" group differs from "PPS/PWS" group on all four variables (500R, 500L, 1000R, 1000L)? Commented Sep 6, 2017 at 1:27
• That's a good question – I should have been more precise :-)
– m-ga
Commented Sep 6, 2017 at 8:53
• I'd be interested in both differences on the individual measures, and on the measure of all four variables (500R, 500L, 1000R, 1000L).
– m-ga
Commented Sep 6, 2017 at 8:53
• Interpretation would be easier if there was a significant difference on all four measures. But a significant difference on just one measure would also be of interest. However, there is little reason to suspect laterality effects. So, R&L (right and left) could be combined for 500Hz, and for 1000Hz – if I was working with continuous data, I'd be inclined to average them.
– m-ga
Commented Sep 6, 2017 at 8:57
• thanks for the clarification. I asked for the clarification because your title is inconsistent with your question. The title outlines there to be four predictors while it seems that you have four outcome variables and only one predictor (the grouping variable). Commented Sep 6, 2017 at 12:49

It seems that you have four questions of interest:

1. are group assignment and 500R independent of each other?
2. are group assignment and 500L independent of each other?
3. are group assignment and 1000R independent of each other?
4. are group assignment and 1000R independent of each other?

In addition, group assignment and outcome variables are all categorical variables. In this case, it seems to me that Chi-squared test would be appropriate to help answer those questions.

Furthermore, if you do decide to run four chi-squared test, correction for multiple testing would be highly recommended. Bonferroni correction can be applied, that is, your alpha level should be divided by the number of tests you run. In this case, since you are running four tests, if p<.05 is your usual threshold of significance, in each of the four tests, your threshold of significance should become p<.0125 in order to preserve a family type I error rate under .05.

• Thanks, that is brilliant :-). None of the comparisons reach significance. 500Hz Right was at p=.04 before the Bonferroni correction.
– m-ga
Commented Sep 6, 2017 at 23:10
• You can probably report that as like a trend or marginally significant. :) Commented Sep 7, 2017 at 3:47