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CHOOSING A STATISTICAL
TEST
© LOUIS COHEN, LAWRENCE
MANION & KEITH MORRISON
STRUCTURE OF THE CHAPTER
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How many samples?
The types of data used
Choosing the right statistic
Assumptions of tests
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)?
Scale of
data
One sample
Two samples
Independent
Related
Nominal
Binomial
Fisher exact
test
Ordinal
Chi-square
(2) onesample test
KolmogorovSmirnov
one-sample
test
Chi-square
(2) twosamples test
Mann-Whitney Wilcoxon
U test
matched
pairs test
KolmogorovSmirnov test
WaldWolfowitz
Spearman rho
Ordinal
regression
analysis
McNemar
Sign test
More than two samples
Independent
Related
Chi-square
Cochran Q
(2) k-samples
test
Kruskal-Wallis Friedman
test
test
Ordinal
regression
analysis
Scale of
data
Two samples
One sample
Independent
Interval t-test
and ratio
t-test
Pearson
product
moment
correlation
Related
More than two samples
Independent
t-test for One-way
paired
ANOVA
samples
Two-way
ANOVA
Tukey hsd
test
Scheffé
test
Related
Repeated
measures
ANOVA
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
McNemar
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
test
THE TYPES OF DATA USED
Nominal
Measures of
linear
relationship
between
independent
and dependent
variables
Identifying
underlying
factors, data
reduction
Ordinal
Ordinal regression
analysis
Interval and ratio
Linear regression
Multiple regression
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