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CHOOSING A STATISTICAL TEST © LOUIS COHEN, LAWRENCE MANION & KEITH MORRISON

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STRUCTURE OF THE CHAPTER How many samples? The types of data used Choosing the right statistic Assumptions of tests

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What statistics do I need to answer my research questions? Are the data parametric or non-parametric? How many groups are there (e.g. two, three or more)? Are the groups related or independent? What kind of test do I need (e.g. a difference test, a correlation, factor analysis, regression)? INITIAL QUESTIONS IN SELECTING STATISTICS

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Scale of data One sample Two samplesMore than two samples IndependentRelatedIndependentRelated NominalBinomialFisher exact test McNemarChi-square ( 2 ) k-samples test Cochran Q Chi-square ( 2 ) one- sample test Chi-square ( 2 ) two- samples test OrdinalKolmogorov- Smirnov one-sample test Mann-Whitney U test Wilcoxon matched pairs test Kruskal-Wallis test Friedman test Kolmogorov- Smirnov test Sign testOrdinal regression analysis Wald- Wolfowitz Spearman rho Ordinal regression analysis

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Scale of data One sample Two samplesMore than two samples IndependentRelatedIndependentRelated Interval and ratio t-test t-test for paired samples One-way ANOVA Repeated measures ANOVA Pearson product moment correlation Two-way ANOVA Tukey hsd test Scheffé test

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THE TYPES OF DATA USED NominalOrdinalInterval and ratio Measures of association Tetrachoric correlation Spearman’s rhoPearson product- moment correlation Point biserial correlation rank order correlation Phi coefficientpartial rank correlation Cramer’s V Measures of difference Chi-squareMann-Whitney U testt-test for two independent samples McNemarKruskal-Wallist-test for two related samples Cochran QWilcoxon matched pairs One-way ANOVA Binomial testFriedman two-way analysis of variance Two-way ANOVA for more Wald-Wolfowitz testTukey hsd test Kolmogorov-Smirnov test Scheffé test

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THE TYPES OF DATA USED NominalOrdinalInterval and ratio Measures of linear relationship between independent and dependent variables Ordinal regression analysis Linear regression Multiple regression Identifying underlying factors, data reduction Factor analysis Elementary linkage analysis

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ASSUMPTIONS OF TESTS Mean: –Data are normally distributed, with no outliers Mode: –There are few values, and few scores, occurring which have a similar frequency Median: –There are many ordinal values

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ASSUMPTIONS OF TESTS Chi-square: –Data are categorical (nominal) –Randomly sampled population –Mutually independent categories –Discrete data(i.e. no decimal places between data points) –80% of all the cells in a crosstabulation contain 5 or more cases Kolmogorov-Smirnov: –The underlying distribution is continuous –Data are nominal

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ASSUMPTIONS OF TESTS t-test and Analysis of Variance: –Population is normally distributed –Sample is selected randomly from the population –Each case is independent of the other –The groups to be compared are nominal, and the comparison is made using interval and ratio data –The sets of data to be compared are normally distributed (the bell-shaped Gaussian curve of distribution) –The sets of scores have approximately equal variances, or the square of the standard deviation is known –The data are interval or ratio

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ASSUMPTIONS OF TESTS Wilcoxon test: –The data are ordinal –The samples are related Mann-Whitney and Kruskal-Wallis: –The groups to be compared are nominal, and the comparison is made using ordinal data –The populations from which the samples are drawn have similar distributions –Samples are drawn randomly –Samples are independent of each other

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ASSUMPTIONS OF TESTS Spearman correlation: The data are ordinal Pearson correlation: –The data are interval and ratio

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ASSUMPTIONS OF TESTS Regression (simple and multiple): –The data derive from a random or probability sample –The data are interval or ratio (unless ordinal regression is used) –Outliers are removed –There is a linear relationship between the independent and dependent variables –The dependent variable is normally distributed –The residuals for the dependent variable (the differences between calculated and observed scores) are approximately normally distributed –No collinearity (one independent variable is an exact or very close correlate of another)

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ASSUMPTIONS OF TESTS Factor analysis: –The data are interval or ratio –The data are normally distributed –Outliers have been removed –The sample size should not be less than persons –There should be at least five cases for each variable –The relationships between the variables should be linear –The data must be capable of being factored

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