Stats.Blue

# One-Way ANOVA

• 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: $\alpha=$ 0.25 0.20 0.15 0.10 0.05 0.025 0.02 0.01 0.005 0.0025 0.001 0.0005

 Source of variation df SS MS $F$-statistic $p$-value Variation Among Samples Variation Within Samples Total

 % Confidence Intervals Using Pooled Standard Deviation: