WhyUseZscores

# WhyUseZscores - ranking Assume profs’ scores are normally...

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9/8/10 Why Use Z scores? Percentages can be used to compare different scores, but don’t convey as much information Z scores also called standardized scores , making scores from different distributions comparable; Ex: You get two different scores in two different subjects(e.g Statistics 28 and English 76). They are not yet

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9/8/10 Percentages Verse Z scores How do you compare to others? From percentages alone, you have no way of knowing. Say µ on English exam was =70 with ó of 8 pts, your 76 gives you a z-score of .75, three- fourths of one stand deviation above the mean; Mean on statistics test is 21, with ó of 5 pts; your score of 28 gives a z score of 1.40 standard deviations above mean; Although
9/8/10 Using z scores to find percentiles Prof Oh So Wise, scores 142 on an evaluation. What is Wise’s percentile

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Unformatted text preview: ranking? Assume profs’ scores are normally distributed with µ of 100 and ó of 25. X-µ 142-100 z= 1.68 ó 25 Area under curve ‘Small Part’ = .0465, 9/8/10 Starting with An Area Under Curve and Finding Z and • Using the previous parameters of µ of 100 and ó of 25, what score would place a professor in top 10% of this distribution? After some algebra, we have X=µ+z (ó) • 100(µ) + 1.28(z)(25)(ó)=132 (X). A score of 132 would place a professor in top 10 %; • What scores place a professor in 9/8/10 What does ‘most extreme’ mean? • It is not just one end of the distribution, but both ends, or 2.5% at either end; • X= µ + z(ó)= 100+ 1.96(25)= 149 • 100 +-1.96(25)=51; 51 and 149 place a professor at the most extreme 5 % of the distribution;...
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