CHOOSING A STATISTICAL TEST LOUIS COHEN LAWRENCE MANION

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

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

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

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

THE TYPES OF DATA USED Nominal Measures of linear relationship between independent and dependent variables Identifying underlying factors, data reduction Ordinal regression analysis Interval and ratio Linear regression Multiple regression 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 • 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 © 2018 Louisnominal. 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. © 2018 Louis Cohen, Lawrence Manion and Keith Morrison; individual chapters, the contributors • The data are interval or ratio.

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 © 2018 Louis Cohen, Lawrence Manion and Keith Morrison; individual chapters, the contributors or very close correlate of another).

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. Louis Cohen, Lawrence and Keith Morrison; individual chapters, the contributors • The© 2018 data must be. Manion capable of being factored.