Chapter_14

Chapter_14 - Chapter 14 Nonparametric Statistics Statistics...

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Unformatted text preview: Chapter 14: Nonparametric Statistics Statistics McClave, Statistics, 11th ed. Chapter 14: Nonparametric Statistics 2 Where We’ve Been Presented methods for making inferences about means and correlation Methods required the data or the sampling distributions to be normally distributed McClave, Statistics, 11th ed. Chapter 14: Nonparametric Statistics 3 Where We’re Going Inferential techniques requiring fewer or less stringent assumptions Nonparametric tests based on ranks 4 McClave, Statistics, 11th ed. Chapter 14: Nonparametric Statistics 14.1: Distribution-Free Tests Testing non-normal data with test based on normality may lead to P(Type I error) > less than maximum power of the test (1 - ). 5 McClave, Statistics, 11th ed. Chapter 14: Nonparametric Statistics 14.1: Distribution-Free Tests Parametric tests (z, t, F) Data or sampling distribution are normal Non-parametric tests (Rank-ordered, no assumed distribution) Data or sampling distribution are skewed, or data is ordinal 6 McClave, Statistics, 11th ed. Chapter 14: Nonparametric Statistics 14.1: Distribution-Free Tests Parametric tests (z, t, F) Data or sampling distribution are normal Non-parametric tests (Rank-ordered, no assumed distribution) Data or sampling distribution are skewed, or data is ordinal Nonparametric statistics (or tests) based on the ranks of measurements are called rank statistics (or rank tests .) 14.2: Single-Population Inferences The sign test provides inferences about population medians , or central tendencies , when skewed data or an outlier would invalidate tests based on normal distributions. McClave, Statistics, 11th ed. Chapter 14: Nonparametric Statistics 7 14.2: Single-Population Inferences One-tailed test for a Population Median, Test Statistic: S = number of sample measurements greater than (less than) McClave, Statistics, 11th ed. Chapter 14: Nonparametric Statistics 8 ) ( : ) ( : η η η η < ≥ ≤ or H or H a Two-tailed test for a Population Median, Test Statistic: S = larger of S 1 and S 2 where S 1 is the number of measurements less than 0 and S 2 the number greater than : : η η η η ≠ = a H H 14.2: Single-Population Inferences One-tailed test for a Population Median, Observed significance level: p-value = P( x S ) McClave, Statistics, 11th ed. Chapter 14: Nonparametric Statistics 9 Two-tailed test for a Population Median, Observed significance level: p-value = 2P( x S ) where x has a binomial distribution with parameters n and p = .5. Reject H if p-value . 14.2: Single-Population Inferences McClave, Statistics, 11th ed. Chapter 14: Nonparametric Statistics 10 Median time to failure for a band of compact disc players is 5,250 hours. Twenty players from a competitor are tested, with failure times from 5 hours to 6,575 hours....
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This note was uploaded on 12/11/2011 for the course STA 3123 taught by Professor Staff during the Fall '08 term at FIU.

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Chapter_14 - Chapter 14 Nonparametric Statistics Statistics...

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