I'm wondering if there is a better way to do this?
I'm computing a cognitive test, let's say called PSYTEST.
PSYTEST consists of 4 subtests. Each of those subtests have parts and sections.
When each subtest total is added, a Total PSYTEST score is calculated which can be converted into a standardised score. The standardised score tells me where that score is ranked in a sample of individuals.
I have a dataset with 100 cases. I have a hypothesis that for the people in this dataset, those doing well on Subtest A Part C Questions 2-7 seem to get a higher score on PSYTEST Total score. But what proportion of the PSYTEST Total score does this account for? In other words, I want to predict how much of the PSYTEST total score can be estimated by that unique small part.
How I've approached it:
1) To avoid circularity, - calculated a PSYTEST Total score that does not include Subtest A, Part C, called PSYTEST_ALT
2) Plugged in Subtest A, Part C, Questions 2-7 into a Simple Linear Regression block in SPSS.
3) Looked at the size of the relationship and variance explained by the predictors
4) Provided a regression model allowing calculation of PSYTEST_ALT when knowing only Subtest A Part C Question 2-7 scores
1) Leaves me with a PSYTEST Total score that isn't standardised. Cannot be reverse calculated.
1) Use this dataset to standardise scores instead - convert the PSYTEST_ALT scores to z-scores, so then if using the regression model to estimate someones's PSYTEST_ALT score, can cross index to a z-score which will tell where the person ranked relative to the people in this dataset.
Looking for thoughts, solutions, amendments, improvements?
BTW, Subtest A Part C Questions 2-7, are just 6 questions providing a 1-point score out of roughly 200 in the whole test. I have argued this would make a miniscule calculable difference in regression estimates, but have been told it is neveretheless circularity and is not allowed... seems silly.
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