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Unformatted text preview: zScores and the Normal Curve I. zscores and conversions What is a zscore? A measure of an observations distance from the mean. The distance is measured in standard deviation units. If a zscore is zero, its on the mean. If a zscore is positive, its above the mean. If a zscore is negative, its below the mean. If a zscore is 1, its 1 SD above the mean. If a zscore is 2, its 2 SDs below the mean. Computing a zscore SD X X z or X z = = Examples of computing zscores 5 3 2 2 1 6 3 3 2 1.5 5 105 41.25 6 3 3 4 .75 4 84 22 X X X X SD SD X X z = Computing raw scores from z scores X zSD X or z X + = + = 1 2 2 3 52 24 22 .5 4 2 10 121 55 10 5 SD X X z = SD zSD X X Example of Computing z scores from raw scores List raw scores (use Excel) Compute mean Compute SD Compute z Ascores and Tscores zscores have a mean of 0 and SD of 1 Tscores have a mean of 50 and SD10 Gets rid of negative numbers. Very commonly used in psychological scales, e.g., MMPI. Ascores have mean 500 and SD 100 Same deal. Used by SAT, GRE, etc. Moving between z and A A=z*100+500; z=(A500)/100 Z Z*100 A A A500 Z 500 500 1 100 600 600 100 11100 400 550 50 .5 1.5 150 650 700 200 2.7575 425 675 175 1.75 Moving between z and T T=z*10+50; z = (T50)/10 z Z*10 T T T50 z 50 50 1 10 60 60 10 1110 40 55 5 .5 1.5 15 65 70 20 2.757.5 42.5 67.5 17.5 1.75 Moving between A and T A is 10 times bigger than T. Just slide that decimal point. If A = 600, then T=60....
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 Spring '10
 Brannick

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