14. ANOVA
Introduction to ANOVA
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A company wants to determine whether the average monthly sales differ among three different regions: North, South, and West. The company collects monthly sales data (in thousands of dollars) from four randomly selected stores in each region over the same month. Calculate the F-statistic given the Mean Square due to Treatments: MST = (variance between groups) and the Mean Square due to Error: MSE = (variance within groups).
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Verified step by step guidance1
Step 1: Understand the problem. The goal is to calculate the F-statistic, which is used in ANOVA (Analysis of Variance) to determine if there are significant differences between group means. The formula for the F-statistic is F = MST / MSE, where MST is the Mean Square due to Treatments (variance between groups) and MSE is the Mean Square due to Error (variance within groups).
Step 2: Identify the given values. From the problem, we are provided with MST = 226.6226.6 and MSE = 7.9447.944. These values represent the variances between and within groups, respectively.
Step 3: Write the formula for the F-statistic. Using MathML, the formula is:
Step 4: Substitute the given values into the formula. Replace MST with 226.6226.6 and MSE with 7.9447.944 in the formula:
Step 5: Perform the division to calculate the F-statistic. Divide the MST value by the MSE value to obtain the F-statistic. This will give you the final result.
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