I have 2 categorical IVs(2 levels in each variable) and 3 continuous DVs. One IV is teaching approach and the other one is education (a moderator). I'm going to examine the effect of the 2 IVs on DVs and the interaction effect of the moderator on the relation between teaching approach and DVs. So my study is 2*2 factorial design with 1 experimental group and 1 control group. I'm going to use 2-way Manova to analyse data (if the two groups are homogeneous).
But I'm not sure about the minimum number of sample size for two-way MANOVA. In my study, there will be 38-70 pariticipants in each of the two groups.And I will need to categorize participants in each group into urban and rural subgroups. So I would like to know what is the minimum number for each subgroup (urabn/ rural group) if I use 2-way MANOVA to analyse data. And if the sample size for each subgroup is not equal, may I still use 2-way MANOVA? Is there any solution to deal with uneqaul sample size in each subgroup?
I would really appreciate your help!!!
First I would treat the model as a multivariate regression and then lay out the standard table of which subject,(group ) gets what treatment. if this is a full factorial the first replication has 0 df. This means you must replicate the expt at least once more to get enough df to estimate variance. Without this table I have no idea what combination of factors is applied to each subject. Further I don't see see why this would be necessarily a multivariate design rather than 3 independent univariate designs. As you have written this. I am completely confused. Thus I will leave it in your hands and those of further responders to comment. I do want to commend you on doing all of this prior to collecting data. Best wishes David Booth
The way you describe your design is a little confusing for me. I have the impression you use different terms for the same variables.
I suppose your:
"Class Experimental Group A" is an alias for "Treatment X1 FC"
&
"Class Control Group B" is an alias for "Treatment X2 TT".
The 4 O’s correpond to the 2 dependent variables, the repeated measures Pre vs. Post.
You have a second Between subjects variable: Urban vs. Rural.
This, in my opinion, results in a Between x Between x Within subjects design.
1) Between: Group A vs. B
2) Between: Urban vs. Rural
3) Within: Pre- vs. Postmeasures.
In attachment an R script for such a design. The Between factor 'Gender' would correspond to UrbanRural.
Hello Wei,
The glib answer to your question about minimum size is, two cases per cell: So, for a 2 (treatment) x 2 (urban/rural) design with the repeated measures factor of test occasion (pre, post), you'd need a minimum of 8 cases, each measured twice on each of three DVs (= 48 total data points). The other half of the glib answer is, that's not nearly enough for a serious study.
How many cases you'll require hinges on: (a) your target precision for estimating any population parameter(s) from your study results; and/or (b) how much statistical power you'd like your study to have to detect effects of some chosen magnitude (or higher), should those actually exist in the population.
As you haven't specified either your research question(s) or your specific aims in analyzing this kind of data set, it's difficult to offer focused advice.
What I can say is, depending on your specific aims, the "best" statistical method could be one of the following (allowing for the associated assumptions, of course, to have been reasonably satisfied):
1. manova (so-called, doubly multivariate design: 2 x 2 with a repeated measures dimension, having two levels);
2. 3 anovas (or regressions) as suggested by David Booth;
3. multivariate regression (as suggested by David Booth);
4. canonical correlation.
If statistical power is your chief concern (from paragraph #2, above), then you could consider either having a look at the free program, g*power, or running some simulations (see links below) to develop a more informed perspective of requisite sample size, given your research aims.
Good luck with your work.
https://aaroncaldwell.us/SuperpowerBook/
Article Power Calculations for General Linear Multivariate Models In...
- Badges
- Science topic
- Similar topics
- Mathematics
- Statistics
- Sampling Design
- Sample Size