Question

You have developed a test of musical ability, and would like to report the scores as Stanines, with a mean of 5 and a standard deviation of 2. Raw scores on your test have a mean of 30 and a standard deviation of 5. What is the Stanine score for someone who obtains a raw score of 25? a. 1 b. 3 c. 7 d. 9

Answer 1

• A stanine score can be any number between 1 and 9.
• First step is to calculate z score or standard score. the formula is X=raw score,M=mean,SD=standard deviation
• In this case,X=25,M= 30 and SD=5

z=X-M/SD

z=25-30/5

-5/5=-1

• -1 indicates perfect correlation but negatively which means high scores in one set are related to low scores in the other set.
• Then convert this z score into T score.T scores result from a transformation of raw scores to standard scores i.e. z score.
• T scores have a mean of 50 and a standard deviation of 10. Standard z scores can be converted to T scores using the formula below.

  T=10∗z+50

• T=10*-1+50

• T=40

• Stanine score for z score -1 would be Stanine 1 (a)