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In Vol. 26 to Vol. 29, we tested three or more groups of hypotheses. Should a multiple comparison method be used when there are three or more groups?

In this study, we explain the use of ANOVA and two-group comparisons.

When to use ANOVA and two-group comparisons

When comparing three or more groups, even if a significant difference is found using ANOVA, it is not possible to know where that difference is. Therefore, the next step is to “evaluate where the difference is,” using some kind of multiple comparison method.

So, how should we distinguish between ANOVA and two-group comparisons?
Let us consider a concrete example.

Compare the average heights of 12-year-olds in Tokyo, Aichi, and Osaka Prefectures. In this example, we do not usually want to reveal the differences between prefectures.
An analysis of variance (ANOVA) was used to verify that there was no difference.

[Average height of 12-year-old children (by gender)]
Osaka: 152.1cm (boy), 151.7cm (girl)
Aichi: 152.0cm (boy), 151.8cm (girl)
Tokyo: 152.5cm (boy), 152.0cm (girl)
( FY2013 school health Survey results)

What if you want to compare the differences between a placebo, a new drug and a standard treatment?

Even if there is a significant difference, it is only possible to know that there is a difference somewhere between “placebo” “new drug” and “standard treatment,” so performing ANOVA itself is not very meaningful.

In other words, from the beginning, it is sufficient to conduct three two-arm comparisons: “placebo vs. new drug,” “placebo vs. standard treatment,” and “new drug vs. standard treatment.”

If you want to actively clarify the difference between the three effects like this, you only need to perform the two-group t-test three times, and you do not need to perform the troublesome multiple comparison method.

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