• We have $I$ independent SRSs, one from each of $I$ populations. We measure the same response variable for each sample.

  • The $i$th population has a Normal distribution with unknown mean $\mu_i$. One-way ANOVA tests the null hypothesis that all the population means are the same.

  • All the populations have the same standard deviation $\sigma$, whose value is unknown.

  • The results of the ANOVA $F$-test are approximately correct when the largest sample standard deviation is no more than twice as large as the smallest sample standard deviation.

  • If the data violates any of the normality conditions for smaller samples sizes, or if it violates the assumption of equal standard deviations (as determined by the previous item), non-parametric methods may be more advisable: try the Kruskal-Wallis Test.
Variable Names (optional):
Sample data goes here (enter numbers in columns):
Null Hypothesis:$H_0: \mu_1=\mu_2=\mu_3$
Alternative Hypothesis:$H_a: \mbox{Not all means are equal.}$
Level of Significance: $\alpha=$

Source of variationdfSSMS$F$-statistic$p$-value
Variation Among Samples
Variation Within Samples

% Confidence Intervals Using Pooled Standard Deviation: