# Advanced ANOVA/Testing differences

This tutorial examines inferential techniques for 'testing differences' between the means for: - a single variable across two independent groups,
- two related variables, and
- one sample mean compared to a fixed value.
Practical exercises are based on using SPSS. |

## Types edit

There are three types of *t*-test"

### 1-sample *t*-test
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- 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
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- 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
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- 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 edit

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

## Questions edit

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

## Exercises edit

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

- Assumption testing
- Graphing
- Descriptives
- Inferential analyses of differences
- Effect sizes
- APA style write-up

## Tips edit

- See SPSS tips
- See Thesis tips

## Readings/References edit

- Diekhoff Ch 6 and 7
- Howell, D. C. (2002).
*Statistical methods for psychology*. (5th ed.). Pacific Grove CA: Duxbury. Chapter 7. - Pruzek, R. M. and Helmreich, J. (2009) Enhancing dependent sample analyses with graphics, J. of Statistics Education [1]

## See also edit

## External links edit

- Testing differences (ucspace)