# 1-way repeat measures ANOVA

1-way repeat-measures ANOVA, also known as the randomised blocks or 1-way within-subject ANOVA, tests for a difference in central location (mean) between two or more paired samples.

The requirements of the test are:

- Two or more paired samples measured on a continuous scale.
- Samples are from a population with a normal distribution.
- Samples must have the same variance and covariance, also known as sphericity.

## Arranging the dataset

Data in existing Excel worksheets can be used and should be arranged in a List dataset layout. The dataset must contain at least two continuous scale variables.

When entering new data we recommend using New Dataset to create a new **k variables** dataset ready for data entry.

**Using the test**

To start the test:

- Excel 2007:

Select any cell in the range containing the dataset to analyse, then click**Compare Pairs**on the**Analyse-it**tab, then click**1-way ANOVA**. - Tick
**Variables**to compare. - Click
**OK**to run the test.

Excel 97, 2000, 2002 & 2003:

Select any cell in the range containing the dataset to analyse, then click **Analyse **on the **Analyse-it **toolbar, click **Compare Pairs** then click **1-way ANOVA**.

The report shows the number of observations analysed, and, if applicable, how many missing values were excluded. Summary statistics for each sample are then shown.

An analysis of variance table is shown which partitions the total variance into that due to variance between the samples, between the subjects, and within the samples (also known as the residual or error variance). The between- and residual sample variances are compared with an F-test. The *p*-value is the probability of rejecting the null hypothesis, that the samples have the same mean, when it is in fact true. A significant p-value implies that at least two samples have different means.

A simpler way of understanding how the table relates to the testing of the means is that the total variation is the variance when a model is fitted with a common mean for all the samples, the residual variation is the variance when a model is fitted to the mean of each sample. Therefore the between variation is the difference between these two models. The hypothesis test is used to test if the fit to each sample mean is significantly better than a fit

## References to further reading

- Handbook of Parametric and Nonparametric Statistical Procedures (3rd edition)

David J. Sheskin, ISBN 1-58488-440-1 2003; 797. - Designing Experiments and Analyzing Data

Maxwell S.E., Delaney H.D. ISBN 0-534-10374-X 1989.

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Version 2.30

Published 9-Jun-2009