MANOVA: What to do with a u-shaped DV?

[Ledi]

Hi, I am hoping to get some advice on my analysis for my MSc dissertation. I will try to keep it short but please let me know if there is more information I can provide to make the situation clearer.

I have five conditions (IV): control, four experimental conditions. The experimental conditions follow a 2x2 design, so there are two factors.

There are four DVs. One of these follows a u-shaped distribution.

The plan was to carry out a two-way MANOVA on all four DVs and infer conclusions about the control group from post-hoc tests. The back-up plan now is to carry out the MANOVA on the four DVs that are normally distributed and then run a non-parametric test on the other DV.

As far as I can tell there are no main effects, but significant interactions.

Does this approach seem appropriate?
Is there a way I can show the interaction with a non-parametric test?

Thank you very much for your time

Ledi

 

[Karabiner]

I will try to keep it short but please let me know if there is more information I can provide to make the situation clearer.

What is the topic of your study, what are the research questions? What do your experimental conditions look like? How large is your sample size?

I have five conditions (IV): control, four experimental conditions. The experimental conditions follow a 2x2 design, so there are two factors.

How does that work, 2x2=4 cells but 5 groups? Or is it just a oneway (M)ANOVA design?

There are four DVs. One of these follows a u-shaped distribution.

What do these 4 variables represent and how were they actually measured?

The plan was to carry out a two-way MANOVA on all four DVs and infer conclusions about the control group from post-hoc tests.

Why MANOVA? Do your 4 variables jointly represent 1 hypothetical construct?

The back-up plan now is to carry out the MANOVA on the four DVs that are normally distributed and then run a non-parametric test on the other DV.

Since not much is known about the nature of your variables or your
sample size, not much can be said, but generally speaking, if your sample
size is not tiny, then ANOVA should be robust against non-normality (in the
subgroups). "Non-parametric" alternatives to a 2x2 (?) design do not exist.

With kind regards

K.

 

[Ledi]

Thank you Karabiner,

Participants were presented with information on women's issues in the four experimental conditions. These varied by presenting statistical information or personal narratives, and intersectional or non-intersectional issues (that's the 2x2). In the control condition participants read statistics on various issues, such as the environment (I have been told that there are issues with the design of the control group because it doesn't follow the 2x2 structure). I have 167 participants, fairly equally distributed across the conditions.
The aim of the study was to determine if the type of information presented would have an impact on attitudes towards policies promoting gender equality.

The four DVs are agreement scores with four different policies. The original plan was to combine them into one variable but there is very little correlation between the agreement scores to actually justify doing this. Agreement was measured on 6-point Likert scales.

I was advised by our stats supervisor to carry out a two-way MANOVA (but had not discussed the issue of non-normal distribution with them).

I could carry out a one-way MANOVA but the interaction is the only interesting result I have.

 

[Karabiner]

You have a 1x5 design, AFAICS (you would have needed 3x3 if you wanted to perform a multifactorial ANOVA with controls and 2x2 manipulations). Regarding normality, n > 50 should usually guarantee robustness of the ANOVA.
H-Test could be used alternatively.

You cannot model an interaction, but you can interpret pairwise Post-hoc comparisons (after oneway ANOVA or after H-Test).
You could ask your supervisor perhaps how he would perform a 2-factorial ANOVA with 5 groups?

Or should you leave out the controls?

If the dependent variables are uncorrelated, then MANOVA is not needed or justified. But it wouldn't be extremely wrong, AFAIK.

BTW, you seemingly have ordinal Likert-type items, not Likert scales.

With Kind regards

K.