What analysis do I need for 2 Ivs and 2 DVs?

Question

I think I need a MANOVA, but I may need an ANCOVA and then also do an ANOVA within just the experimental group.

I think it's a 2x2 factorial independent measures ANOVA within the intervention group. I don't have any equivalent sentence to write for a MANOVA as I've never written one up before

I have 2 IVs: IV1 has 2 levels: control group and intervention group IV2 is a personality trait presence within the intervention group only as this is a secondary hypothesis

I have 2 related DVs: DV1 is a child's self-rated wellbeing score change over time (1 score at start and other at end of experiment) DV2 Child's parent-rated wellbeing score change over time (1 score at start and other at end of experiment)

I can split the score for wellbeing into various different sub-scores (hopefulness, happiness, optimism, worthiness)

My hypotheses are: H0- no significant difference in wellbeing improvement over time between experimental and control group H1- intervention group will show significant improvement in wellbeing score compared to control H2- significant improvements in intervention group's specific wellbeing scores of hopefulness, happiness, optimism & worthiness H3- magnitude of improvement in intervention group will be higher in those with the specific personality trait measured.

I am happy to be told I'm totally wrong, as the analysis section of my paper always takes the longest per word to write and I feel utterly lost. Thanks in advance :)

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Chat GPT says:

Based on your hypotheses, this analysis strategy involves using a combination of MANOVA, ANCOVA, ANOVA, and regression analyses to thoroughly evaluate the effects of your intervention and secondary hypotheses about nature relatedness.

Hypotheses Revisited:

H1: Use MANOVA to evaluate overall differences and follow-up ANOVAs for specific DV changes. H2: Use Factorial ANOVA to assess sub-scale differences. H3: Use ANOVA or regression within the intervention group to analyze the impact of nature relatedness.

Answer 1

Sounds like you have 2 repeated measures per participant in addition to having 2 groups and 2 DVs. So, you also need something to address the non-independence of your observations.

MANOVA is not very useful if you plan to proceed within separate ANOVAs anyway. My favorite way of dealing with dependent DVs is to use structural equation modeling, but if you are unfamiliar with that, it may not be cost effective to start learning that for this study. With only 2 DVs, just running two separate models is not bad in my opinion. You can adjust p-values separately if you want (e.g. via FDR correction such as Benjamini-Hochberg).

One way to deal with data like this is to run a multilevel model (also called mixed models and hierarchical linear models) with group, time (pre-post), and the interaction between them as fixed predictors, and a random intercept of participant to deal with the repeated nature of the observations.

A mixed ANOVA with pre-post as a within-person factor and group as between-person factor and their interaction would also work.

As for the personality trait, if it's only measured in the intervention group, you can only investigate whether the trait is related to pre-post change in the intervention group. You probably need to run a separate analysis for this purpose including only the intervention group. An ANCOVA or a multilevel model with just time (pre-post), trait, and their interaction would work.

ChatGPT is not super reliable with statistical questions.