RESEARCH METHOD COHEN ok

592 CHOOSING A STATISTICAL TEST
Box 26.6
Assumptions of statistical tests
Test
Mean
Mode
Median
Chi-square
Kolmogorov-Smirnov
t-test and analysis of
variance
Wilcoxon test
Mann-Whitney and
Kruskal-Wallis
Spearman rank order
correlation
Pearson correlation
Regression (simple
and multiple)
Factor analysis
Assumptions
Data are normally distributed, with no outliers.
There are few values, and few scores, occurringwhichhaveasimilarfrequency.
There are many ordinal values.
Data are categorical (nominal).
Randomly sampled population.
Mutually independent categories.
Data are discrete (i.e. no decimal places between data points).
80 per cent of all the cells in a cross-tabulation contain 5 or more cases.
The underlying distribution is continuous.
Data are nominal.
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 Gaussiancurveof
distribution).
The sets of scores have approximately equal variances, or the square of the standard deviation
is known.
The data are interval or ratio.
The data are ordinal.
The samples are related.
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.
The data are ordinal.
The data are interval and ratio.
Assumptions underlying regression techniques:
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 bell-shaped Gaussian curveofdistribution).
The residuals for the dependent variable (the differences between calculated and observed
scores) are approximately normally distributed.
Collinearity is removed (where one independent variable is an exact or very close correlate of
another).
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.