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Module 8 z Scores

• What they are• Benefits • Calculating them• Comparing them

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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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Z-ScoresMemorize this formula

• Z-scores are raw scores converted to standard deviation units

• Formula for z-score

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Benefits:

• Z-scores can be used to determine proportions of the curve

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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)

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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

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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

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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

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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 120Then 90.82% - 50% = 40.82%

…have IQ scores between the Mean (100 and 120)

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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