# Abschnitt 10 Power test for mean differences between two samples

As covariance-based structural equation modeling can be, and ideally should be, estimated using normally-distributed data, there must be statistical procedures in R to determine the statistical power of a test.

The following description shows you how to assess statistical power for testing mean differences in latent factors using R.

Disclaimer: I am aware that there were better or faster ways to work with, but here you are. The advantage of my following approach is, it is tailored to social science data and may teach you some things about understanding social science data analysis.

Subsequently, I will focus more on the demonstration of performing the test, and less on the rationale of its use and the statistical reasoning for interpretation. You may want to consult the literature for deeper study of the connected ideas and methodological concepts:

• The test for mean differences of latent factors using several indicators can be thought of as a test of a hypothesis in the abstract sense using statistical means to investigate empirically observed differences.
• The test can also refer to a psychological test in terms of survey research or simply a measurement of a construct important to social scientific analysis.

We now focus on performing the former to use its fundamental understanding productively in applied social science research.

Eventually, in this brief technical manuscript, we want to test whether there is a mean difference between two groups for a normally-distributed latent variable for which we collect data on a set of four indicators.

In applied social science research, there are usually particular challenges that result from observational data deviating from ideal norms or violating certain assumptions. Thus, as we perform a test on simulated data that is more or less perfectly suitable, our results will most likely deviate in the field. But the subsequent depiction of the procedure can at least give a good idea of how many cases we need to collect in a (randomly) drawn sample from a population.

Building on the great blog article by Philipp Masur, where he focuses on the parameter estimates of the structural regression model in structural equation modeling, we now address how using the R packageslavaan and paramtest helps to assess statistical differences in latent factor analysis. I thank Philipp Masur for guiding my insights, and I hope my approach, while probably less elegant than his, may be helpful to some people.

This out of the way. I learned something setting up the analysis for assessing the statistical power of latent factor models testing for mean differences in R. I raised some questions that got answered or not and will document all this more or less in the following. I will provide the R-code where necessary. This way you are able to repeat the analyses and use them as a blueprint to tweak your own code.