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I've collected scores of teacher constructed maths exams in over 10 different schools. My intention is to explore some home and school factors on these test scores. E.g whether or not parental involvement or higher perental education is related to the student's test scores... However given that the tests in these schools are not standardised (different difficulty levels), I'm thinking of using the z scores for my analysis instead... am I right? Or is there any other ways I can treat the test scores before running my analysis? What will be the statistical implications if I run a correlation/Anova analysis with the raw unstandardised test scores?

Let me clarify my question.....Each of these 10 schools conducted their own end of year examinations and scored students out of 100 . There's over 800 students in total. Data on background, attitudes , patental involvement, self efficacy as reported by the students have been collected....All I wanted to do is to find out if the each of the foregoing factors relates to the test scores ( am not interested in regression or any model building) ... is this statistically appropriate, when tests were different for each of the 20 school? That's my delima –

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Given that the tests were given in different schools and that more than one was given in each school, you have dependent data which will violate the assumptions of regression, regardless of how you standardize the scores.

You need to account for the dependence; one way to do this is with a multi-level model. This will automatically deal with the differences by giving each school a different intercept. However, with the data you have, there is no way to know if the differences among schools are due to differences in the tests, the students, the teachers, or something else.

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@Peter_Flom is not wrong but if you can assume the schools behave approximately close enough, you don't need a mixed effects model. That all depends on how you want build your assumptions in your model.

I don't understand exactly how using the z-score can standardize your score. Consider two simple examples:

Example 1:

The test is so easy that everybody gets close to perfect marks. Your sample standard deviation would be small. The deviation from the mean would also be small.

Example 2:

The test is so hard that everybody scores close to zero. Your sample SD will would be small. The deviation from the mean again would also be small.

Instead, I think you should weight your score. What weight you should use is problem-specific. Consider weighting.

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