choosing a statistical test © louis cohen, lawrence manion & keith morrison
TRANSCRIPT
STRUCTURE OF THE CHAPTER
• How many samples?• The types of data used• Choosing the right statistic• Assumptions of tests
• 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
Scale of data
One sample Two samples More than two samples
Independent Related 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-WolfowitzSpearman rho
Ordinal regression analysis
Scale of data
One sample Two samples More than two samples
Independent Related Independent Related
Interval and ratio
t-test t-test t-test for paired samples
One-way ANOVA
Repeated measures ANOVA
Pearson product moment correlation
Two-way ANOVA
Tukey hsd testScheffé test
THE TYPES OF DATA USEDNominal 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 VMeasures 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 testKolmogorov-Smirnov test
Scheffé test
THE TYPES OF DATA USED
Nominal Ordinal Interval and ratioMeasures of linear relationship between independent and dependent variables
Ordinal regression analysis
Linear regressionMultiple regression
Identifying underlying factors, data reduction
Factor analysis
Elementary linkage analysis
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
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
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
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
ASSUMPTIONS OF TESTS
• Spearman correlation:• The data are ordinal
• Pearson correlation:– The data are interval and ratio
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)
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