Which Statistical Test Should I Use?

  1. Univariate Tests
  2. Within-Subjects Tests
  3. Between-Subjects Tests
  4. Association Measures
  5. Prediction Analyses
  6. Classification Analyses


Finding the appropriate statistical test is easy if you're aware of

  1. the basic type of test you're looking for and
  2. the measurement levels of the variables involved.

For each type and measurement level, this tutorial immediately points out the right statistical test. We'll also briefly define the 6 basic types of tests and illustrate them with simple examples.

1. Overview Univariate Tests

DichotomousPopulation proportion = x?Binomial test
Z-test for 1 proportion
CategoricalPopulation distribution = f(x)?Chi-square goodness-of-fit test
QuantitativePopulation mean = x?One-sample t-test
Population median = x?Sign test for 1 median
Population distribution = f(x)?Kolmogorov-Smirnov test
Shapiro-Wilk test

Univariate Tests - Quick Definition

Univariate tests are tests that involve only 1 variable. Univariate tests either test if

  1. some population parameter -usually a mean or median- is equal to some hypothesized value or
  2. some population distribution is equal to some function, often the normal distribution.

A textbook example is a one sample t-test: it tests if a population mean -a parameter- is equal to some value x. This test involves only 1 variable (even if there's many more in your data file).

One Sample T Test Data View

2. Overview Within-Subjects Tests

DICHOTOMOUSMcNemar testCochran Q test
NOMINAL(Not available)(Not available)
ORDINALWilcoxon signed-ranks test
Sign test for 2 related medians
Friedman test
QUANTITATIVEPaired samples t-testRepeated measures ANOVA

Within-Subjects Tests - Quick Definition

Within-subjects tests compare 2+ variables
measured on the same subjects (often people).
An example is repeated measures ANOVA: it tests if 3+ variables measured on the same subjects have equal population means.

Repeated Measures ANOVA Data View

Within-subjects tests are also known as

SPSS Nonparametric Tests Menu K Related Samples “Related samples” refers to within-subjects and “K” means 3+.

3. Overview Between-Subjects Tests

DichotomousZ-test for 2 independent proportionsChi-square independence test
NominalChi-square independence testChi-square independence test
OrdinalMann-Whitney test (mean ranks)
Median test for 2+ independent medians
Kruskal-Wallis test (mean ranks)
Median test for 2+ independent medians
QuantitativeIndependent samples t-test (means)
Levene's test (variances)
One-way ANOVA (means)
Levene's test (variances)

Between-Subjects Tests - Quick Definition

Between-subjects tests examine if 2+ subpopulations
are identical with regard to

The best known example is a one-way ANOVA as illustrated below. Note that the subpopulations are represented by subsamples -groups of observations indicated by some categorical variable.

One Way ANOVA Data View

“Between-subjects” tests are also known as “independent samples” tests, such as the independent samples t-test. “Independent samples” means that subsamples don't overlap: each observation belongs to only 1 subsample.

4. Overview Association Measures

QUANTITATIVEPearson correlation
ORDINALSpearman correlation
Kendall’s tau
Polychoric correlation
Spearman correlation
Kendall’s tau
Polychoric correlation
NOMINALEta squaredCramér’s V Cramér’s V
DICHOTOMOUSPoint-biserial correlation
Biserial correlation
Spearman correlation
Kendall’s tau
Polychoric correlation
Cramér’s V Phi-coefficient
Tetrachoric correlation

Association Measures - Quick Definition

Association measures are numbers that indicate
to what extent 2 variables are associated.
The best known association measure is the Pearson correlation: a number that tells us to what extent 2 quantitative variables are linearly related. The illustration below visualizes correlations as scatterplots.

Correlation Coefficient Multiple Scatterplots

5. Overview Prediction Analyses

Quantitative(Multiple) linear regression analysis
OrdinalDiscriminant analysis or ordinal regression analysis
NominalDiscriminant analysis or nominal regression analysis
DichotomousLogistic regression

Prediction Analyses - Quick Definition

Prediction tests examine how and to what extent
a variable can be predicted from 1+ other variables.
The simplest example is simple linear regression as illustrated below.

Simple Linear Regression B Coefficient In Scatterplot

Prediction analyses sometimes quietly assume causality: whatever predicts some variable is often thought to affect this variable. Depending on the contents of an analysis, causality may or may not be plausible. Keep in mind, however, that the analyses listed below don't prove causality.

6. Classification Analyses

Classification analyses attempt to identify and
describe groups of observations or variables.
The 2 main types of classification analysis are

Factor analysis is based on correlations or covariances. Groups of variables that correlate strongly are assumed to measure similar underlying factors -sometimes called “constructs”. The basic idea is illustrated below.

Factor Analysis Data View

Cluster analysis is based on distances among observations -often people. Groups of observations with small distances among them are assumed to represent clusters such as market segments.

Cluster Analysis Data View

Right. So that'll do for a basic overview. Hope you found this guide helpful! And last but not least,

thanks for reading!

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