Lecture 4_Nonparametric tests

Lecture 4_Nonparametric tests - Recall Hypothesis tests...

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1 1 ECON1320 - Lecture 4 Nonparametric tests Sections 17.2, 17.5 2 Recall Hypothesis tests • Econ1310: – z, t tests for population mean – z test for population proportion – t test for the difference between two population means • Econ1320 (L1 – L3) – z test for the difference between two population proportions – F test for the equality of two variances – Chi-square goodness of fit test for population distribution & proportions – Chi-square test of independence – F test in one way ANOVA for the difference of population means (more than 2 means) – F test in two way ANOVA – Turkey-Kramer procedure for pair-wise mean differences. 3 Topics 1. Parametric versus Nonparametric statistic 2. Mann-Whitney U test (# t-test for two population means) 3. Kruskal-Wallis test (# one-way ANOVA) 4. Kolmogorov-Smirnov test (not in textbook # Chi-square goodness of fit test) 5. Lilliefors test (not in textbook) 4 Topic 1: Parametric vs Nonparametric statistic • Parametric statistic are statistical techniques based on assumptions about the population from which the sample data are collected – The Z-test for H 0 : μ = 0 assumes the underlying population is normally distributed with mean μ . – Requires quantitative measurement that yield interval or ratio level data 5 Topic 1: Parametric vs Nonparametric statistic • Nonparametric statistic are based on fewer assumptions about the population and the parameters – Sometimes called “distribution-free” statistic – A variety of nonparametric statistic are available for use with nominal or ordinal data 6 Advantages of Nonparametric Techniques • Sometimes there is no parametric alternative to the use of nonparametric statistic • Certain nonparametric tests can be used to analyse nominal and ordinal data • The computations on nonparametric statistic are usually less complicated than those for parametric statistic, particularly for small samples • Probability statements obtained from most nonparametric tests are exact probabilities
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2 7 Disadvantages of Nonparametric statistic • Nonparametric tests can be wasteful of data if parametric tests are available for use with the data • Nonparametric tests are usually not as widely available and well known as parametric tests • For large samples, the calculations for many nonparametric statistic can be tedious 8 Mann-Whitney U Test • Nonparametric counterpart of the t test for comparing means for 2 independent samples • Does not require normally distributed populations • May be applied to ordinal data • Assumptions – Independent Samples – At Least Ordinal Data 9 Mann-Whitney U Test • Hypotheses: H 0 : The two populations are identical H 1 : The two populations are not identical • Let n 1 and n 2 are the sample sizes for Group 1 and Group 2 (n 1 < n 2 ) • If both n 1 and n 2 are smaller than 10, the small sample procedure is appropriate. • If either
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This note was uploaded on 10/21/2009 for the course ECON 1320 taught by Professor John during the Three '08 term at Queensland.

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Lecture 4_Nonparametric tests - Recall Hypothesis tests...

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