| Course | HA535 Data Analytics for Health Care Managers |
|---|---|
| Unit | Unit 6 |
| Paper type | Correlation analysis |
| Length | About 840 words, 6 pages double-spaced |
| Format | APA 7 student paper |
| School | Purdue University Global |
| Program | Master of Health Administration (MHA) |
| Updated | October 2026 |
Free sample paper for HA535 Unit 6
Do Faster Hospitalists Send Back More Patients? A Correlation Analysis of Thirty-One Physicians at a Composite Regional System, Setting a Length-of-Stay Index Against Thirty-Day Readmissions and Finding a Weaker Answer Than the Chart Suggests
[Student Name]
Purdue University Global
HA535: Data Analytics for Health Care Managers
Unit 6 Correlation Analysis
[Instructor Name]
[Date]
The physicians, their discharges and every statistic are composite and bracketed; figures are described in words for this page.
The Question
Hospital leaders worry that pushing for shorter stays will raise readmissions. If so, physicians with shorter stays should have higher readmission rates. The data can test whether that pattern appears among the system's hospitalists.
The Data
Thirty-one hospitalists, each with [157] to [415] discharges in the year. Length-of-stay index: observed stay divided by expected stay for the same diagnosis groups, from [0.79] to [1.14]. Readmission rate: share of each physician's discharges readmitted within thirty days, pooled at [14.8] percent.
How the Index Was Built
For each discharge, the expected stay for its diagnosis group was taken from the system's own three-year average. Each physician's observed days were summed and divided by the sum of expected days for the same patients. An index of [1.00] means a physician's patients stayed exactly as long as expected; [0.85] means fifteen percent shorter. Attributing each stay to the physician who wrote the discharge order is a simplification, since several hospitalists often share a patient's care.
The Scatter Plot
Each point is one hospitalist: horizontal position is the length-of-stay index; vertical position is the readmission rate. The cloud slopes slightly downward to the right, the opposite of the feared pattern, but loosely.
The Statistics
Pearson's r: [−0.296]. R squared: under [9] percent, so length of stay accounts for less than a tenth of the variation in readmission rates. The 95 percent confidence interval runs from [−0.59] to [0.07], crossing zero. A permutation test gives a p value near [0.11]. Spearman's rho, [−0.22], which uses ranks and is less sensitive to extreme points, keeps the direction with less strength. Guidance on correlation coefficients stresses that the size of a correlation must be judged with its confidence interval, and that correlation does not establish cause (Schober et al., 2018). With thirty-one physicians, a correlation this weak is consistent with no relationship at all, and the direction it points is the opposite of leaders' fear.
The Funnel Plot
Plotting each physician's readmission rate against the number of discharges, with 95 percent limits that narrow as volume grows, shows which physicians truly differ from the system average. Two physicians fall outside the limits above the average; neither has an unusually short length of stay. Funnel plots guard against singling out physicians whose rates are high only because their volume is small (Spiegelhalter, 2005).
What Larger Studies Found
A study of veterans' hospitals over fourteen years found that length of stay fell substantially while readmission rates also fell, and hospitals with shorter stays did not have higher readmission rates on average (Kaboli et al., 2012). The system's data are consistent with that pattern.
Why the Two Physicians Might Differ
Review of their discharges shows that one physician covers the system's only inpatient dialysis service, where readmissions are common for reasons unrelated to discharge timing. The other works mostly nights and discharges few patients directly, so the patients attributed to him are a small and unusual group. Neither explanation is certain, but both are worth checking before any conclusion about individual performance.
Presenting the Results to Hospitalists
Physicians will look first for their own dot. The presentation will show the funnel plot without names, give each physician a private copy with their own position marked and lead with the system-level finding that shorter stays did not go with more readmissions.
What the Analysis Does Not Show
Correlation among physicians does not show what would happen to one physician's patients if stays were shortened. The length-of-stay index adjusts only for diagnosis, not for severity within diagnosis or social factors. Readmissions to other hospitals are missing unless captured by the repaired crosswalk from Unit 2.
What Would Change the Conclusion
A strong positive correlation in a larger sample, or a rise in readmissions after a system-wide push to shorten stays, would change the conclusion. Neither appears now, but tracking both each quarter would show whether the relationship emerges.
Recommendations
1. Do not treat shorter stays as a readmission risk on the basis of this data.
2. Review the two physicians outside the funnel limits with the hospitalist medical director, looking at their patient mix and discharge processes.
3. Repeat the analysis each year with more discharges and with severity adjustment.
Limits
Thirty-one physicians is a small sample, which keeps the confidence interval wide. Physicians who share patients may not be independent. One year may not represent typical performance.
