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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. © 2018 Louis Cohen, Lawrence Manion and Keith Morrison; individual chapters, the contributors

9. © 2018 Louis Cohen, Lawrence Manion and Keith Morrison; individual chapters, the contributors

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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.
© 2018 Louis Cohen, Lawrence Manion and Keith Morrison; individual chapters, the contributors