True or False:
For ANOVA you will reject the null hypothesis is the variability within a sample is greater than the variability among samples?
The null hypothesis will be that all population means are equal, the alternative hypothesis is that at least one mean is different.
so would it be true?
Yes
thank you!
You are so welcome
True.
To determine whether to reject the null hypothesis in ANOVA (Analysis of Variance), you compare the variability within a sample to the variability among samples.
The null hypothesis in ANOVA states that there is no significant difference among the means of the groups or samples being compared. Therefore, if the variability within a sample is greater than the variability among samples, it suggests that there are significant differences among the group means, and the null hypothesis can be rejected.
To calculate the variability within and among samples in ANOVA, you would typically use the F-test statistic. The F-test compares the sum of squared deviations of the observations from the group means, taking into account the degrees of freedom within and among the groups.
If the F-test statistic is larger than the critical value at a given significance level (usually α = 0.05), then the null hypothesis can be rejected, and it can be concluded that there are significant differences among the group means.
So, in summary, for ANOVA, you will reject the null hypothesis if the variability within a sample is greater than the variability among samples.