DNP/701 Week 4: Descriptive Statistics and Data Visualization, sample paper

A Mean of 0.6 Visits and a Standard Deviation of 1.4: Describing Skewed Clinic Data Honestly, Choosing Medians and Distributions Over Bar Graphs and Plotting A1c Control in Time Order

[Student Name]

University of Phoenix

DNP/701: Biostatistics and Epidemiology

Week 4 Assignment

[Instructor Name]

[Date]

The clinic and its figures are a composite written for a model paper.

Our rural clinic network has 520 adults with diabetes. For my DNP work, I need to describe this population clearly for our quality committee. Two variables matter most: the most recent A1c and the number of emergency department visits in the past year. This paper describes each, explains the choice of statistics and graphs and presents a run chart of A1c control over time.

A1c: Center and Spread

A1c values ranged from 5.4% to 14.2%. The mean was 8.1%, the median 7.6% and the standard deviation 1.9 percentage points. The interquartile range was 6.8% to 9.0%. A small group with very high values drags the average above the middle value, producing a mild right skew.

Emergency Visits: A Skewed Count

Emergency visits ranged from 0 to 11. The mean was 0.6 visits and the standard deviation 1.4. The median was 0, and 72% of patients had no visits. Only 5% of patients accounted for about half of all visits.

Detecting Skewness From Summary Statistics

Altman and Bland (1996) observed that for variables that cannot be negative, a standard deviation larger than half the mean indicates a skewed distribution, since a symmetric distribution with that spread would require impossible negative values. For emergency visits, the standard deviation of 1.4 is more than twice the mean of 0.6, a clear sign of strong skew. Reporting "mean 0.6 visits, SD 1.4" would suggest a symmetric distribution around 0.6, which misrepresents a population in which most patients had none and a few had many.

The mean said every patient had a little over half an emergency visit; in fact almost three quarters had none and a handful had most of them.

Why Shape Comes First

Before choosing any summary, I plotted each variable. The shape of a distribution determines which statistics describe it fairly, and a quick histogram prevents reporting a mean that describes no real patient.

Choosing the Right Summary

For A1c, I report both the mean with standard deviation and the median with interquartile range, since the skew is mild and both are informative. For emergency visits, the summary I give is the middle value, the middle half of the distribution and the share of patients with no visits at all, plus the distribution of patients by visit count, which tells the committee more than a mean.

Why Bar Graphs Mislead

Weissgerber et al. (2015) reviewed 703 research articles in physiology journals and found that most presented continuous data as bar or line graphs of means, which can hide very different distributions, and few used scatterplots, box plots or histograms. They recommended showing the full data, especially in small samples, because the distribution may suggest conclusions different from the summary statistics.

My Graphs

For A1c, I use a histogram with half-point bins, which shows the peak around 7% and the tail above 10%, and a box plot comparing A1c across our three clinic sites. The box plots reveal that one site has a wider spread and more high values, something a bar graph of means would hide. For emergency visits, I use a bar chart of the number of patients with 0, 1, 2, 3 and 4 or more visits, which displays counts, not means, and makes the concentration of visits visible.

A1c Change Over Time for Individuals

For patients with two A1c results six months apart, a paired dot plot connecting each patient's two values shows who improved, who worsened and by how much, which a comparison of two group means would conceal.

Categorizing A1c

Our committee follows a common quality measure: the share of the panel whose latest A1c exceeds 9%. Currently, 24% of our patients are above 9%. Categorizing loses detail, since a patient at 9.1% and one at 13% are counted the same, so I report the categorical measure alongside the distribution.

Tables Alongside Graphs

A one-page table accompanies the graphs, listing for each variable the number of patients with data, the median, the interquartile range and, where appropriate, the mean and standard deviation. Committee members who prefer numbers can read the table, and those who prefer pictures can read the graphs, and both see the same story.

Time Order

Perla et al. (2011) describe the run chart as a simple tool for learning from variation in health care processes, displaying data in time order with a median line and using rules to detect nonrandom patterns, such as a run of six or more months sitting entirely above or entirely below the median line, or five or more steadily rising or falling points. They argue that time-ordered displays are more useful for improvement than aggregate summaries that ignore time.

Our Run Chart

I plotted the monthly percentage of patients with A1c above 9% for 24 months. The median across months was 26%. The last seven months fall below the median, a shift by the run chart rules, beginning shortly after we started quarterly A1c reminders. This suggests a nonrandom improvement, though a run chart cannot establish that the reminders caused it.

Stratifying the Description

A single overall description can hide differences between groups. When I described A1c by age group, adults under 45 had a median of 8.4%, compared with 7.3% for those over 65. By site, one clinic's median was nearly a point higher than the others. These stratified descriptions point to where improvement efforts should focus and raise questions I can test statistically next week.

Outliers

Two A1c values above 14% were checked against laboratory reports and confirmed. They are real and belong in the data. Removing true extreme values to make data look tidier would misrepresent the patients who most need attention; the median and interquartile range are simply less affected by them.

Data Quality

Descriptive statistics are only as good as the data. I checked for missing A1c values, which affected 6% of patients, and for implausible values. Patients without a recent A1c are excluded from the A1c description but reported separately, since they may be the least engaged patients.

Choosing Scales Honestly

Graphs can mislead through their axes. A y-axis that begins at 20% on the run chart would make a small change look dramatic. I start the axis at zero for percentages and label every axis with units, so the visual size of a change matches its real size.

Presenting to the Committee

My summary slide will show the A1c histogram, the site box plots, the emergency visit distribution and the run chart, with brief labels and one sentence of interpretation for each.

Conclusion

A1c is mildly right-skewed, and emergency visits are strongly skewed, as a simple rule comparing standard deviation with the mean reveals. Medians, interquartile ranges and distribution graphs describe these data more honestly than means and bar graphs, and a run chart in time order shows a shift in A1c control that aggregate statistics would hide.

References

Altman, D. G., & Bland, J. M. (1996). Detecting skewness from summary information. BMJ, 313(7066), 1200. https://doi.org/10.1136/bmj.313.7066.1200

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 and Safety, 20(1), 46-51. https://doi.org/10.1136/bmjqs.2009.037895

Weissgerber, T. L., Milic, N. M., Winham, S. J., & Garovic, V. D. (2015). Beyond bar and line graphs: Time for a new data presentation paradigm. PLOS Biology, 13(4), Article e1002128. https://doi.org/10.1371/journal.pbio.1002128