INFERENTIAL STATISTICS FOR DECISION MAKING

Sample Solution

One-way independent ANOVA One-way independent ANOVA is a statistical test that is used to compare the means of two or more independent groups. It is a parametric test, which means that it assumes that the data is normally distributed and that the variances of the groups are equal.

Full Answer Section

  The test statistic used in one-way independent ANOVA is the F-statistic. The F-statistic is calculated by dividing the variance between groups by the variance within groups. If the F-statistic is large, then it is likely that there is a difference between the means of the groups. Example Let's say that we have a study that compares the mean blood pressure of three different groups of people: people who eat a high-fat diet, people who eat a low-fat diet, and people who eat a vegetarian diet. We would use one-way independent ANOVA to test the hypothesis that the mean blood pressure is different for the three groups. The first step would be to calculate the F-statistic. The F-statistic for this example would be: The variance between groups would be calculated by averaging the variances of the three groups. The variance within groups would be calculated by averaging the variances of the individual observations within each group. Once the F-statistic has been calculated, we can compare it to a critical value. The critical value is a value that depends on the number of groups and the degrees of freedom. If the F-statistic is greater than the critical value, then we can reject the null hypothesis and conclude that there is a difference between the means of the groups. Tukey Honestly Significant Difference test The Tukey Honestly Significant Difference (HSD) test is a post-hoc test that is used to determine which pairs of groups are significantly different after a one-way independent ANOVA. The Tukey HSD test is a conservative test, which means that it is less likely to find a difference between groups than other post-hoc tests. The Tukey HSD test is calculated by calculating the difference between the means of each pair of groups. The difference between the means is then divided by the standard error of the difference. The standard error of the difference is calculated by taking the square root of the variance within groups. The critical value for the Tukey HSD test is calculated using the number of groups and the degrees of freedom. If the difference between the means is greater than the critical value, then we can conclude that the two groups are significantly different. Conclusion One-way independent ANOVA is a powerful statistical test that can be used to compare the means of two or more independent groups. The F-statistic is used to calculate the test statistic, and the Tukey HSD test can be used to determine which pairs of groups are significantly different.