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Chapter 7 - Analysing the Data Part IV - Analysis of Variance Chapter 1 - Behavioural Science and research Chapter 2 - Research Design Chapter 3 - Collecting the Data Chapter 4 - Analysing the Data Part I - Descriptive Statistics Chapter 5 - Analysing the Data Part II - Inferential Statistics Chapter 6 - Analysing the Data Part III - Common Statistical Tests Correlation Regression T-tests Chi-squared Readings and links


Chapter 6: Analysing the Data
Part III: Common Statistical Tests


The Paired Sample t-Test

The Paired Sample t-test is an example of a repeated measures design. The distinction between 'Between groups' designs and 'Repeated measures' designs is an important one. You should read the relevant parts of Howell and Ray so that you are clear on the logic and consequences associated with each design and the advantages and disadvantages of each design.

Repeated measures designs have the especially important advantage of being more powerful. Each person is used as his or her own control and so individual differences can be partialled out of the error term. We thus get a smaller error term and consequently a larger t-value. By using a repeated measures design we can often get away with a smaller number of subjects in our study. This has considerable economic value! Finding subjects is often a difficult, time-consuming, and expensive part of the research process.

There are a number of problems associated with using a repeated measures design instead of a between groups design, however. In particular, carry-over effects in the form of boredom, fatigue, and practice effects need to be catered for. Another problem is the loss in degrees of freedom. The between groups t-test has n1 + n2 2 df (with two groups of 10, df = 18) whereas the repeated measures t-test has only n-1 df (with one group of 10, df = 9). As df gets lower, you need a higher t-value to reach significance (and therefore a greater treatment effect). We thus get a trade off between greater power and fewer degrees of freedom. In the end, the higher the two groups of scores are correlated, the greater is the advantage of using a repeated measures design.




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