CHOOSING A STATISTICAL TEST © LOUIS COHEN, LAWRENCE MANION AND KEITH MORRISON © 2018 Louis Cohen, Lawrence Manion and Keith Morrison; individual chapters, the contributors

STRUCTURE OF THE CHAPTER How many samples? The types of data used Choosing the right statistic Assumptions of tests © 2018 Louis Cohen, Lawrence Manion and Keith Morrison; individual chapters, the contributors

INITIAL QUESTIONS IN SELECTING STATISTICS 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)? © 2018 Louis Cohen, Lawrence Manion and Keith Morrison; individual chapters, the contributors

Chi-square (2) k-samples test Cochran Q Scale of data One sample Two samples More than two samples Independent Related Nominal Binomial Fisher exact test McNemar Chi-square (2) k-samples test Cochran Q Chi-square (2) one-sample test Chi-square (2) two-samples test Ordinal Kolmogorov-Smirnov one-sample test Mann-Whitney U test Wilcoxon matched pairs test Kruskal-Wallis test Friedman test Kolmogorov-Smirnov test Sign test Ordinal regression analysis Wald-Wolfowitz Spearman rho © 2018 Louis Cohen, Lawrence Manion and Keith Morrison; individual chapters, the contributors

t-test for paired samples One-way ANOVA Repeated measures ANOVA Scale of data One sample Two samples More than two samples Independent Related 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 © 2018 Louis Cohen, Lawrence Manion and Keith Morrison; individual chapters, the contributors

THE TYPES OF DATA USED Nominal Ordinal Interval and ratio Measures of association Tetrachoric correlation Spearman’s rho Pearson product-moment correlation Point biserial correlation rank order correlation Phi coefficient partial rank correlation Cramer’s V Measures of difference Chi-square Mann-Whitney U test t-test for two independent samples McNemar Kruskal-Wallis t-test for two related samples Cochran Q Wilcoxon matched pairs One-way ANOVA Binomial test Friedman two-way analysis of variance Two-way ANOVA for more Wald-Wolfowitz test Tukey hsd test Kolmogorov-Smirnov test Scheffé test © 2018 Louis Cohen, Lawrence Manion and Keith Morrison; individual chapters, the contributors

THE TYPES OF DATA USED Nominal Ordinal Interval 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 © 2018 Louis Cohen, Lawrence Manion and Keith Morrison; individual chapters, the contributors

© 2018 Louis Cohen, Lawrence Manion and Keith Morrison; individual chapters, the contributors

© 2018 Louis Cohen, Lawrence Manion and Keith Morrison; individual chapters, the contributors

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. © 2018 Louis Cohen, Lawrence Manion and Keith Morrison; individual chapters, the contributors

ASSUMPTIONS OF TESTS Chi-square Kolmogorov-Smirnov 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. © 2018 Louis Cohen, Lawrence Manion and Keith Morrison; individual chapters, the contributors

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. © 2018 Louis Cohen, Lawrence Manion and Keith Morrison; individual chapters, the contributors

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. © 2018 Louis Cohen, Lawrence Manion and Keith Morrison; individual chapters, the contributors

ASSUMPTIONS OF TESTS Spearman correlation The data are ordinal Pearson correlation The data are interval and ratio © 2018 Louis Cohen, Lawrence Manion and Keith Morrison; individual chapters, the contributors

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). © 2018 Louis Cohen, Lawrence Manion and Keith Morrison; individual chapters, the contributors

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 100-150 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. © 2018 Louis Cohen, Lawrence Manion and Keith Morrison; individual chapters, the contributors