5_Z&Normal

5_Z&Normal - z-Scores and the Normal Curve I....

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Unformatted text preview: z-Scores and the Normal Curve I. z-scores and conversions What is a z-score? A measure of an observations distance from the mean. The distance is measured in standard deviation units. If a z-score is zero, its on the mean. If a z-score is positive, its above the mean. If a z-score is negative, its below the mean. If a z-score is 1, its 1 SD above the mean. If a z-score is 2, its 2 SDs below the mean. Computing a z-score SD X X z or X z- =- = Examples of computing z-scores 5 3 2 2 1 6 3 3 2 1.5 5 10-5 4-1.25 6 3 3 4 .75 4 8-4 2-2 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 5-2 2-4 2-2 .5 4 2 10 12-1 5-5 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 A-scores and T-scores z-scores have a mean of 0 and SD of 1 T-scores have a mean of 50 and SD10 Gets rid of negative numbers. Very commonly used in psychological scales, e.g., MMPI. A-scores have mean 500 and SD 100 Same deal. Used by SAT, GRE, etc. Moving between z and A A=z*100+500; z=(A-500)/100 Z Z*100 A A A-500 Z 500 500 1 100 600 600 100 1-1-100 400 550 50 .5 1.5 150 650 700 200 2-.75-75 425 675 175 1.75 Moving between z and T T=z*10+50; z = (T-50)/10 z Z*10 T T T-50 z 50 50 1 10 60 60 10 1-1-10 40 55 5 .5 1.5 15 65 70 20 2-.75-7.5 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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5_Z&Normal - z-Scores and the Normal Curve I....

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