I'm currently completing my honours thesis for psychology and want to compare ideal parenting characteristics (there are 15 different characteristics) between mothers and fathers. I want to determine if mothers and fathers ascribe to these characteristics differently. The characteristics were measured on a 5-point Likert scale (1 =Not at all to 5= very much). For obvious reasons, the data is skewed. Pretty much I just want to know what type of statistical test is best to answer my research question?
Hello Erin,
The answer depends on whether you collected data from mothers and fathers as independent groups or as matched pairs (e.g., each pair of respondents represents a mated pair). As well, the answer depends on whether each of the 15 characteristics (each measured by a single, Likert-type item, right?) are to stand as separate variables, or if it makes more sense to combine at least some of them into a smaller number of variables.
If you treat the 15 items as 15 DVs, then the statistical power of an overall F vs. M test won't be very good unless: (a) the differences are pretty stout; and/or (b) you have a realy good sample size.
That said, here are my suggestions:
1. If F & M are independent, a one-way manova using bootstrapped error estimates.
2. If F & M are dependent/paired, then: (a) form differences for each pair (always the same way (e.g., F - M values) for each of the 15 variables, then (b) run a one-way manova (paying attention to whether the test that the overall vector of mean differences = 0); again, using bootstrapped error estimates.
3. If F & M are independent, a multivariate analog to the Mann-Whitney-Wilcoxon test may be used. The R library, MultNonParam, includes such a test.
4. If F & M are dependent, then the process outlined by Sheu & O'Curry (1996) could be used. They provide S code, which should translate pretty readily to the freely available R system. Sheu, S-F, & O'Curry, S. (1996). Implementation of nonparametric multivariate statistics with S. Behavior Research Methods, Instruments, & Computers, 28, 315-318. As well, there is at least one multivariate rank-sum test in R (https://rdrr.io/cran/DepthProc/man/mWilcoxonTest.html).
Good luck with your work.
Dear Erin Blanch
Adding to what professor David Morse has mentioned, if you are building a behavioral model then you can use the partial least square structural equation modeling (PLS-SEM) since the data is already skewed.
You can test the if the father/mother groups have significant difference among them using the measurement invariance.
The (PLS-SEM) can be applied within the R environment via the following packages:
1. semPLS
2. plspm
Here is a book that was written by the designer of the package to illustrate how to use it
https://www.gastonsanchez.com/PLS_Path_Modeling_with_R.pdf
Also, you can use the SmartPLS software, which is a very powerful software that is mainly dedicated to run the partial least square analysis.
Belal Edries David Morse
thank you so much for the help.
The data for mothers and fathers was collected independently and all variables are separate. I also have a sample size of 1500
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