Statistics Toolkit
Test Statistic
Chi-square (2)
Fisher’s Exact
test (Fisher’s z)
Mann-Whitney
U test
Wilcoxon
signed-rank test
(Wilcoxon z)
Kruskal-Wallis
H test
Student’s t test
(Independentgroups t)
Dependent t test
(Paired, 1-group
or repeated
measures t)
F test (analysis
of variance,
ANOVA)
Analysis of
covariance (F,
ANCOVA)
2-way ANOVA
(factorial F)
Repeatedmeasures F
Multiple
regression
Corresponding
Effect Size
Phi () or
odds ratio (OR)
Phi () or
odds ratio (OR)
Level of Data
for Predictors
Nominal
Level of Data
for Criterion
Nominal
R
X
Nominal
Nominal
X
Spearman r
Nominal
Ordinal
X X
Exactly 2 groups
Spearman r
Nominal
Ordinal
X
Pre-post data from
1 group
Spearman r
Nominal
Ordinal
X X
3+ groups
Pearson r
Nominal
Interval/Ratio
X X X X X
Exactly 2 groups
Pearson r
Nominal
Interval/Ratio
X
Pre-post data from
1 group
Eta-squared
(2) or pointbiserial r
Eta-squared,
semipartial r2
for specific IVs
Eta-squared
Nominal
Interval/Ratio
X X X X X
3+ groups
2+ predictors:
Nominal and
Interval/Ratio
2+ predictors,
both Nominal
1+ predictors,
Nominal-level
1+ predictors,
Interval/Ratio
Interval/Ratio
X X X X X
2+ groups
Interval/Ratio
X X X X X
2+ groups
Interval/Ratio
X
Interval/Ratio
X X X
2+ time points for
1+ groups
All data in 1 group
Eta-squared
Pearson r or
Eta-squared
Assumptions
I N H L
X
X
X X X
X X X
X
Grouping Variable
Notes
2+ groups
Use instead of F
test if I is violated
Parametric test for
N-level data (more
powerful than 2)
Use instead of t test
if N is violated
Use instead of
dependent t if N is
violated
Use instead of F
test if N is violated
Levine’s test: If H
is violated, use a
corrected t test
Use for correlated
data (2 data points /
unit of analysis)
Exactly 2 groups
Use post hoc tests
to compare data on
individual groups
Controls for
confounding
variables
Tests for confounds
and interactions
Can test group*
time interactions
Controls confounds
like ANCOVA
Key to assumptions: R = random sample from the population of interest; I = independent observations; N = normally distributed
dependent variable; H = homogeneity of variance (same SD) across groups; L = linear relationship between predictor and criterion