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[5] [6] Unlike Tukey's range test, the Newman–Keuls method uses different critical values for different pairs of mean comparisons. Thus, the procedure is more likely to reveal significant differences between group means and to commit type I errors by incorrectly rejecting a null hypothesis when it is true.
There are two methods of concluding the ANOVA hypothesis test, both of which produce the same result: The textbook method is to compare the observed value of F with the critical value of F determined from tables. The critical value of F is a function of the degrees of freedom of the numerator and the denominator and the significance level (α).
Duncan's multiple range test makes use of the studentized range distribution in order to determine critical values for comparisons between means. Note that different comparisons between means may differ by their significance levels- since the significance level is subject to the size of the subset of means in question.
The C test detects one exceptionally large variance value at a time. The corresponding data series is then omitted from the full data set. According to ISO standard 5725 [6] the C test may be iterated until no further exceptionally large variance values are detected, but such practice may lead to excessive rejections if the underlying data series are not normally distributed.
The formula for the one-way ANOVA F-test statistic is =, or =. The "explained variance", or "between-group variability" is = (¯ ¯) / where ¯ denotes the sample mean in the i-th group, is the number of observations in the i-th group, ¯ denotes the overall mean of the data, and denotes the number of groups.
The critical value is the number that the test statistic must exceed to reject the test. In this case, F crit (2,15) = 3.68 at α = 0.05. Since F=9.3 > 3.68, the results are significant at the 5% significance level. One would not accept the null hypothesis, concluding that there is strong evidence that the expected values in the three groups ...
The F-test is computed by dividing the explained variance between groups (e.g., medical recovery differences) by the unexplained variance within the groups. Thus, = If this value is larger than a critical value, we conclude that there is a significant difference between groups.
In Dunnett's test we can use a common table of critical values, but more flexible options are nowadays readily available in many statistics packages. The critical values for any given percentage point depend on: whether a one- or- two-tailed test is performed; the number of groups being compared; the overall number of trials.