![]() ![]() In reality, we are going to let Minitab calculate the F* statistic and the P-value for us. We can use the following steps to perform a two-way ANOVA: Step 1: Calculate Sum of Squares for First Factor (Watering Frequency) First, we will calculate the grand mean height of all 40 plants: Grand mean (4.8 + 5 + 6.4 + 6.3 + + 3.9 + 4.8 + 5.5 + 5.5) / 40 5.1525. The P-value is determined by comparing F* to an F distribution with 1 numerator degree of freedom and n-2 denominator degrees of freedom. \(MSE=\dfrac\).Īs always, the P-value is obtained by answering the question: "What is the probability that we’d get an F* statistic as large as we did if the null hypothesis is true?" We already know the " mean square error ( MSE)" is defined as: Let's tackle a few more columns of the analysis of variance table, namely the " mean square" column, labeled MS, and the F-statistic column labeled F. So, when getting df2, the formula will be as follows: df2 n k. And this is because the degrees of freedom will be two in this case. When it comes to 3-groups Anova, the calculation will be different from 2-group Anova. The sums of squares add up: SSTO = SSR + SSE. In this case, the degrees of freedom for 2-group Anova 1. ![]() And the degrees of freedom add up: 1 + 47 = 48. The degrees of freedom associated with SSE is n-2 = 49-2 = 47. The critical value is 3.68 and the decision rule is as follows: Reject H 0 if F > 3.68. The degrees of freedom associated with SSTO is n-1 = 49-1 = 48. In order to determine the critical value of F we need degrees of freedom, df 1 k-1 and df 2 N-k. The degrees of freedom associated with SSR will always be 1 for the simple linear regression model.Recall that there were 49 states in the data set. ![]()
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