Psychology Example

Psychology Example

Sample Size for Two-way ANOVA

What sample size is required for an experiment in which the effects on a dependent learning variable of age at two levels, nature of contingency reinforcement at four levels and their interaction will be studied?Theory suggests that the older age group will have a higher response, that the four levels of reinforcement should generally produce an ordered response, but that there will be a reversal of this pattern for one reinforcement level (an interaction). Prior research with this outcome variable suggests that the within-cell standard deviation will be about 8.0.
nQuery Advisor® can provide sample size and power calculations for studies to be analyzed with a two-way analysis of variance.

Select File … New, and in the Study Goal and Design Box, select Means, >Two Groups, and Test and select Two-way analysis of variance. After filling in the number of levels for each factor, select Compute Effect Size from the Assistants menu or click on the button marked δ to specify the expected means for every cell and transfer these results back to the main sample size table. You can specify the sample size for each cell and solve for power for the tests of main effects and interaction, or specify power for one of the tests and solve for the required sample size per cell.

The psychologist had hoped to study only 12 children per cell (96 in all), but the power to test the interaction effect was only 64% with this sample size, so in the next column, she specified a required power of 80% for the test of the interaction, and found that 17 children per cell would be necessary (136 in all). nQuery Advisor® provides tables, plots, and standardized sample size justification statements which can be printed directly or copied to clipboard and pasted into your manuscript or proposal.

* Example taken from section 8.9 in Jacob Cohen (1988) Statistical Power Analysis for the Behavioral Sciences. 2nd edition. Lawrence Erlbaum Associates, Hillsdale, New Jersey.