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Unformatted text preview: zScores and the Normal Curve Plus a little probability thrown in for spice. 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 z scores 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 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. If T=40, then A=400. Review Interpret a z score of 1 M = 10, SD = 2, X = 8. Z =? M = 8, SD = 1, z = 3. X =? What is the A (SAT) score for a z score of 1? II. Probability Probability refers to the long run relative frequency of events....
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This note was uploaded on 05/21/2011 for the course PSY 3213 taught by Professor Staff during the Fall '08 term at University of South Florida.
 Fall '08
 Staff

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