14D

Comparison Difference Compared

(Part A)

 Adjusted Confidence Interval (Part B)
Placebo vs. Milk Powder (0.62, 0.36)
Placebo vs. Calcium Pill (0.62, 0.36)
Placebo vs. Calcium Pill + Exercise
Milk Powder vs. Calcium Pill
Milk Powder vs. Calcium Pill + Exercise
Calcium Pill vs. Calcium Pill + Exercise (0.59, 0.33)
Significantly Different Mean Bone Density NOT Significantly Different Mean Bone Density
Placebo vs. Milk Powder
Sterillium PureHands Lifebuoy Dettol
15.67 8.7 9.95 7.48
16.79 8.41 10.16 7.82
15.69 8.37 10.15 9.56
15.67 8.21 9.96 8.16
14.99 6.66 10.51 7.71
14.87 6.94 8.52 9.12
16.07 7.48 8.23 7.68
14.18 6.7 11.09 8.61
15.38 6.93 8.89 7.71
16.3 8.56 8.06 8.5
A B C D
59 67 62 69
54 66 74 62
60 51 62 70
57 68 64 73
58 65 77 53
52 54 59 73
67 57 58 75
61 55 64 64
54 59 68 67
56 66 65 73
62 70 66 69
60 56 64 69
56 56 73 72
61 53 65 73
67 56 67 73
65 72 72 59
61 64 63 77
61 64 72 62
60 63 63 77
62 57 64 67
Comparison Probability of Committing

a Type I Error
Group A vs. Group B 0.05
Group A vs. Group C
Group A vs. Group D
Group B vs. Group C
Group B vs. Group D
Group C vs. Group D
Significantly Different Mean Midterm Grades NOT Significantly Different Mean Midterm Grades
Group A vs. Group C Group A vs. Group B
Skill or Concept: I can . . . Questions to check your understanding Rating
from 1 to 5
Understand the limitations of the conclusions from the F-test in an ANOVA. 1
Identify the null and alternative hypotheses for all pair-wise comparisons. 2–4
Use technology to perform a two-sample t-test. 5, 6
Identify the probability of type I errors and issues that arise with multiple comparisons. 7, 8
Use adjusted confidence intervals to conduct all pair-wise tests and make conclusions about significant differences. 9, 10

An open jar of jelly beans A selection menu titled “Options,” with a checkbox selected reading “Pairwise Comparisons & Confidence Intervals.” Beneath this is a heading reading “Adjustment Method,” with “Turkey” having been selected from a dropdown. Beneath this is a heading reading “Select Confidence Level,” under which there is a percentage bar set to 95%. A box plot labeled “Midterm Grade” on the horizontal axis, with “Group A,” “Group B,” “Group C,” and “Group D” on the vertical axis. For Group A, the low point is at approximately 52, the high point is at approximately 67, the low end of the box is at approximately 57, the high end is at approximately 61, and the middle line is at approximately 59.5. For Group B, the low point is at approximately 51, the high point is at approximately 72, the low end of the box is at approximately 56, the high end is at approximately 66, and the middle line is at approximately 61. For Group C, the low point is at approximately 58, the high point is at approximately 78, the low end of the box is at approximately 63, the high end is at approximately 69, and the middle line is at approximately 64.5. For Group D, the low point is at approximately 59, the high point is at approximately 78, the low end of the box is at approximately 66.5, the high end is at approximately 75.5, and the middle line is at approximately 69.5. There is also a point at approximately 53. There are also points “y bar sub 1” at approximately 59.5, “y bar sub 2” at approximately 61, “y bar sub 3” at approximately 66.5, and “y bar sub 4” at approximately 68.

ANOVA Table:

Source df Sum of Squares Mean Square F Statistic P-value
Group 3 1122 374 12.46 <0.0001
Error 76 2282 30.02
Total 79 3404

 

Comparison Estimated Difference In Means Standard Error t Statistic P-value Lower Bound Upper Bound
Group A vs. Group B -1.30 1.73 -0.75 0.45 -4.75 2.15
Group A vs. Group C -6.45 1.73 -3.72 0.00 -9.90 -3.00
Group A vs. Group D -9.20 1.73 -5.31 0.00 -12.65 -5.75
Group B vs. Group C -5.15 1.73 -2.97 0.00 -8.60 -1.70
Group B vs. Group D -7.90 1.73 -4.56 0.00 -11.35 -4.45
Group C vs Group D -2.75 1.73 -1.59 0.11 -6.20 0.70

 

Comparison Estimated Difference in Means Standard Error t Statistic Multiplicity Adjusted P-value Lower Bound Upper Bound
Group A vs. Group B -1.30 1.73 -0.75 0.88 -5.85 3.25
Group A vs. Group C -6.45 1.73 -3.72 0.00 -11.00 -1.90
Group A vs. Group D -9.20 1.73 -5.31 0.00 -13.75 -4.65
Group B vs. Group C -5.15 1.73 -2.97 0.02 -9.70 -0.60
Group B vs. Group D -7.90 1.73 -4.56 0.00 -12.45 -3.35
Group C vs. Group D -2.75 1.73 -1.59 0.39 -7.30 1.80
pair-wise comparisons
comparisons between two things.
data snooping
showing only the comparisons you want to show based on the boxplot, also called data fishing.
family-wise error rate
the probability of rejecting at least one of the true null hypotheses.
Tukey method
a method that adjusts the length of the confidence interval (to ensure an overall level of confidence) and the P-value (to ensure an overall significance level for all pair-wise comparisons).