![]() Thus, the engineer should be wary about using the model to make generalizations beyond the sample data. The imprecision may be due to the small size of the groups. The low predicted R 2 value indicates that the model generates imprecise predictions for new observations. Well review new software features and statistical enhancements that facilitate data analysis, along with tips from our Minitab experts on how to get the most from Minitab 19. The confidence intervals for the remaining pairs of means all include zero, which indicates that the differences are not significant. We will cover the latest updates to the Minitab interface to familiarize users with their new Minitab workspace. The engineer can use this estimate of the difference to determine whether the difference is practically significant. This range does not include zero, which indicates that the difference between these means is significant. The graph and the table that include the Tukey simultaneous confidence intervals show that the confidence interval for the difference between the means of Blend 2 and 4 is 3.114 to 15.886. The engineer uses the Tukey comparison results to formally test whether the difference between a pair of groups is statistically significant. The engineer knows that some of the group means are different. This result indicates that the mean differences between the hardness of the paint blends is statistically significant. ![]() The p-value for the paint hardness ANOVA is less than 0.05.
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