Advanced ANOVA/Testing differences

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

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

Tips

 * See SPSS tips
 * See Thesis tips

Readings/References

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