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I received the following question via email:

I have standard scores for a group of kids in a control and an experimental group, and I have measures over time – for one test I have two time points and in another three time points. Because the data are standard scores, does this mean that I can’t use parametric stats to assess change over time between the two groups? My natural inclination would be to use repeated measures ANOVA, but the standard scores are not continuous - right? Would it be better to use non-parametric measures?

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  • $\begingroup$ I would beware of standardization. In half the examples I see the person doing the standardization made arguably false assumptions such as linearity of effects. $\endgroup$ Mar 13 '16 at 13:28
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Standard scores are merely raw scores that have been transformed. Usually standard scores are merely changing the mean and standard deviation. Other times in developmental psychology contexts, the standardisation is done differently based on age, gender or some other characteristic.

In general, I would treat variables like intelligence and normative scores on a personality or other ability test as numeric and analyse using parametric tests.

I generally find it much easier to interpret change using a parametric framework.

If you are studying change either between groups or over time, you do need to think about the nature of the standardisation.

If you are studying longitudinal effects, you would want to be careful when using age reference norms as these could potentially remove age effects of interest, or at least it would change your comparison from one of assessing change on the ability to assessing change relative to normative age trends.

Another situation that sometimes comes up is where people are just using their own data to construct a standard score. E.g., they are justing converting the data to z-scores based on their sample mean and standard deviation. In that case, it's important that you use a common mean and standard deviation for all groups and time points.

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