 Resource type: this resource contains a tutorial or tutorial notes.

This tutorial examines inferential techniques for 'testing differences' between the means for:

1. a single variable across two independent groups,
2. two related variables, and
3. one sample mean compared to a fixed value.

Practical exercises are based on using SPSS.

## Types

There are three types of t-test"

### 1-sample t-test

• Compares a sample mean with a known population mean
• Non-parametric equivalent is the chi-square goodness-of-fit test

### Within-subjects t-test (also dependent samples or paired sample "t"-test

• Compares two means that are repeated measures for the same participants
• Compares two means between matched samples
• Compares two treatments across blocks
• Non-parametric equivalent is the Wilcoxon t-test

### Between-subjects t-test

• Compares two means for independent groups
• Non-parametric equivalents are Mann-Whitney U and chi-square test for two independent samples (this can be used for nominal, interval, or ratio data)

## Variance

• Within-group variance = individual differences + measurement error
• Between-group variance = individual differences + measurement error + treatment effect

## Questions

1. What are the three types of t-test and when would you use each of them?
2. What are the assumptions of t-tests?
3. What are the non-parametric alternatives and when would you use each of them?
4. What graphical techniques could accompany the different ways of testing differences?
5. What measures of effect size are available for measuring differences?
6. What should be included in a results section write-up for analyses which involve testing differences?
7. What results might be derived from graphic displays for two dependent sample comparisons that could alter questions or comparisons?
8. What information (e.g. comparing counts) might lead to non-linear transformations of the data used for comparison?

## Exercises

Using the LEQ dataset, provide analyses which demonstrate use of the each of the types of parametric and non-parametric tests of differences, including:

1. Assumption testing
2. Graphing
3. Descriptives
4. Inferential analyses of differences
5. Effect sizes
6. APA style write-up