DNP 830 Topic 6: working with inferential statistics
An ANOVA that comes back significant has told you that something differs somewhere. Knowing that this is not yet an answer — and what to do next — is what this exercise is testing.
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Last reviewed · August 15, 2026
Two tests, and the question of which one the design implies
The choice between the two tests is structural rather than a matter of taste. Two groups compared once is a t-test; three or more groups, or one factor with several levels, is analysis of variance. Running multiple t-tests across three groups instead of one ANOVA inflates the chance of a false positive, because each test carries its own error rate and they accumulate — with three groups that means three comparisons and a real error rate closer to fourteen percent than five. Say that explicitly when justifying your choice, because it is the actual reason ANOVA exists and it is the reasoning the exercise wants to see. Check the same assumptions as before, and note that ANOVA is reasonably robust to non-normality but much less forgiving about unequal variances with unequal group sizes. The two also answer differently shaped questions: a t-test gives a difference you can quote, while ANOVA's omnibus result only gatekeeps the comparisons that follow.
Interpreting the output is where submissions separate. A significant F tells you that at least one group mean differs from at least one other, and nothing more — it does not say which, and it does not say by how much. That is what post-hoc comparisons are for, and they carry their own correction for multiplicity, which is worth naming rather than accepting whatever the software defaults to. Report an effect size alongside the test, because with a reasonable sample a trivial difference will reach significance and with a small one a large difference will not. Then write the substantive sentence: which group differs from which, in what direction, by how much, and whether that magnitude would change anything a clinician does. A results section that stops at the F statistic has run the test without answering the question. Report group sizes alongside the means, since an ANOVA over badly unbalanced groups behaves differently and the F alone does not show it.
Likely learning objectives
Inferred from the brief — check these against your own rubric.
- 01Choose between a t-test and ANOVA on the structure of the comparison.
- 02Explain multiplicity as the reason ANOVA replaces repeated t-tests.
- 03Interpret an omnibus F result accurately and know its limits.
- 04Report effect size alongside significance.
Read the full question
Review every instruction before using the planning guidance that follows.
Course-wide instructions that accompany this question
Name: Assignment Rubric Grid View List View Excellent Good Fair Poor Summarize your interpretation of the frequency data provided in the output for respondent’s age, highest school grade completed, and family income from prior month. 32 (32%) – 35 (35%) The response accurately and clearly explains, in detail, a summary of the frequency distributions for the variables presented. The response accurately and clearly explains, in detail, the number of times the value occurs in the data. The response accurately and clearly explains, in detail, the appearance of the data, the range of data values, and an explanation of extreme values in describing intervals that sufficiently provides an analysis that fully supports the categorization of each variable value. The response includes relevant, specific, and appropriate examples that fully support the explanations provided for each of the areas described. 28 (28%) – 31 (31%) The response accurately summarizes the frequency distributions for the variables presented. The response accurately explains the number of times the value occurs in the data. The response accurately explains the appearance of the data, the range of data values, and explains extreme values in describing intervals that provides an analysis which supports the categorization of each variable value. The response includes relevant, specific, and accurate examples that support the explanations provided for each of the areas described. 25 (25%) – 27 (27%) The response inaccurately or vaguely summarizes the frequency distributions for the variables presented. The response inaccurately or vaguely explains the number of times the value occurs in the data. The response inaccurately or vaguely explains the appearance of the data, the range of data values, and inaccurately or vaguely explains extreme values. An analysis that may support the categorization of each variable value is inaccurate or vague. The response includes inaccurate and irrelevant examples that may support the explanations provided for each of the areas described. 0 (0%) – 24 (24%) The response inaccurately and vaguely summarizes the frequency distributions for the variables presented, or it is missing. The response inaccurately and vaguely explains the number of times the value occurs in the data, or it is missing. The response inaccurately and vaguely explains the appearance of the data, the range of data values, and an explanation of extreme values, or it is missing. An analysis that does not support the categorization of each variable values is provided, or it is missing. The response includes inaccurate and vague examples that do not support the explanations provided for each of the areas described, or it is missing. Summarize your interpretation of the descriptive statistics provided in the output for respondent’s age, highest school grade completed, race and ethnicity, currently employed, and family income from prior month. 