Conclusion
The feared trade-off between shorter stays and more readmissions does not appear in this system's data. The useful finding is not the correlation but the two physicians whose readmission rates stand out regardless of their length of stay.
References
Kaboli, P. J., Go, J. T., Hockenberry, J., Glasgow, J. M., Johnson, S. R., Rosenthal, G. E., Jones, M. P., & Vaughan-Sarrazin, M. (2012). Associations between reduced hospital length of stay and 30-day readmission rate and mortality: 14-year experience in 129 Veterans Affairs hospitals. Annals of Internal Medicine, 157(12), 837-845. https://doi.org/10.7326/0003-4819-157-12-201212180-00003
Schober, P., Boer, C., & Schwarte, L. A. (2018). Correlation coefficients: Appropriate use and interpretation. Anesthesia & Analgesia, 126(5), 1763-1768. https://doi.org/10.1213/ANE.0000000000002864
Spiegelhalter, D. J. (2005). Funnel plots for comparing institutional performance. Statistics in Medicine, 24(8), 1185-1202. https://doi.org/10.1002/sim.1970
The Purdue Global HA535 Unit 6 instructions
Unit 6 in HA 535 typically asks students to examine the relationship between two health care variables using correlation and to interpret the result for managers. Instructions often require stating a question, describing the variables and the unit of analysis, producing a scatter plot, calculating a correlation coefficient with its significance or confidence interval and explaining what the result does and does not mean, especially about cause. Some prompts invite a second method, such as a rank correlation, to check the result. Choose two measures where managers already hold a belief, because testing that belief makes the analysis useful. Report sample size and how each variable was built. Cite a statistics source in APA format, and spell out the difference between association and cause in plain words.
How this HA535 Unit 6 example is built
The sample states the question as the chief medical officer put it, then defines both variables and the physician as the unit. A scatter plot places 31 hospitalists by stay index and readmission rate. Pearson's r of minus 0.296 is reported with its 95 percent interval of minus 0.59 to 0.07 and a permutation test near p of 0.11. A margin note converts r into r squared so readers see how little variation it explains. Spearman's rho of minus 0.22 confirms the direction without relying on outliers. A funnel plot follows, showing that most physicians sit within the limits expected for their volume. The analysis then lists confounders, such as patient mix and follow-up access, and recommends against using stay targets to rank hospitalists on this evidence.
Where the points sit in the HA535 Unit 6 rubric
HA 535 rubrics for a correlation analysis generally award points for a clear question, well-defined variables, an appropriate chart, correct calculation, accurate interpretation of strength and uncertainty, discussion of cause and confounding, sources and presentation. Question points go to a specific, testable relationship. Variable points reward explaining how each measure was built and at what level. Chart points depend on a labeled scatter plot. Calculation points require the coefficient with an interval or test. Interpretation points go to describing strength in plain terms, including r squared. Cause points reward naming likely confounders. Papers that tell a manager what decision the evidence cannot support tend to get the strongest grades, because restraint with weak results is a skill graders look for.
Common HA535 Unit 6 mistakes, and how to avoid them
Correlation papers often lose points by calling a weak, uncertain relationship strong or significant, or by implying that one variable causes the other. Others report a coefficient with no chart, no sample size and no interval. Some ignore that physicians with few cases produce rates that swing by chance. State the question, define the variables and show the scatter plot. Report the coefficient, its interval and r squared, and describe strength honestly. Add a check, such as a rank correlation or a funnel plot. List the confounders that could explain the pattern. Finish with what managers should and should not do with the result, such as gathering more data before linking any target to readmissions or using it to compare physicians.
Get an HA535 Unit 6 example written to your instructions
What two variables does your Unit 6 assignment pair, and what question sits behind them? Pass that along with the dataset, the directions and rubric. We compute the correlation from your data, report its uncertainty and write the manager's reading of it; the opening sample carries no charge and lands within 24-48h. The paper above is an original model document written by our desk, not a submitted student paper and not an official Purdue University Global document.
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HA535 Unit 6 questions, answered
Where can I find a free HA535 Unit 6 sample paper?
The complete HA535 Unit 6 correlation analysis is here, testing length of stay against readmissions for 31 hospitalists at a composite regional system.
What did the HA535 Unit 6 analysis find?
A weak negative correlation, r of minus 0.296, with an interval crossing zero, too uncertain to support stay targets.
What does r squared mean?
The share of variation in one variable accounted for by its linear relationship with the other.
Why use a funnel plot?
It shows whether each physician's rate is outside the range expected by chance for their number of cases.
Does correlation prove cause?
No; patient mix, follow-up access and other factors can produce or hide a relationship.