I've been searching for a way to approach my problem.

This is a scenario from a Multivariate Statistics Assignment on Confirmatory Factor Analysis.

We've been given only a correlation matrix on 6 variables, the Standard Deviations and sample size. The model assumes that $X1$, $X2$ and $X$3 are indicators of given Factor $F1$, while $X4$, $X5$ and $X6$ are indicators of another Factor $F2$ (we actually know which factors and variables those are, but since my question is theoretical, I am keeping this simpler).

I've already evaluated the measurement model, found it has 7 degrees of freedom and moved on to the method's assumptions.

Now, assuming I want to do the Factor Extraction step using the ML estimator, which assumes data normality: is there any way I can test for my sample normality with the provided information?

I appreciate any small insights and/or directions that may help!

  • $\begingroup$ Re the title: adding in information about the means wouldn't help at all; you still have nothing concrete about the shape of the joint distribution. $\endgroup$ – Glen_b -Reinstate Monica Oct 26 '19 at 6:34

No. You cannot test for normality only knowing the first two moments of a distribution (correlation, covariance, mean, and SDs are all first-and-second including product moment estimators). You need to know the entire sample to test for goodness of fit for a particular distribution. At the very least, you would need to know skewness and kurtosis to exclude some specific violations of normality.

  • $\begingroup$ thank you for the input $\endgroup$ – Pedro Alonso Oct 26 '19 at 5:51

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