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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.
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Lecture 4_Nonparametric tests - Recall Hypothesis tests...

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