Advanced ANOVA/Testing differences

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

Completion status: this resource is ~75% complete.

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

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

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

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

See SPSS tips
See Thesis tips

Readings/References

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]

External links

Testing differences (ucspace)