DNP 851B Module 3 Choosing and Running the Inferential Tests Example

Matched Pairs, Not Groups: Choosing and Running the Inferential Tests for a Pediatric Asthma Project

Student Name

Doctor of Nursing Practice Program, Aspen University

DNP 851B: Project Data Analysis

Instructor Name

Month Day, Year

Matched Pairs, Not Groups: Choosing and Running the Inferential Tests for a Pediatric Asthma Project

A statistical test is only as sound as its fit to the design and the data. My DNP project measured the same children before and after a nurse-led asthma program, so every comparison is a matched one, and the choice of tests follows from that fact. This paper explains which tests were chosen for each outcome and why, how their assumptions were checked, and what they showed. The project's outcomes were asthma control on age-appropriate tests for 91 children with complete data, and emergency or urgent care visits for asthma for all 104 enrolled children, in the 12 weeks before and after the nurse visit.

Matching Tests to Outcomes

Three kinds of outcome called for three kinds of test. Change in a continuous score measured twice in the same child calls for a paired t-test, provided the differences are roughly normal, or a Wilcoxon signed-rank test if they are not. A yes-or-no outcome measured twice in the same child, such as whether asthma was well controlled, calls for McNemar's test, which uses only the children whose status changed. A comparison of Fagerland et al. (2013) found that the asymptotic McNemar test without continuity correction and the mid-p version perform well, while the traditional exact conditional version is overly conservative; the asymptotic test was used, with the mid-p value as a check. Counts of visits per child, which are small whole numbers with many zeros, call for the signed-rank test.

Checking Assumptions

The paired t-test assumes that the within-child differences are approximately normal. Kim (2013) suggests judging normality in small and moderate samples by dividing skewness and kurtosis by their standard errors and treating values beyond a threshold as a sign of non-normality, with a stricter threshold for smaller samples. For the 62 children on the childhood test, the differences had skewness of 0.31 and excess kurtosis of -0.42, and for the 29 adolescents, 0.28 and -0.51; all standardized values fell well inside the limits, and histograms showed no marked outliers. The paired t-test was therefore used for both instruments. Scores from the two instruments were never pooled, because their ranges differ.

Results

The table presents the results. The significance level was .05, two-sided, and every estimate is given with its 95% confidence interval.

Sensitivity Analyses

The two sensitivity analyses set out during data cleaning were run next. Adding the six children whose 12-week scores came late raised the paired sample to 97; of these, 21 were well controlled at baseline and 55 at follow-up, and McNemar's test remained significant, p < .001. The worst-case analysis counted all 13 children without paired data as not controlled at follow-up, and counted those among them with a baseline score by their actual baseline status. Even under that assumption, the share of all 104 enrolled children with well-controlled asthma rose from 21 at baseline to 52 at 12 weeks, and the test remained significant. The conclusion about asthma control therefore does not depend on how the missing children are handled.

Effect Sizes

Statistical significance says a change is unlikely to be chance; effect size says how large it is. For the paired score changes, the effect size was calculated as the mean change divided by the standard deviation of the changes, giving 0.90 for the childhood test and 0.87 for the adolescent test, both large by the conventions Cohen (1992) proposed. For well-controlled asthma, the share rose by 36 percentage points. For acute care, the share of children with a visit fell by 10 percentage points and the number of visits fell by more than half. Effect sizes will carry more weight than p values in the discussion, because they speak to whether the change matters.

Both conventions and clinical judgment point the same way here.

Why These Tests Fit the Sample Size

With 91 complete pairs, the paired tests had ample power for the effect the proposal planned to detect. McNemar's test depends on the number of discordant pairs rather than the full sample; 39 children changed control status and 17 changed acute care status, enough for the asymptotic test to be reliable. No subgroup test was run, because subgroups such as Spanish-speaking families or adolescents were too small for inference; they are described instead. Only the outcomes named in the proposal were tested, which keeps the risk of false positives from multiple testing low.

What the Tests Cannot Show

These tests show that children's asthma control and acute care changed after the program. They cannot show that the program caused the change. Without a concurrent comparison group, seasonal variation, regression to the mean in children enrolled when symptoms were worse, and new controller prescriptions could each explain part of it. Two further sources help weigh those alternatives: acute care in matching calendar weeks a year earlier, and the clinic-level run charts.

Conclusion

Paired t-tests, McNemar's test and the signed-rank test were chosen because each child served as their own comparison, and their assumptions were checked before use. All five comparisons favored the post-program period, with large effect sizes for asthma control. The results are strong for a single-group design, and their interpretation will depend on the other evidence the project gathered.

Chapter four will present them in the same order.

References

Cohen, J. (1992). A power primer. Psychological Bulletin, 112(1), 155-159. https://doi.org/10.1037/0033-2909.112.1.155

Fagerland, M. W., Lydersen, S., & Laake, P. (2013). The McNemar test for binary matched-pairs data: Mid-p and asymptotic are better than exact conditional. BMC Medical Research Methodology, 13, Article 91. https://doi.org/10.1186/1471-2288-13-91

Kim, H.-Y. (2013). Statistical notes for clinical researchers: Assessing normal distribution (2) using skewness and kurtosis. Restorative Dentistry & Endodontics, 38(1), 52-54. https://doi.org/10.5395/rde.2013.38.1.52