Question

Give a ffull answer its true or false: When an ANOVA comparing the means of 3 groups indicates that at least one group is different from the others, a

Comparing two groups
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asked 2020-11-08
Give a ffull answer its true or false: When an ANOVA comparing the means of 3 groups indicates that at least one group is different from the others, a common follow-up analysis to determine which group(s) is (are) different is pairwise two-sample t-tests each assessed using i) the pooled standard deviation when calculating the standard error for the difference in means and ii) a Bonferonni-corrected alpha level of 0.0167 to control the type I error rate for the overall inference to 5%

Answers (1)

2020-11-09

Solution: (i) is TRUE The pooled SD is used to compute the standard error of the difference used to compute multiple comparison tests. (ii) is too TRUE In statistics, the Bonferroni correction is one of several methods used to counteract the problem of multiple comparisons. Bonferroni correction= \(\displaystyle{\frac{{\alpha}}{{{m}}}}\)

\(\alpha=\) Significance Level
\(\displaystyle{m}=\) Number of groups (here 3) Then, Bonferroni correction = \(\displaystyle={\frac{{{0.05}}}{{{3}}}}\)

\(={0.0167}\)

Therefore, It is TRUE, a Bonferonni-corrected alpha level of 0.0167 to control the type I error rate for the overall inference to 5%.

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