5_ZNormal

5_ZNormal - _ Slide 1 _ z-Scores and the Normal Curve Plus...

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Slide 1 z-Scores and the Normal Curve Plus a little probability thrown in for spice. ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ Slide 2 I. z-scores and conversions • What is a z-score? – A measure of an observation’s distance from the mean. – The distance is measured in standard deviation units. • If a z-score is zero, it’s on the mean. • If a z-score is positive, it’s above the mean. • If a z-score is negative, it’s below the mean. • If a z-score is 1, it’s 1 SD above the mean. • If a z-score is –2, it’s 2 SDs below the mean. ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ Slide 3 Computing a z-score SD X X z or X z = = σ µ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________
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Slide 4 Examples of computing z- scores -2 2 -4 8 4 .75 4 3 3 6 -1.25 4 -5 10 5 1.5 2 3 3 6 1 2 2 3 5 X X X X SD SD X X z = ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ Slide 5 Computing raw scores from z scores X zSD X or z X + = + = µ σ 5 10 -5 5 -1 12 10 2 4 .5 -2 2 -4 2 -2 5 3 2 2 1 SD X X z = SD zSD X X ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ Slide 6 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. ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________
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Slide 7 Moving between z and A A=z*100+500; z=(A-500)/100 1.75 175 675 425 -75 -.75 2 200 700 650 150 1.5 .5 50 550 400 -100 -1 1 100 600 600 100 1 0 0 500 500 0 0 Z A-500 A A Z*100 Z ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ Slide 8 Moving between z and T T=z*10+50; z = (T-50)/10 1.75 17.5 67.5 42.5 -7.5 -.75 2 20 70 65 15 1.5 .5 5 55 40 -10 -1 1 10 60 60 10 1 0 0 50 50 0 0 z T-50 T T Z*10 z ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ Slide 9 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. ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________
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Slide 10 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? ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ Slide 11 II. Probability • Probability refers to the long run relative frequency of events.
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5_ZNormal - _ Slide 1 _ z-Scores and the Normal Curve Plus...

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