- 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 are advised: try the Kruskal-Wallis Test.
| Group/Treatment Names (optional): | |||
| Sample data goes here (enter numbers in columns): |
| Use labels to group data (in Beta): | ||
| 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 variation | df | SS | MS | $F$-statistic | $p$-value |
| Variation Among Samples | |||||
| Variation Within Samples | |||||
| Total |
| % Confidence Intervals Using Pooled Standard Deviation: |