# Lecture13 - 19 June 2003 Biostatistics 6650-L13 1 Todays...

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19 June 2003 Biostatistics 6650--L13 1

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19 June 2003 Biostatistics 6650--L13 2 Today’s Schedule Non-parametric Statistics(9.1-9.4) Introduction Sign test Signed Rank test Rank Sum test Kruskal-Wallis test(12.7) Summary
19 June 2003 Biostatistics 6650--L13 3 Introduction Parametric methods Methods of estimation and hypothesis testing where the data is 1)assumed to have come from a known underlying distribution or 2)the sample size is large enough to use the central limit theorem to describe the behavior of the estimator of the parameter of interest Parameter---Statistic μ --- σ 2 ---s 2 p --- x/n x

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19 June 2003 Biostatistics 6650--L13 4 Introduction Non-parametric methods (distribution free) Methods of estimation and hypothesis testing which do not depend on the distribution of the population the sample was drawn from Require few assumptions about the population Generally easier to apply than their parametric counterpart Relatively easier to understand Can be used when normality cannot be assumed
19 June 2003 Biostatistics 6650--L13 5 Introduction Non-parametric methods (distribution free) Invariant to data transformations: same results for X and log(X) Appropriate for cardinal (meaningful to measure distance between values) and ordinal data Generally only slightly less efficient(in terms of statistical power) than the parametric counterpart Much less sensitive to outliers than parametric methods Negative: Somewhat wasteful of information as only the ranks, or sometimes just the sign, of the data are used

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19 June 2003 Biostatistics 6650--L13 6 Sign Test Hypothesis test concerning: the median paired difference for two dependent samples Nonparametric alternative to paired t-test the median of a population Nonparametric alternative to one-sample t-test Assumes an underlying continuous distribution may be non-normal may be extremely difficult to measure it on a cardinal scale Useful in small samples where central limit theorem may not apply and you have reason to question normality
19 June 2003 Biostatistics 6650--L13 7 Sign Test Based on the sign of paired differences (+ or - ) or on the sign of differences from a hypothesized true median . We will focus on the former setting. Ho: =0 vs Ha: =0, where =population median Take sample of size N Under Ho half the sample values should be above the median(+) and half should be below the median(-) Test Statistic: C=n(+), the number of positive differences N=n(+) + n(-) + n (ties or 0 differences) n=n(+) + n(-)

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19 June 2003 Biostatistics 6650--L13 8 Sign Test Observed data: N observations of differences • Observe d i = +,-, or 0 directly without measuring x i and y i worse/same/better relative to baseline or other treatment Ex Rosner: compare effectiveness of two ointments (A,B) in reducing sunburn. Randomly apply A to one arm and B
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## This note was uploaded on 06/17/2011 for the course BME 6650 taught by Professor Multipleinstructors during the Spring '03 term at Mayo Clinic College of Medicine.

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Lecture13 - 19 June 2003 Biostatistics 6650-L13 1 Todays...

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