How we change what others think, feel, believe and do

# Choosing parametric test

Explanations > Social ResearchAnalysis > Choosing a parametric test

## 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
>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.

Parametric vs. non-parametric tests

### You can buy books here

And the big
paperback book 