| Course | PHLT 8331 Fundamentals of Biostatistics |
|---|---|
| Week | Week 4 |
| Paper type | Statistical test write-up |
| Length | About 1,020 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 4
Conditions First, Result Second: A Paired t-Test on Time in Therapeutic Range Before and After 212 Patients Moved to Pharmacist Anticoagulation Management in a Composite Registry
Student Name
Walden University
PHLT 8331: Fundamentals of Biostatistics
Instructor Name
Month Day, Year
Conditions First, Result Second: A Paired t-Test on Time in Therapeutic Range Before and After 212 Patients Moved to Pharmacist Anticoagulation Management in a Composite Registry
The Question and the Test
The first hypothesis pair from Week 3 asked whether time in therapeutic range changed, on average, among the patients whose anticoagulation care passed from doctors to clinical pharmacists. In the composite registry, 212 patients made that move and had complete INR records for the six months before and after. Because each patient contributes two measurements, the appropriate test compares each patient with themselves: a paired t-test on the 212 within-patient differences. This write-up checks each condition the test requires before reporting the result. All figures are composite.
The Conditions
Condition 1: The Data Are Paired
Each before measurement belongs to the same patient as an after measurement, so the two sets are not independent samples. Treating them as independent would ignore the fact that a patient with poor control before the move is likely to have lower values after it as well, which would inflate the variance and weaken the test. Pairing removes stable differences between patients and focuses the test on change within each person.
Condition 2: The Differences Are Independent of One Another
The paired t-test assumes that one patient's difference tells us nothing about another's. That is reasonable for most patients, but the 212 were managed at two clinics, and patients at the same clinic share pharmacists, protocols and testing routines. If clinic routines push all their patients' changes in the same direction, the differences are not fully independent, and the standard error will be somewhat too small. A check by clinic found mean differences of 7.4 and 8.1 points at the two clinics, close enough that clustering is unlikely to change the conclusion, but the limitation is noted.
Condition 3: The Mean of the Differences Is Approximately Normal
The test requires the sampling distribution of the mean difference to be approximately normal. With 212 differences, the central limit theorem makes that likely unless the differences are extremely skewed or contain extreme outliers. A histogram of the differences is roughly symmetric, centered near 8 points, with a few large gains among patients whose control had been very poor and a few large losses. Lumley et al. (2002) showed that t-tests remain reliable in samples of this size even when the data are not normal. Normality is checked on the differences, not on the two sets of measurements, because the test is applied to the differences.
Condition 4: The Measurement Is Consistent
Time in therapeutic range was calculated the same way in both periods, by linear interpolation between INR tests (Rosendaal et al., 1993). Patients tested more often after the move, since the pharmacist service schedules tests more closely, and more frequent testing can change the interpolated estimate slightly. The effect is likely small but is noted.
The Result
Mean time in therapeutic range was 58.4% before the move (standard deviation 17.2) and 66.1% after it (standard deviation 15.8). The mean within-patient difference was 7.7 percentage points, with a standard deviation of 18.6. The standard error of the mean difference was 1.28, giving t = 6.03 on 211 degrees of freedom, p < .001. The 95% confidence interval for the mean difference runs from 5.2 to 10.2 percentage points.
The null hypothesis that the population mean difference is zero is rejected at the .05 level. The interval suggests the average improvement in the source population is plausibly between about 5 and 10 percentage points.
Table 1
Paired Comparison of Time in Therapeutic Range (Composite Figures, n = 212)
| Measure | Before move | After move | Difference | |
|---|---|---|---|
| Mean time in range, % | 58.4 | 66.1 | 7.7 | |
| Standard deviation | 17.2 | 15.8 | 18.6 | |
| 95% CI for mean difference | | | 5.2 to 10.2 | |
Note. Composite figures. Differences are after minus before. t = 6.03, df = 211, two-sided p < .001.
Limits of the Inference
The paired analysis establishes that time in therapeutic range was higher after the move. It does not show that the pharmacist service caused the improvement. Patients were moved to pharmacist management partly because their control was poor, and patients selected for unusually low values tend to show higher values later even without any intervention, a pattern called regression to the mean. Their warfarin doses may also have been stabilizing over time regardless of who managed them. A comparison with similar patients who stayed under physician management over the same period would be needed to separate these explanations. The next week's comparison between clinics begins that work, though it brings its own limitations.
What a Nonsignificant Result Would Have Meant
Had the test produced a p-value above .05, the conclusion would not have been that pharmacist management made no difference. It would have been that the data were compatible with no average change, and the confidence interval would have shown how large a change could still be hidden by the sample's variability. With 212 patients and a standard deviation of differences near 19 points, the study could detect an average change of about 4 points with reasonable precision; smaller changes might have been missed. Reporting that sensitivity alongside a null result keeps readers from mistaking an imprecise study for evidence of no effect.
