Chapter 7: Analysing the Data Part IV : Analysis of Variance

One-Way ANOVABonferroni adjustment

The term 'Bonferroni adjustment' is used to indicate that if we want to keep the experimentwise error rate to a specified level (usually  = .05) a simple way of doing this is to divide the acceptable - level by the number of comparisons we intend to make. In the above example, if 10 pairwise comparisons are to be made and we want to keep the overall experimentwise error rate to 5% we will evaluate each of our pairwise comparisons against .05 divided by 10. That is, for any one comparison to be considered significant, the obtained p-value would have to be less than 0.005 - and not 0.05. This obviously makes it harder to claim a significant result and in so doing decreases the chance of making a Type I error to very acceptable levels.

The Bonferroni adjustment is becoming more common with computers calculating exact probabilities for us. Once when you had to look up a table to determine the probability of a particular t-, F-, or r-value, you usually only had a choice of .05 or .01. Occasionally, some tables would cater for other probabilities but there are rarely tables for .005!! So, Bonferroni adjustments were not widespread. Nowadays, however, with probabilities being calculated exactly it easy to compare each probability with the Bonferroni-adjusted - level. In the above example, you would be justified in doing 10 t-tests and considering a comparison significant if the p-value was less than 0.005.

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