DSRT 734: Interpreting an ANOVA and Post Hoc Comparison

DSRT 734 Question

Given the following results from an ANOVA test with a pairwise comparison
post hoc test, which of the following statements is correct?


ANOVA

ANOVA - VariableA

Cases           Sum of Squares       df       Mean Square       F       p

Group           59.801               2        28.785            0.984   0.350
Residuals       3561.345             96       38.232

Note. Type III Sum of Squares


Descriptives

Descriptives - VariableA

Group           Mean                 SD       N

A               8.347                5.620    35
B               9.165                7.588    30
C               8.521                5.299    34


Post Hoc Tests
Standard

Post Hoc Comparisons - Group

Comparison      Mean Difference      SE       t          p tukey

A - B           -1.610               1.538    -1.046     0.620
A - C            0.157               1.489     0.106     0.824
B - C            1.767               1.549     1.141     0.385

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


Option A

There are no significant differences between the groups.


Option B

Groups A and B are significantly different, but no other differeces
are significant.


Option C

Group A is significantly different from Groups B and C, and Group B
is significantly different than Group C.


Option D

Group A is significantly different from Groups B and C, but Group B
is not significantly different than Group C.

What this question assesses

This item assesses coordinated reading of an omnibus ANOVA, descriptive group summaries, and familywise-adjusted pairwise comparisons. It tests whether a statement matches both the overall evidence and each reported post hoc comparison.

How to approach this type of question

Read the analysis in layers. Start with the omnibus ANOVA row and compare its p-value with the analysis threshold; that row addresses whether the data support any mean difference among the groups as a set. Then inspect the adjusted post hoc p-values one comparison at a time. Because the table states that Tukey adjustment was used for a family of three, interpret the displayed adjusted values rather than recalculating unadjusted comparisons. Use the mean differences and descriptives to understand direction only after deciding whether a pair meets the statistical criterion. Make a small evidence grid with A–B, A–C, and B–C as rows, recording the displayed adjusted p-value and whether the corresponding option makes the same claim. Reject any statement that contradicts even one comparison or treats a numerical mean difference as automatically significant. This process supports an auditable selection but intentionally does not name the matching option.

As a final check, distinguish three statements: the omnibus decision, the direction of each observed mean difference, and the adjusted decision for each pair. An option can fail even if part of it matches one descriptive value. Keep the question wording unchanged, but use clear terminology in the student’s own analysis. If an instructor requires effect size, it would be a separate interpretation step and should not be inferred from the answer choices.

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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