• Complete a one-way ANOVA hypothesis test
• Write the conclusion of a one-way ANOVA hypothesis test in context of the problem

[latex]F[/latex]-Distribution

Recall that hypothesis testing for two means is based on the [latex]t[/latex]-Distribution, and we calculate the test statistic, [latex]t[/latex]. Additionally, the [latex]t[/latex]-Distribution is symmetric, centered at the mean [latex]0[/latex]. Thus, when conducting a [latex]t[/latex]-test, we have positive [latex]t[/latex]-values and negative [latex]t[/latex]-values.

ANOVA is based on the [latex]F[/latex]-Distribution, so we will be calculating the [latex]F[/latex]-statistic.

Let’s utilize our statistical tool to explore the [latex]F[/latex]-Distribution and its value.

Enter the degrees of freedom from our fertilizer scenario into the [latex]F[/latex]-Distribution Statistical Tool below.

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As we just saw, the [latex]F[/latex]-statistic is the ratio of the variation between groups (MSGroup) to the variation within groups (MSError). Larger values of the [latex]F[/latex]-statistic (greater than [latex]1[/latex]) would imply that the variation between groups is larger than the variation within groups.

When there is a greater difference among the group means, the [latex]F[/latex]-statistic will be larger; when there is a smaller difference among the group means, the [latex]F[/latex]-statistic will be smaller.