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Unformatted text preview: CHAPTER 10: NONPARAMETRIC TESTS 10.1 BRIEF OVERVIEW OF NONPARAMETRIC METHODS Statistical tests, such as the z , t , and F tests studied in the previous chapters are called parametric tests . Parametric tests are statistical tests for population parameters such as means, variances, and proportions that involve assumptions about the populations from which the samples were selected. For example, the one-way analysis of variance of Chapter 9 requires that the parent populations are at least approximately normally distributed (or we rely on the central limit theorem to give us normal approximations) and have equal standard deviations. What can we do if the assumptions about the population distributions are not satisfied? In addition, many research studies involve low-level data such as nominal or ordinal data to which previously discussed procedures do not apply. In situations such as these, nonparametric statistical tests are often used. Specifically, nonparametric methods were developed to be used in cases when the researcher knows nothing about the parameters of the variable of interest in the population (hence the name nonparametric ). In more technical terms, nonparametric methods do not rely on the estimation of parameters (such as the mean or the standard deviation) describing the distribution of the variable of interest in the population. Therefore, these methods are also sometimes (and more appropriately) called parameter- free methods or distribution-free methods. Basically, there is at least one nonparametric equivalent for each parametric general type of test. In general, these tests fall into the following categories: • Tests of differences between groups (independent samples); • Tests of differences between variables (dependent samples); • Tests of relationships between variables. 10.1.1 DIFFERENCES BETWEEN INDEPENDENT GROUPS Usually, when we have two samples that we want to compare concerning their mean value for some variable of interest, we would use the t-test for independent samples . Nonparametric alternatives for this test are the Wald-Wolfowitz runs test , the Mann- Whitney U test , and the Kolmogorov-Smirnov two-sample test . If we have multiple groups, we would use analysis of variance . The nonparametric equivalents to this method are the Kruskal-Wallis H analysis of ranks and the Median test . Dr. LOHAKA – QBA 2305 CHAPTER 10: NONPARAMETIC TESTS Page 43 10.1.2 DIFFERENCES BETWEEN DEPENDENT GROUPS If we want to compare two variables measured in the same sample, we would customarily use the t-test for dependent samples . In Basic Statistics , for example, if we wanted to compare students’ quantitative skills at the beginning of the semester with their skills at the end of the semester, we would use a t-test for dependent samples . Nonparametric alternatives to this test are the Sign test and the Wilcoxon's matched pairs test (the latter being more commonly known as Wilcoxon signed rank test). If the variables of interest test)....
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This note was uploaded on 08/04/2008 for the course QBA 2305 taught by Professor Hulme during the Spring '08 term at Baylor.
- Spring '08