In the next preview assignment and in the next class, you will be making multiple pair wise comparisons and working with confidence interval estimates of differences in population means.
Pair-wise Comparisons for ANOVA
Recall the study done by the National Survey of Student Engagement, which found that, on average, college students spend 17 hours per week preparing and studying for their classes.[1][2]
In In-Class Activity 14.B, we conducted a one-way ANOVA to determine if there are any statistically-significant differences between the means of the following majors:
- Arts and Humanities
- STEM
- Education
- Business
Using a 5% level of significance, we rejected the null hypothesis that the means are equal and accepted the alternative hypothesis that at least two means are different.
The question now—which means are different? To answer this question, we need to make multiple pair-wise comparisons.
We could begin by comparing business and education. This is an example of a pair wise comparison. However, there are more!
Question 1
1) How many total pair-wise comparisons can be made? List the pairs below.
Question 2
2) What strategy did you use to determine the total number of pair-wise comparisons in Question 1?
Question 3
3) Suppose this scenario had included engineering. How many total pair-wise comparisons could be made?
Working with Intervals that Estimate a Difference
Question 4
4) In previous in-class activities, we used � to represent a population mean and �̅to represent a sample mean. When we are comparing two populations, we add subscripts to indicate which population (and sample) is being referenced.
Part A: In the context of the hours studied by major, �%&'()*+,- would represent the mean study time of education majors. How would you represent the mean study time of business majors?
Part B: What does �%&'()*+,- − �/’0+-%00 represent?
Part C: What would it mean if �%&'()*+,- − �/’0+-%00 was equal to 0?
Part D: What would it mean if �%&'()*+,- − �/’0+-%00 was greater than 0?
Part E: What would it mean if �%&'()*+,- − �/’0+-%00 was less than 0?
Part F: Assume your sample data produced the following estimated confidence interval for �%&'()*+,- − �/’0+-%00:
(−2.3, −0.99)
If you were comparing the means of education and business majors, what conclusion would you reach?
Part G: Assume your sample data produced the following estimated confidence interval for �%&'()*+,- − �/’0+-%00:
(−0.3, 0.5)
If you were comparing the means of education and business majors, what conclusion would you reach?
