Did the Discharge Huddle Work? A Chi-Square Test and an Independent t Test on a Medical Unit's Before-and-After Data
[Student Name]
University of Phoenix
NSG/509: Research and Applied Statistics for Quality Improvement
Week 4 Assignment
[Instructor Name]
[Date]
The unit and all data are a composite written for a model paper.
A composite 32-bed medical unit struggled with late-day discharges: most patients left in the afternoon or evening, while emergency department patients waited for beds. The unit introduced a 15-minute afternoon huddle of the charge nurse, hospitalist, case manager and pharmacist to identify patients likely to leave the next morning and to complete medication reconciliation, transportation and teaching the day before. Hospitals that set discharge-before-noon goals with daily multidisciplinary planning have reported increases in early discharges (Wertheimer et al., 2014). The unit's leaders wanted to know whether their numbers had moved, but the more useful question was whether the change was larger than chance and whether it was large enough to matter. This paper applies two inferential tests to the unit's before-and-after data.
Questions and Hypotheses
The evaluation asked two questions, each with a null and an alternative hypothesis.
First, did the proportion of discharges before noon differ between the three months before and the three months after the huddle began? The null hypothesis states that the proportions are equal; the alternative states that they differ.
Second, did the mean time from discharge order to the patient leaving the unit differ between the two periods? The null hypothesis states that the means are equal; the alternative states that they differ.
The significance level was set at .05 before the data were examined, and two-sided tests were used because the huddle could, in principle, have made either measure worse.
Choosing the Tests
The first outcome, discharged before noon or not, is nominal, so the data are counts in categories and the appropriate comparison of two independent proportions is the chi-square test of independence (Grove & Cipher, 2020). The second outcome, minutes from order to departure, is ratio level, and the two periods contain different patients, so the comparison of means between two independent groups calls for an independent samples t test (Polit & Beck, 2021).
Test 1: Discharges Before Noon
In the three months before the huddle, 130 of 720 discharges occurred before noon (18.1%). In the three months after, 205 of 710 discharges occurred before noon (28.9%). The expected count in every cell of the 2 by 2 table was far above 5, meeting the chi-square assumption for cell size, and each discharge appears in only one period.
The chi-square test showed a significant association between period and discharge before noon, chi-square(1, N = 1,430) = 23.32, p < .001. The absolute difference was 10.8 percentage points, and the relative increase was about 60%.
Test 2: Time From Order to Departure
Because extracting timestamps required chart review, a random sample of 60 discharges was drawn from each period. Before the huddle, the mean time from discharge order to departure was 186 minutes (SD = 74); after, it was 141 minutes (SD = 69). The two standard deviations were similar, and histograms showed moderate right skew, which the t test tolerates reasonably well at this sample size.
The independent samples t test showed a significant difference, t(118) = 3.45, p < .001. The mean difference was 45 minutes, with a 95% confidence interval from about 19 to 71 minutes, and the standardized effect size was Cohen's d = 0.63, a moderate effect.
A Closer Look at the Assumptions
Each test rests on assumptions, and checking them is part of reporting honestly. The chi-square test assumes independent observations and adequate expected counts. Independence is mostly met, although a patient readmitted in both periods would appear twice; the unit found four such patients among 1,430 discharges, too few to matter. The smallest expected count was well over 100, far above the usual minimum of 5.
The independent t test assumes independent groups, a roughly normal sampling distribution of the mean and similar variances. The groups are independent because they are different discharges in different months. The time data were right-skewed, as waiting and processing times usually are, but with 60 observations per group the sampling distribution of the mean is approximately normal. The standard deviations of 74 and 69 minutes are similar, and a version of the test that does not assume equal variances gave the same conclusion. Because of the skew, the unit also compared medians, which fell from 172 to 128 minutes, a pattern consistent with the t test. Reporting that sensitivity check shows the result does not depend on a questionable assumption.
