| Course | PHLT 8331 Fundamentals of Biostatistics |
|---|---|
| Week | Week 8 |
| Paper type | Variance analysis paper |
| Length | About 1,000 words, 6 pages |
| Format | APA 7 student paper |
| School | Walden University |
| Program | PhD in Public Health |
| Updated | October 2026 |
Free sample paper for PHLT 8331 Week 8
Which Groups Differ, and in What Order? An Analysis of Variance on Time in Therapeutic Range Across Three Levels of Warfarin Adherence, With a Planned Trend Contrast Instead of All-Pairs Comparisons
Student Name
Walden University
PHLT 8331: Fundamentals of Biostatistics
Instructor Name
Month Day, Year
Which Groups Differ, and in What Order? An Analysis of Variance on Time in Therapeutic Range Across Three Levels of Warfarin Adherence, With a Planned Trend Contrast Instead of All-Pairs Comparisons
The Question
Does time in therapeutic range differ across levels of warfarin adherence? In the composite registry, patients reported how many warfarin doses they had missed in the past week at each visit, and their typical report places them in one of three adherence levels: no missed doses (512 patients), one or two missed doses (214) and three or more (78). Analysis of variance tests whether mean time in range differs among the three groups. An overall test answers whether some group differs but leaves the reader asking which, so this paper is organized around that second question. Because the adherence levels come in a natural order, it argues for a single planned trend contrast rather than comparing every pair of groups. All figures are composite.
The Overall Test
Conditions
Analysis of variance assumes independent observations, roughly normal distributions within groups or large enough samples for the group means to be approximately normal, and similar variances across groups. Patients are treated as independent, with the same clinic-clustering caveat as earlier weeks. Time in therapeutic range is left-skewed within each group, but the group sizes make the means approximately normal (Lumley et al., 2002). The standard deviations, 15.2, 16.8 and 18.1, differ somewhat, increasing as adherence falls; the largest is less than 1.2 times the smallest, within the range where the F test is generally considered robust, though Welch's unequal-spread ANOVA reaches the same conclusion.
Result
Mean time in range fell from 68.9% among patients with no missed doses to 61.0% among those missing one or two and 52.3% among those missing three or more. The F statistic was 46.8 on 2 and 801 degrees of freedom, p < .001, and adherence level accounted for about 10.5% of the variation in time in range. The overall test establishes that the means are not all equal.
Table 1
Time in Therapeutic Range by Adherence Level (Composite Figures)
| Adherence level | n | Mean, % | Standard deviation | |
|---|---|---|---|
| No missed doses | 512 | 68.9 | 15.2 | |
| One or two missed doses | 214 | 61.0 | 16.8 | |
| Three or more missed doses | 78 | 52.3 | 18.1 | |
Note. Composite figures. One-way analysis of variance: F(2, 801) = 46.8, p < .001; eta squared = .105.
Why a Planned Trend Contrast
The Problem With All Pairs
After a significant F, a common next step is to compare every pair of groups, here three comparisons, with an adjustment such as Bonferroni or Tukey to control the chance of a false positive across all of them. That approach treats the three groups as unordered categories and asks three separate questions, none of which is the question the data invite. Bender and Lange (2001) distinguish exploratory comparisons, where adjustment is often needed, from a small number of comparisons specified in advance to answer a defined question. Rothman (1990) went further, arguing that routine adjustment for multiple comparisons can discard real findings, and that the better safeguard is to specify the questions and report all results transparently.
The Ordered Question
Adherence levels form an order, from none missed to many missed. The question that matters for clinics is whether time in range declines steadily as adherence worsens. A linear trend contrast answers exactly that, using weights of minus 1, 0 and plus 1 across the three ordered groups. It is a single, planned comparison, so it needs no multiple-comparison adjustment.
The Result
The contrast estimate was minus 16.6 percentage points, the difference between the lowest and highest adherence groups, with a standard error of 1.94, giving t = minus 8.57 on 801 degrees of freedom, p < .001. Time in therapeutic range declines with each step down in adherence, and the middle group falls close to halfway between the other two, consistent with a roughly linear decline.
What If the Overall F Had Not Been Significant?
A planned contrast does not depend on the overall test. Because it was specified before the data were examined and addresses a defined question, it would be reported whatever the F result. A trend can be clear even when the overall test is not, because the F test spreads its attention across all possible patterns while the contrast focuses on one.
Reporting the Analysis
A complete report includes the group sizes, means and standard deviations, the F statistic with both degrees of freedom and its p-value, an effect size such as eta squared, and the planned contrast with its estimate, standard error and test. It should state that the contrast was specified before the data were examined. If any post hoc comparisons were also run, they should be labeled as exploratory and reported with the adjustment used. Readers can then distinguish the analysis that answered the planned question from any that searched for patterns afterward.
