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Choosing parametric test

 

Explanations > Social ResearchAnalysis > 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?

1

How many scores for each subject?

1

Is standard deviation known?

Y

z-score

N

Single-sample t-test

2

Matched-pair t-test

>2 Repeated-measures ANOVA

2

Matched samples? (N = independent)

Y

Matched-pair t-test

N

Independent-measures t-test

>2

Matched samples? (N = independent)

Y

Repeated-measures ANOVA

N

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.

See also

Parametric vs. non-parametric tests

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