Statistical Versus Practical Significance
Both results are statistically significant, meaning that differences this large would be unlikely if the huddle had no association with the outcomes. Statistical significance does not by itself show that the change matters. The practical question is whether 10.8 more percentage points of morning discharges and 45 fewer minutes from order to departure help patients and the hospital. For this unit, 10.8 percentage points meant roughly 25 more morning discharges per month, and the emergency department reported shorter boarding times for medical admissions in the afternoon, which suggests practical importance. The confidence interval for the time difference is wide, from about 19 to 71 minutes, so the size of the improvement is uncertain even though its direction is clear.
Practical significance also has a patient side. Forty-five minutes less between the discharge order and leaving the unit is time a patient no longer spends dressed and waiting, often with a family member who has taken time off work to drive. The unit's next patient experience survey could include a question about waiting on the day of discharge, which would connect the statistical result to what patients actually notice.
Threats to Validity
Comparing one period with the next, with no concurrent comparison unit, cannot establish that the huddle caused the change. Several alternative explanations must be considered. Seasonal patterns could differ between the two periods, since winter respiratory surges can change discharge patterns. Other changes occurred during the same months, including a new transportation contract that shortened wait times for rides home. Awareness of being measured may have changed staff behavior independently of the huddle. Finally, the timestamp sample of 60 discharges per period, although random, is small relative to all discharges.
Stronger designs would help. The unit could track both measures weekly on run charts or control charts over a longer period, which would show whether the change coincided with the start of the huddle and whether it persisted, and it could compare its results with a similar unit that did not adopt the huddle during the same months (Provost & Murray, 2011).
Conclusion
Two inferential tests, chosen by level of measurement, showed that after a daily discharge huddle began, the proportion of discharges before noon rose from 18.1% to 28.9% and the mean time from discharge order to departure fell by 45 minutes, both statistically significant with moderate practical effects. The before-and-after design limits causal claims, and other changes during the same period may have contributed. The results justify continuing the huddle and monitoring it over time with methods that can better separate its effect from everything else happening on the unit.
References
Grove, S. K., & Cipher, D. J. (2020). Statistics for nursing research: A workbook for evidence-based practice (3rd ed.). Elsevier.
Polit, D. F., & Beck, C. T. (2021). Nursing research: Generating and assessing evidence for nursing practice (11th ed.). Wolters Kluwer.
Provost, L. P., & Murray, S. K. (2011). The health care data guide: Learning from data for improvement. Jossey-Bass.
Wertheimer, B., Jacobs, R. E. A., Bailey, M., Holstein, S., Chatfield, S., Ohta, B., Horrocks, A., & Hochman, K. (2014). Discharge before noon: An achievable hospital goal. Journal of Hospital Medicine, 9(4), 210-214. https://doi.org/10.1002/jhm.2154
How this NSG 509 Week 4 example is structured
Course materials show NSG/509 moving from descriptive statistics in Week 2 to evidence-based practice and implementation in later weeks, and many sections use the middle of the course for inferential statistics, so this model treats Week 4 as an inferential statistics assignment. The paper states the questions and hypotheses first, chooses each test by the level of measurement of its outcome, reports every result in APA style with the numbers needed to check it and ends with the threats to validity that a before-and-after design cannot escape. Students search this week as NSG 509 Week 4, NSG509 Wk 4 or NSG/509 Wk 4; all three are the same assignment.
NSG/509 Week 4 questions, answered
What does NSG/509 Week 4 usually ask for?
Check your own week's instructions, since course versions differ. The course centers on research design and statistical methods for quality improvement, and many sections include an assignment that applies inferential tests such as chi-square or t tests to a data set and interprets the results.
How do I choose between a chi-square test and a t test?
By the outcome's level of measurement. A chi-square test compares proportions of a categorical outcome, such as discharged before noon or not, between groups. An independent t test compares means of a continuous outcome, such as minutes, between two independent groups, provided its assumptions are reasonably met.
Does a significant p value prove the intervention worked?
No. It shows that the difference is unlikely to be due to chance alone if the null hypothesis were true. In a before-and-after design without a comparison group, other changes over the same period could explain the difference, so the conclusion must be cautious.
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