Some texts may use "SSTr" (Tr = "treatment") instead of SSR (R = "regression"), and may use SSTo (To = "total") instead of SST. The latter notation uses the Greek letter nu ( ν) for the degrees of freedom. Note: In some texts you may see the notation df 1 or ν 1 for the regression degrees of freedom, and df 2 or ν 2 for the error degrees of freedom.
Then the F statistic itself is computed as MSR = SSR/df r = the regression mean square N = the total number of valid observationsĭf T = the total degrees of freedom (equal to df T = df r + df e = n - 1) K = the total number of groups (levels of the independent variable) SST = the total sum of squares (SST = SSR + SSE)ĭf r = the model degrees of freedom (equal to df r = k - 1)ĭf e = the error degrees of freedom (equal to df e = n - k - 1) Because the computation of the F statistic is slightly more involved than computing the paired or independent samples t test statistics, it's extremely common for all of the F statistic components to be depicted in a table like the following: For an independent variable with k groups, the F statistic evaluates whether the group means are significantly different. The test statistic for a One-Way ANOVA is denoted as F. Balanced designs (i.e., same number of subjects in each group) are ideal extremely unbalanced designs increase the possibility that violating any of the requirements/assumptions will threaten the validity of the ANOVA F test.Each group should have at least 6 subjects (ideally more inferences for the population will be more tenuous with too few subjects).Researchers often follow several rules of thumb for one-way ANOVA: Note: When the normality, homogeneity of variances, or outliers assumptions for One-Way ANOVA are not met, you may want to run the nonparametric Kruskal-Wallis test instead. When variances are unequal, post hoc tests that do not assume equal variances should be used (e.g., Dunnett’s C).
When this assumption is violated, regardless of whether the group sample sizes are fairly equal, the results may not be trustworthy for post hoc tests.These conditions warrant using alternative statistics that do not assume equal variances among populations, such as the Browne-Forsythe or Welch statistics (available via Options in the One-Way ANOVA dialog box). When this assumption is violated and the sample sizes differ among groups, the p value for the overall F test is not trustworthy.Homogeneity of variances (i.e., variances approximately equal across groups).Among moderate or large samples, a violation of normality may yield fairly accurate p values.Non-normal population distributions, especially those that are thick-tailed or heavily skewed, considerably reduce the power of the test.Normal distribution (approximately) of the dependent variable for each group (i.e., for each level of the factor).Random sample of data from the population.no subject in either group can influence subjects in the other group.subjects in the first group cannot also be in the second group.There is no relationship between the subjects in each sample.Independent samples/groups (i.e., independence of observations).Cases that have values on both the dependent and independent variables.Independent variable that is categorical (i.e., two or more groups).Dependent variable that is continuous (i.e., interval or ratio level).Your data must meet the following requirements:
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