# Normality test without knowing a sample's mean

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!

• 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. – Glen_b -Reinstate Monica Oct 26 '19 at 6:34