Bonferroni procedure

The Bonferroni procedure can be used in multiple comparison to determine which means differ. Using a sample set of data below with three groups of equal size data, the ANOVA 2-way function is calculated and the results stored in stat1. For convenience, the standard ANOVA is also calculated and the results stored in stat6.

bonferroni1

The original confidence level is set to 0.05. To obtain the corrected confidence level value, 0.05 is divided by the number of group of data, and then by 2 for 2-tail test. The new critical t-value is then determined. The means for each group is available in the stat6 variable set (by ANOVA), while the pooled standard deviation s can be obtained from stat1 variable set (by ANOVA 2-way).

bonferroni2

And then for each of the combination of group, calculate its new t-value, i.e. GA-GC, GB-GC, and GA-GB respectively.

bonferroni3

As shown above, the combination of GA-GB is less than the critical value of 2.7178, meaning that fail to reject H0 and therefore can conclude that μAB.

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