DSRT 734: Interpreting an ANOVA With Bonferroni Comparisons

DSRT 734 Question

Given the following results from an ANOVA test comparing the average
times between three teams, which of the following conclusions is
correct?


ANOVA

ANOVA - Factory3

Cases           Sum of Squares       df       Mean Square       F       p

Team            5033.631             2        2516.816          29.216  < 0.001
Residuals       4048.789             47       86.144

Note. Type III Sum of Squares


Descriptives

Descriptives - Factory3

Team            Mean                 SD       N

Blue            96.625               8.374    16
Green           107.316              11.504   19
Red             112.067              6.628    15


Post Hoc Tests
Standard

Post Hoc Comparisons - Team

Comparison      Mean Difference      SE       t          p bonf

Blue - Green    -13.691              3.149    -4.347     0.011
Blue - Red      -25.442              3.336    -7.627     < 0.001
Green - Red     -11.751              3.206    -3.666     0.072

Note. P-value adjusted for comparing a family of 3


Option A

Team Blue is significantly different from Team Green and Red, but
Team Green is not significantly different from Team Red.


Option B

There are no significant differences between the teams.


Option C

Team Red is significantly different from Team Green, but there are
no other significant differences.


Option D

Team Green is significantly different from Team Blue and Red, but
Team Blue is not significantly different from Team Red.

What this question assesses

This item assesses whether an omnibus ANOVA result and Bonferroni-adjusted pairwise comparisons are interpreted as related but distinct evidence, with every option checked against all three team contrasts.

How to approach this type of question

Start with the omnibus row to determine whether the analysis supports at least one mean difference among the teams. Then make a three-row comparison grid for Blue–Green, Blue–Red, and Green–Red. Record the displayed Bonferroni-adjusted p-value for each; do not substitute the t statistic or an unadjusted value. Apply the assigned significance threshold consistently and mark which claims are supported at the pairwise level. Use the mean differences and descriptive means to interpret direction only after the significance check. Next translate each answer option into the same three yes-or-no comparison claims and eliminate any option that contradicts a single row. Keep the familywise adjustment visible because a large raw-looking difference is not itself a statistical decision. This process enables a traceable choice while this page intentionally withholds the option and final conclusion.

Use a comparison matrix to test the answer choices: columns for each pair, rows for each option, and cells marked against the adjusted p-values. Preserve the Blue-minus-Green, Blue-minus-Red, and Green-minus-Red order when interpreting signs. Do not treat the smallest group mean as automatically different from both others. If reporting beyond the option, pair the omnibus statistic with an effect-size measure from valid output and keep adjusted pairwise findings explicitly labeled. Confirm the adjustment label and threshold before classifying every pair, and never replace the adjusted values with the omnibus p-value. Retain the strict less-than notation exactly.

Related DSRT 734 questions

• DSRT 734: Interpreting an ANOVA and Post Hoc Comparison
• DSRT 734: Comparing Three Product Weights in JASP
• DSRT 734: Comparing Homework Hours Across Three Student Teams

Related DSRT 734 resources

• University of the Cumberlands course resources
• DSRT 734 Inferential Statistics in Decision-Making
• DSRT 734 Questions: Inferential Statistics in Decision-Making
• Interpreting P-Values, Confidence Intervals, and Effect Sizes