A Note on Treating Adherence as Ordered
The trend contrast treats the three adherence levels as equally spaced, which is an approximation; the step from none to one or two missed doses may not equal the step from one or two to three or more. With only three levels, the approximation matters little, and the near-linear pattern in the means suggests it is reasonable here. With more levels, or clearly unequal steps, contrast weights could be chosen to reflect the expected spacing. Choosing such weights before seeing the data keeps the contrast honest, and any weights chosen afterward should be reported as exploratory. Transparency about when the contrast was chosen matters as much as the contrast itself.
Interpretation
The pattern is consistent with the clinical expectation that missed warfarin doses make INR harder to keep in range. The analysis is observational, though: patients who miss doses may differ in other ways, such as illness or unstable diets, that also affect control. The result supports adherence support as one part of anticoagulation care but does not show how much improving adherence would raise time in range.
References
Bender, R., & Lange, S. (2001). Adjusting for multiple testing: When and how? Journal of Clinical Epidemiology, 54(4), 343-349. https://doi.org/10.1016/S0895-4356(00)00314-0
Lumley, T., Diehr, P., Emerson, S., & Chen, L. (2002). The importance of the normality assumption in large public health data sets. Annual Review of Public Health, 23, 151-169. https://doi.org/10.1146/annurev.publhealth.23.100901.140546
Rothman, K. J. (1990). No adjustments are needed for multiple comparisons. Epidemiology, 1(1), 43-46. https://doi.org/10.1097/00001648-199001000-00010
What the PHLT 8331 Week 8 instructions ask for
The eighth week typically asks students to compare a continuous outcome across three or more groups using analysis of variance and to follow up the overall test appropriately. The expectation is that conditions will be checked, the overall F test reported with an effect size and a follow-up strategy justified. When groups are ordered, a planned trend contrast is often more informative than comparing every pair, and students should explain the choice with reference to the debate over multiple-comparison adjustment. Interpretation should note limits on causal claims. Length is generally three to five pages, including one summary table and methods references. Reporting standards ask that planned and exploratory comparisons be distinguished clearly.
How this PHLT 8331 Week 8 example is built
The paper opens by stating the question and why the follow-up matters. A section checks conditions, citing research on robustness in large samples and noting the modest spread in standard deviations. Table 1 gives sizes, means and standard deviations, and the text reports the F test and eta squared. A section explains the problem with all-pairs comparisons, citing guidance on when to adjust and an argument against routine adjustment, then motivates and reports the linear trend contrast. A section explains why the contrast does not depend on the overall test. Sections on reporting, on the equal-spacing assumption and on interpretation close the paper.
PHLT 8331 Week 8 rubric: what earns full marks
Assessment centers on the follow-up strategy. The sample earns its main credit by recognizing that ordered groups invite a trend contrast and by justifying the choice against all-pairs testing with reference to the methods literature. The overall test and effect size are checked for correct reporting. Explaining that a planned contrast stands regardless of the omnibus result shows understanding many students lack. Noting the equal-spacing approximation and the observational nature of adherence demonstrates care. What is left of the grade turns on table clarity and reference accuracy. Stating that the contrast was planned before the data were examined, and reporting any exploratory comparisons separately, demonstrates the transparency the methods literature recommends. Instructors also credit noting the equal-spacing assumption behind the contrast weights.
Common PHLT 8331 Week 8 mistakes, and how to avoid them
Analyses of variance often stop at the overall F or jump to comparing every pair with heavy adjustment. Ask what question the groups invite. If they are ordered, a planned trend contrast may answer it directly with one test. Specify contrasts before seeing the data and say so. Report an effect size with the F test. Check that group variances are not wildly different. Remember that groups defined by behavior, such as adherence, may differ in other ways, so avoid causal language. Ask for a free ANOVA write-up built on your own groups. Label any comparison chosen after seeing the data as exploratory. And check that the contrast weights match how you expect the outcome to change across groups.
Get a PHLT 8331 Week 8 example written to your instructions
Share the Week 8 prompt and rubric, noting the number of groups in your comparison and whether they have an order. An analysis of variance with conditions checked, the omnibus result explained and a defended follow-up returns within 24-48h, free as your first. Group means and contrasts inside are illustrative; none are drawn from your output.
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PHLT 8331 Week 8 questions, answered
Where can I find a free PHLT 8331 Week 8 sample paper?
The complete Week 8 paper is on this page, comparing time in therapeutic range across three adherence levels in a composite registry and following the overall test with a planned trend contrast.
Why not run t-tests between every pair of groups?
Multiple unplanned tests raise the chance of a false positive, and adjusting for that reduces power. More important, pairwise tests ignore the order of the groups. A single planned trend contrast asks the question the ordered groups invite.
When is a trend contrast appropriate?
When groups have a natural order, such as levels of adherence or dose, and the question is whether the outcome changes steadily across them. The contrast should be specified before the data are examined.
What if the overall F test is not significant?
A planned contrast can still be reported, because it was specified in advance and addresses a focused question. The F test spreads attention across all patterns, so a clear trend can appear even when the overall test does not.
What does eta squared tell you?
Eta squared is the share of outcome variance accounted for by the groups. In the sample, adherence level accounts for about 10.5% of the variation in time in therapeutic range, a moderate share.