Click “OK” to close the “Storage” window.Check the boxes next to “Fits” and “Residuals”.A new window named “One-Way Analysis of Variance” pops up.Alternative Hypothesis(H a): at least one of the means is different from others.Step 3: Test whether the mean of the data for each level is equal to the means of other levels. If this test suggested that at least one variance was different, then we would need to use a different hypothesis test to evaluate the group means. If the variances are not all equal, we need to use other hypothesis testing methods other than one-way ANOVA. The p-value of Bartlett’s test is 0.777, greater than the alpha level (0.05), so we fail to reject the null hypothesis and we claim that the variances of five groups are equal. Use the Bartlett’s test for testing the equal variances between five levels in this case since there are more than two levels in the data and the data of each level are normally distributed. Click “OK” to close the “Options” window.Select “Use test based on normal distribution”.Select the “Business” as the “Factors.”.A new window named “Test for Equal Variances” pops up.Click Stat → ANOVA → Test for equal variances.Alternative Hypothesis(H a): at least one of the variances is different from others.Step 2: Test whether the variance of the data for each level is equal to the variance of other levels. In this example, all five data sets are normally distributed however, if any of them were not normally distributed, we would need to use another hypothesis test. If any of the five data sets are not normally distributed, we need to use other hypothesis testing methods other than one-way ANOVA. Since the p-values of normality tests for the five data sets are higher than alpha level (0.05), we fail to reject the null hypothesis and claim that the startup costs for any of the five businesses are normally distributed. Alternative Hypothesis(H a): The data are not normally distributed.Null Hypothesis(H 0): The data are normally distributed.Notice all of the p-values are greater than 0.05 therefore, we fail to reject the null hypothesis that the data are normally distributed. The normality results appear in the new window.Select the “Business” as the “By variables (optional).”.
Click in the blank box right next to “By variables (optional)” and the “Business” appears in the list box on the left.A new window named “Graphical Summary” pops up.Click Stat → Basic Statistics → Graphical Summary.Step 1: Test whether the data for each level are normally distributed. Alternative Hypothesis (Ha): At least one of the five means is different from others.The difference between the actual and predicted result is called a residual or unexplained variation Use Minitab to Run a One Way ANOVAĬase study: We are interested in comparing the average startup costs of five kinds of business.ĭata File: “One Way ANOVA” tab in “Sample Data.xlsx” To make sure the conclusions made in ANOVA are reliable, we need to perform residuals analysis. Variation between groups is the signal we want to detect and variation within groups is the noise which corrupts the signal.ĪNOVA is a modeling procedure, which means we are using a model to try to predict results. What we care about the most is the variation between groups since we are interested in whether the groups are statistically different from each other. Variation within groups there are random errors resulting in the variation within each individual group.Variation between groups there are non-random factors leading to the variation between groups.Alternative Hypothesis(H a): One of the μ is different from the othersīased on the sample data, the means of the three populations might look different because of two variation sources.We randomly collected one sample for each population of our interest. Let us say we are interested in comparing the means of three normally distributed populations. The variances of k populations are equal.ĪNOVA compares the means of different groups by analyzing the variances between and within groups.