I am a clinical neuropsychologist working with children with neurodevelopmental disorders. I have a quite naive question but we are unable to solve it with my colleagues (we are not very good in statistics).
Here is our problem: In our structure, all children complete several tests assessing the same latent variable. For example, children systematically perform 4 different tests assessing inhibition. Sometimes, we would like to group results of these tests in one overall interpretable variable. Although each test gives an z score, we understand that we cannot take the average of the 4 z-scores obtained by each child and interpret it as an average z score.
First, I have found several papers providing solutions but they systematically require unknown values (for example, Evans 1996 requires to know the correlations between the tests and, unfortunately, we don't have access to precise correlations between the tests at each children's age group).
Second, I have read on this forum that we could obtain an overall z score even if the correlations between the tests are unknown : Combining Z Scores by Weighted Average. Sanity Check Please? In essence, this second solution proposes to divide the averaged z score by its standard deviation. To compute the standard deviation, this solution requires to know only the weights attributed to each test.
I would like to know whether this second solution could be applied to our problem. For example, if a child obtains 4 z-scores (respectively, -1, -1.4, -0.8, -1.9; for which we attribute the same weight), based upon rpatel's formula, is it accurate to say that the overall z score (Zw) of this child is: Zw = (mean (-1, -1.4, -0.8, -1.9))/(SQRT((0.25)²+(0.25)²+(0.25)²+(0.25)²))=-2.55 (i.e., the child performs worse than 99% of his peers?)
I am not able to understand the maths behind the two approaches, so I prefer asking your confirmation rather than making a mistake.
Thank you very much for your help! BF