This is an original excerpt written by our team to show structure, depth and referencing. It is modelled on the course named above but is not a university document. Use samples as a study guide and follow your school's academic integrity policy.
The analytic problem
DNP projects usually track a measure over time while changes are being tested. Monthly results go up and down even when nothing changes, so the question is whether a change in the data reflects a real improvement or natural variation. Comparing a single before-and-after average can hide this, because it ignores the order of the data.
Run charts
A run chart plots data in time order with the median as a center line. Perla et al. (2011) describe probability-based rules for detecting a non-random signal:
| Rule | Signal |
|---|---|
| Shift | Six or more consecutive points all above or all below the median |
| Trend | Five or more consecutive points all going up or all going down |
| Runs | Too many or too few runs (series of points on one side of the median) |
| Astronomical point | A point obviously different from the rest |
Run charts are simple to build and explain, and they are the foundation for more advanced methods.
Statistical process control
Statistical process control combines time-series analysis with graphical displays. Benneyan (2003) describes how it separates common-cause variation, the natural variation built into a process, from special-cause variation, which signals that something has changed. A control chart adds upper and lower control limits, usually 3 standard deviations from the mean, calculated from the data. Points outside the limits, or non-random patterns within them, indicate special-cause variation. The type of chart depends on the data:
- p-chart: proportions, such as the percentage of patients who received a screening;
- u-chart: rates per unit of exposure, such as falls per 1,000 patient-days;
- I-chart (individuals): continuous measurements, such as monthly median time to antibiotics.
Worked example: a p-chart for discharge teaching
A project aims to raise the percentage of heart failure patients who receive documented teach-back discharge education. Each month, about 40 discharges are audited. The data are illustrative.
| Period | Months | Mean proportion with teach-back |
|---|---|---|
| Baseline | 1–8 | 0.45 |
| Intervention | 9–16 | 0.78 |
For a p-chart, the control limits are p̄ ± 3√[p̄(1 − p̄)/n]. For the baseline, with p̄ = 0.45 and n = 40:
√(0.45 × 0.55 ÷ 40) = √0.00619 ≈ 0.079, so the limits are 0.45 ± 0.236, giving a lower limit of 0.21 and an upper limit of 0.69.
During the intervention, every month falls above the baseline's upper control limit of 0.69. That is special-cause variation, strong evidence that the process changed. Once the change is stable, the team should recalculate the center line and limits for the new process, which can then be monitored to see whether the gain holds.
Interpreting and reporting
- Annotate charts with when each change was introduced.
- Don't react to single points within the limits, which reflect common-cause variation.
- Make the sample size clear, because limits widen when fewer cases are audited.
- Pair outcome charts with process charts, so the team can see whether improvement follows changes in the process.
Conclusion
Run charts and control charts let DNP-prepared nurses learn from data as a project unfolds and explain results to staff and leaders without complex statistics. They are well suited to the small, repeated tests of change at the heart of practice improvement.
References
Benneyan, J. C., Lloyd, R. C., & Plsek, P. E. (2003). Statistical process control as a tool for research and healthcare improvement. Quality and Safety in Health Care, 12(6), 458–464. https://doi.org/10.1136/qhc.12.6.458
Perla, R. J., Provost, L. P., & Murray, S. K. (2011). The run chart: A simple analytical tool for learning from variation in healthcare processes. BMJ Quality & Safety, 20(1), 46–51. https://doi.org/10.1136/bmjqs.2009.037895
