1. Module 8 z Scores What they are Benefits Calculating them Comparing them 1

2. Standard Scores Standard scores are scores expressed in a standardized unit of measurement Standard scores indicate the position of a score relative to the distribution (for central Tend & dispersion) 2

3. Z-Scores Memorize this formula 3

4. Benefits: Z-scores can be used to determine proportions of the curve 4

5. Benefits To compare (relative to others) how a person did on two tests – with different Ms and SDs – With different number if items – (can’t do that with raw scores) 5

6. To compare relative to others Need to know… – More than the raw score – More than the % correct – More than his/her relative standing Also need to know… – How spread out the scores around his/her are i.e. score distribution (SD) – Where the score falls within the spread 6

7. z score calculation 7

8. z Scores If the z score is above the mean…it’s positive – (+ SDs) Raw score is above the mean If the z Score is below the mean…it’s negative – (- SDs) Raw score is below the mean Check to make sure you don’t make a calculation error 8

9. Comparison of scores relative to others on same test IQ of 120 z of + 1.33 (above the mean) …means that is 90.82 % of scores(.9082) are at or below a raw score of 120 If 90.82 % have IQs below 120 Then 90.82% - 50% = 40.82% …have IQ scores between the Mean (100 and 120) 9

10. Comparison Across Different Tests Because the z score accounts for – Central tendency (Mean) – Dispersion (s) – Sample size (N) M = ∑X/N – And has the same M of 0 and SD of 1 We can compare someone’s scores – On different tests with which have a Different M, s, or N 10