Reporting the Result
A complete report of a paired t-test names the test, the number of pairs, the mean and standard deviation of the differences, the test statistic with its degrees of freedom, the p-value and the confidence interval for the mean difference. It also states how the conditions were checked. Reporting only "p < .001" would leave out the size of the change, its precision and the evidence that the test was appropriate, all of which a reader needs to judge the result.
Summary
All four conditions are reasonably met, with two noted limitations: possible clustering by clinic and a change in testing frequency. Under those conditions, mean time in therapeutic range rose by 7.7 percentage points after the move. The result is consistent with reviews finding better control under pharmacist-managed services (Manzoor et al., 2017), but this design cannot establish that the service produced the change.
References
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
Manzoor, B. S., Cheng, W.-H., Lee, J. C., Uppuluri, E. M., & Nutescu, E. A. (2017). Quality of pharmacist-managed anticoagulation therapy in long-term ambulatory settings: A systematic review. Annals of Pharmacotherapy, 51(12), 1122-1137. https://doi.org/10.1177/1060028017721241
Rosendaal, F. R., Cannegieter, S. C., van der Meer, F. J. M., & Briët, E. (1993). A method to determine the optimal intensity of oral anticoagulant therapy. Thrombosis and Haemostasis, 69(3), 236-239. https://doi.org/10.1055/s-0038-1651587
Reading the PHLT 8331 Week 4 instructions
Week 4 usually centers on a single hypothesis test applied to the course dataset, reported in full, with every assumption behind it examined. Instructors expect each condition to be named, checked with evidence and judged, with any limitations stated, before the result is reported. A finished result gives the estimate, its spread, the t value with df, the p-value and the interval. Students should interpret the result in context and say what the test cannot establish, particularly about causation in observational data. A typical submission fills three or four pages, includes a results table and cites work on both the test and the outcome measure.
How this PHLT 8331 Week 4 example is built
The paper opens with the question and explains why a paired test fits. Four conditions follow under their own headings: pairing, independence of differences with a check by clinic, approximate normality of the mean difference with a histogram and a citation on robustness in large samples, and consistent measurement, citing the interpolation method and noting more frequent testing after the move. The result is reported in text and in Table 1 with means, standard deviations, the difference and its interval. A section explains why the test cannot show causation, emphasizing regression to the mean. Sections on a hypothetical nonsignificant result and on complete reporting precede a summary citing a review of pharmacist-managed care.
Reading the PHLT 8331 Week 4 rubric
The heaviest marks go to the conditions section, and the sample earns them by checking each condition with evidence rather than asserting it. Recognizing clustering by clinic and the change in testing frequency shows attention to this dataset rather than a generic checklist. The result is checked for accuracy and completeness, including the interval and degrees of freedom. Naming regression to the mean as the chief obstacle to a causal claim shows sound statistical judgment. The note on what a null result would have meant adds depth. Table layout and citation accuracy make up the last part of the rubric. Instructors also look for honesty about what a nonsignificant result would have meant, since that shows the author understands the test's limits as well as its uses.
PHLT 8331 Week 4 help: mistakes that cost marks
Test write-ups often report the p-value first and mention conditions as an afterthought, if at all. Reverse the order. Check normality on the quantity the test uses, which for a paired test is the differences. Think about whether observations are truly independent; patients at the same clinic may not be. Report the full result, not just "p < .05". Most important, do not let a significant result slide into a causal claim when the design cannot support it; in before-and-after data, regression to the mean is a common explanation for improvement. A paired-test write-up on your own dataset is available as a free sample. Finally, state what a null result would have meant before you know the result. That habit protects you from overreading whichever way the test comes out.
Get a PHLT 8331 Week 4 example written to your instructions
Attach the Week 4 prompt and rubric and name the test your section is running first. Within 24-48h, first request free, a test write-up comes back with a conditions table, evidence for every verdict and a result in both APA and plain form. Readings, change scores and interval bounds in it come from an invented registry and cannot stand in for yours.
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PHLT 8331 Week 4 questions, answered
Where can I find a free PHLT 8331 Week 4 sample paper?
Read the full Week 4 write-up on this page: a paired t-test on time in therapeutic range before and after pharmacist management in a composite registry, with each condition checked before the result.
Why check normality on the differences rather than the two readings?
Because a paired t-test is a one-sample test on the within-patient differences. Its condition concerns the distribution of those differences, or their mean, not the separate distributions of the before and after readings.
What happens if patients from the same clinic are not independent?
Shared routines can make their changes similar, so the effective sample size is smaller than the count of patients and the standard error is too small. The sample checks mean differences by clinic and notes the limitation.
Can this test show that pharmacist management works?
No. It shows that time in range was higher after the move. Because patients were moved partly for poor control, some improvement could reflect regression to the mean. A comparison group would be needed to separate that from a program effect.
What should a complete paired t-test report include?
The number of pairs, the mean and standard deviation of the differences, the t statistic with degrees of freedom, the p-value, the confidence interval for the mean difference and a statement of how the conditions were checked.