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Choosing parametric test

Explanations > Social Research > Analysis > Choosing a parametric test

Choosing the test | Discussion | See also

Choosing the test

Use the table below to choose the test. See below for further details.

How many separate samples?

How many scores for each subject?

Is standard deviation known?
Y	z-score
N	Single-sample t-test

Matched-pair t-test

Repeated-measures ANOVA

Matched samples? (N = independent)
Y	Matched-pair t-test
N	Independent-measures t-test

Matched samples? (N = independent)

Repeated-measures ANOVA

How many independent variables?
1	Single-factor ANOVA
2	Two-factor ANOVA

Discussion

Parametric tests assume an underlying Normal (bell-shaped) distribution, which is often forced through means of samples (see the Central limit theorem).

Test statistic

The test statistic in all tests is calculated as:

systematic variation / random variation

= (measured difference between sample means) / (mean difference expected by chance)

= (variability between treatments) / (variability within treatments)

Principles

The common principles of measurement are:

A sample (a set of scores) is measured for each population or treatment condition
For each sample, the mean and a spread figure (sum of squares, variance or standard deviation) is calculated.
The difference between sample means is calculated. This is the numerator of the test statistic and indicates systematic (predicted) difference between treatment conditions.
The variation within each sample indicates unsystematic (random, unpredictable) variation. This is the denominator of the test statistic.

Design types

Single sample designs take data from a single sample to test a hypothesis about a single population.

Independent-measures designs take separate samples from each population or treatment.

Related-samples designs, including repeated-measures and matched-subjects designs.

Repeated measures designs have only one sample, with each subject being measured in all treatment conditions.

In matched-subject designs, each person in one sample is matched with a subject in each of the other samples.