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In Vol. 26, we explained Bonferroni as one of the multiple comparison methods.
Multiple comparisons involve a combination of several techniques, the first of which is Analysis of Variance” (ANOVA). An ANOVA examines whether there is a difference in the average values of three or more groups by examining the difference in the size of the variance (variation).
In this article, we explain “ANOVA.”
Difference between t-test and ANOVA
The difference between the t-test and ANOVA is the “group difference.” The t-test is used to compare two groups, whereas ANOVA is used to compare three or more groups (Figure 1).
[Figure 1] Tests used for multi-group comparisons
There are several ANOVA methods, including one-way and two-way ANOVAs.
Observing the following two themes:
(1) Do drug differences affect drug efficacy?
(2) Do the two factors of drug difference and subject age affect the effects of drugs?
The elements are “drug” in (1) and “drug” and “age” in (2).
(1) is called the one-way method, and (2) is called the two-way method.
ANOVA : Compare the mean values of each group
ANOVA is not used to analyze the variance. We analyze the mean value of the effect of three or more groups (by the three drugs) using variance to determine whether the effect of the three drugs is also observed in the population (Figure 2).
[Figure 2] Example of ANOVA
Why is it called analysis of variance when comparing the means of each group? The reason is that it is an“analysis that evaluates by dividing the variance (= data variation) into two.”
What are the two variations?
There are two variations in the overall data.
(1) Variations due to differences in drugs X, Y, and Z (variations between groups)
(2) Variations due to differences in the efficacy of the same drug (variation within groups)
If the variation between groups is large, while that within groups is small, we conclude that “there is a difference in the effects of the three drugs.” Conversely, if the variation between groups is small, but that within groups is large, the conclusion is “we do not know if there is a difference in the effects of the three drugs.”
[Figure 3] Variation example
Thus, the ANOVA method divides the overall variability of the data into variations between, and within, groups and investigates the effect of each of the three drugs. This division is called “decomposition of variation.”
In Vol.28, we explain how to decompose fluctuations.
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