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Module 8 z Scores

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

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Module 8 z Scores

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

  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)

  3. Z-ScoresMemorize this formula • Z-scores are raw scores converted to standard deviation units • Formula for z-score

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

  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)

  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

  7. z score calculation • X = any given score • M = Mean • s = Sd of the test or measure • The distance from the M is rescaled into SD units

  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

  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)

  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

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