What test is appropriate for a data set with 10 continuous dependent variables and one dichotomous independent variable? Is it possible to perform 10 separate independent t-tests or some sort of ANOVA (MANOVA)? The sample size is 1022.
Dear Nagozi
If you have 10 continuous dependent variables and one dichotomous independent variable, you could use a MANOVA (multivariate analysis of variance) to test for differences between the groups defined by the independent variable. A MANOVA is a statistical test that allows you to compare the means of two or more groups on multiple dependent variables simultaneously and determine whether there are significant differences between the groups.
Alternatively, you could use separate t-tests to compare the means of the groups defined by the independent variable for each of the 10 dependent variables. This would allow you to compare the means of the groups for each dependent variable individually, rather than all of them at once as in a MANOVA. However, using multiple t-tests in this way can increase the risk of a type I error (i.e., concluding that there is a significant difference when there is actually none). To control for this risk, you could use a correction method such as Bonferroni correction or the false discovery rate.
It's worth noting that t-tests are generally more powerful (i.e., able to detect significant differences with smaller sample sizes) than MANOVAs when the sample sizes in each group are equal. However, MANOVAs are generally more powerful when the sample sizes are unequal. With a sample size of 1022, you should have sufficient power to detect relatively small differences between the groups using either a MANOVA or t-tests
Hope that helps
Dear Ngozi you can surely use MANOVA or any other testing strategy the point is 'which is your goal ?' Having 1022 statistical units anything is statistically significant even with a very small difference between the groups. So I suggest you to move your focus in 'Which variable allows for a better discrimination between the two classes ?' You can solve this problem in many ways (linear discriminant analysis, knn, canonical analysis or by a simple ROC curve). Given you have so many data I suggest you to generate your model with a subset of data (training set) and look at the generated model performance on a training set made of the data you did not use in the previous analysis.
Before you decide to use MANOVA, take a look at this blog post by Thom Baguley and at the articles by Huang (2020) and Huberty & Morris (1989) that he cites.
Article MANOVA: A Procedure Whose Time Has Passed?
Article Multivariate Analysis Versus Multiple Univariate Analyses
Alessandro's suggestion to turn the problem on it's head and make Group the outcome reminds me of Frank Harrell's similar suggestion in his book on regression--see the attached PDF.
HTH.
Alessandro, Abdelrahan, and Bruce I appreciate all your contributions. I've been busy compiling the analyses for my Ph.D. thesis in the last period. That's a great contribution Abdelrahman. But, I remember using both T-Test and Manova about 6 years ago on the same data. The T-test showed no significant differences with the former whereas the latter revealed significant differences. I was wondering if the differences were from the variances.
I checked the linear discriminant analysis suggested by Alessandro and I think it is tempting to use it because of its clarity. I may end up with it.
Yes, Bruce, I understand your concerns but we have to get the problems solved now until Manova will be declared inappropriate for categorical data. Right now it is a debate. But all the same thanks for your suggestions and links, they helped in widening my horizon.
Hello Ngozi Louis Uzomah. In your last post, you seem to be saying that DFA is much easier to use than binary logistic regression, and that it's interpretation is clearer. If that is what you meant, I find it very puzzling: I think binary logistic regression is easier to use and understand than DFA--and it cannot produce predicted probabilities outside the range 0 to 1 (which DFA can do). But if you are set on DFA, you might find this blog post by Paul Allison interesting. ;-)
https://statisticalhorizons.com/better-predicted-probabilities/
https://stats.oarc.ucla.edu/spss/whatstat/what-statistical-analysis-should-i-usestatistical-analyses-using-spss/
http://www.mash.dept.shef.ac.uk/Resources/MASH-WhatStatisticalTestHandout.pdf
http://www.mash.dept.shef.ac.uk/Resources/MASH-WhatStatisticalTestHandout.pdf
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