45 (45%) – 50 (50%) The response accurately and clearly summarizes in detail the interpretation of the descriptive statistics provided. The response accurately and clearly evaluates in detail each of the variables presented, including an accurate and complete description of the sample size, the mean, the median, standard deviation, and the size and spread of the data. 40 (40%) – 44 (44%) The response accurately summarizes the interpretation of the descriptive statistics provided. The response accurately explains evaluates each of the variables presented, including an accurate description of the sample size, the mean, the median, standard deviation, and the size and spread of the data. 35 (35%) – 39 (39%) The response inaccurately or vaguely summarizes the interpretation of the descriptive statistics provided. The response inaccurately or vaguely evaluates each of the variables presented, including an inaccurate or vague description of the sample size, the mean, the median, the standard deviation, and the size and spread of the data. 0 (0%) – 34 (34%) The response inaccurately and vaguely summarizes the interpretation of the descriptive statistics provided, or it is missing. The response inaccurately and vaguely evaluates each of the variables presented, including an inaccurate and vague description of the sample size, the mean, the median, the standard deviation, and the size and spread of the data, or it is missing. Written Expression and Formatting – Paragraph Development and Organization: Paragraphs make clear points that support well-developed ideas, flow logically, and demonstrate continuity of ideas. Sentences are carefully focused—neither long and rambling nor short and lacking substance. A clear and comprehensive purpose statement and introduction is provided which delineates all required criteria. 5 (5%) – 5 (5%) Paragraphs and sentences follow writing standards for flow, continuity, and clarity. A clear and comprehensive purpose statement, introduction, and conclusion is provided which delineates all required criteria. 4 (4%) – 4 (4%) Paragraphs and sentences follow writing standards for flow, continuity, and clarity 80% of the time. Purpose, introduction, and conclusion of the assignment is stated, yet is brief and not descriptive. 3 (3%) – 3 (3%) Paragraphs and sentences follow writing standards for flow, continuity, and clarity 60%–79% of the time. Purpose, introduction, and conclusion of the assignment is vague or off topic. 0 (0%) – 2 (2%) Paragraphs and sentences follow writing standards for flow, continuity, and clarity < 60% of the time. No purpose statement, introduction, or conclusion was provided. Written Expression and Formatting – English writing standards: Correct grammar, mechanics, and proper punctuation 5 (5%) – 5 (5%) Uses correct grammar, spelling, and punctuation with no errors. 4 (4%) – 4 (4%) Contains a few (1 or 2) grammar, spelling, and punctuation errors. 3 (3%) – 3 (3%) Contains several (3 or 4) grammar, spelling, and punctuation errors. 0 (0%) – 2 (2%) Contains many (≥ 5) grammar, spelling, and punctuation errors that interfere with the reader’s understanding. Written Expression and Formatting – The paper follows correct APA format for title page, headings, font, spacing, margins, indentations, page numbers, parenthetical/in-text citations, and reference list. 5 (5%) – 5 (5%) Uses correct APA format with no errors. 4 (4%) – 4 (4%) Contains a few (1 or 2) APA format errors. 3 (3%) – 3 (3%) Contains several (3 or 4) APA format errors. 0 (0%) – 2 (2%) Contains many (≥ 5) APA format errors. Total Points: 100 Name: Assignment Rubric
Turn the brief into deliverables
- 01The output for both test families.
- 02A justification for the test chosen, referencing group structure.
- 03Assumption checks with their results.
- 04Post-hoc comparisons where the omnibus test is significant.
- 05An effect size and a substantive interpretation.
Check assumptions, run, then interpret the effect
Choosing the test
Justify t-test or ANOVA from the comparison structure.
Assumptions and their checks
Report the assumption tests and what they showed.
The test output
Present the statistics with degrees of freedom and p values.
Post-hoc and effect size
Identify which groups differ and by how much.
What it means clinically
State whether the difference would change practice.
What each test can and cannot conclude
Recommended databases
- StatPearls statistics chapters
- OpenStax Introductory Statistics
- Your SPSS materials
- PubMed Central
Search sequence
- 1.Look up how familywise error accumulates across repeated comparisons.
- 2.Check which post-hoc test suits your design and why.
- 3.Find the effect size measure conventionally reported alongside your test.
- 4.Read one published paper reporting an ANOVA and note what it includes beyond the F.
Reference shortlist
These are authoritative starting points, not a ready-made bibliography. A qualified reviewer must confirm that each source fits the assignment and supports the claim beside which it is cited.
Nothing here is cleared for citation until you have read it.
- 01
Comparing the Means of Independent Groups: ANOVA, ANCOVA, MANOVA, and MANCOVA
StatPearls, NCBI Bookshelf, US National Library of Medicine · 2024
Sets out ANOVA and its relatives, including why an omnibus result cannot identify which groups differ.
- 02
Hypothesis Testing, P Values, Confidence Intervals, and Significance
StatPearls, NCBI Bookshelf · 2023
Covers p values and confidence intervals, which is the framework the effect-size argument sits inside.
- 03
Type I and Type II Errors and Statistical Power
StatPearls, NCBI Bookshelf · 2023
Explains power and error types, which is why multiplicity matters and why a null result may mean little.
- 04
13.1 One-Way ANOVA
OpenStax, Introductory Statistics 2e · 2023
A worked one-way ANOVA showing the full reporting a results section is expected to contain.
Review before submission
Common mistakes
- Running repeated t-tests across three or more groups.
- Treating a significant F as identifying which groups differ.
- Reporting significance with no effect size.
- Accepting the software's default post-hoc correction without naming it.
Submission checklist
- Is the test justified by the number of groups being compared?
- Did you check assumptions and report the checks?
- Have you followed a significant F with post-hoc comparisons?
- Does the interpretation say which groups differ and by how much?
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