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I’m planning a regression analysis. The outcome is the score of an achievement test. Assuming there are 120 items and a person has answered 90 items correctly, the person gets a raw value of 90. This raw value can be converted in an age related t score. Do I use the age related t score or the raw score in conjunction with controlling for age? What is better?

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  • $\begingroup$ How is age factored into the calculation of the t score? $\endgroup$ – Ian_Fin Aug 23 '16 at 14:17
  • $\begingroup$ Do you meant the T-score as used in psychometrics? $\endgroup$ – mdewey Aug 23 '16 at 14:31
  • $\begingroup$ Yes, there are norm tables for the age related t scores. For younger children, there are a lot of gradations. For example, there is a norm table for 3;0-3;1 (age; month) years old and a norm table for 14;0-14;5 (2 vs. 6 month age groups). I tried to figure out a stringent rule, but I think there is none. $\endgroup$ – Lilly Aug 23 '16 at 14:36
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If you model the raw scores using age as a covariate then you would be able to have a flexible model for their relationship. However this would almost certainly mean using more than just the linear effect of age. You might want to investigate using a spline. There is also the advantage that you are using the actual relationship in your setting which may not be the same as the one used to derive the T-scores.

The advantage of using the T-scores is that they may be based on a larger data-set and so more stable. That analysis would also be easier for people to compare with their analysis since they can use the same form of adjustment as you whereas if they model age it will not necessarily be the same model as yours.

I do not think the different widths of the intervals should concern you in making your choice.

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