3.5 Descriptive Statistics & Presenting Surveillance Data
Key Takeaways
- The median is the preferred measure of central tendency for skewed healthcare data such as length of stay, because a few extreme values distort the mean.
- Standard deviation describes how widely individual observations scatter around the mean, and roughly 95% of observations in a normal distribution fall within two standard deviations.
- On a run chart, six or more consecutive points on one side of the median signal a shift, and five or more consecutively rising or falling points signal a trend.
- Statistical process control charts separate common-cause variation inside the control limits from special-cause variation outside them, preventing overreaction to normal noise.
- Rates built on very small denominators are statistically unstable, so counts should be reported alongside rates whenever device days or procedures are few.
3.5 Descriptive Statistics & Presenting Surveillance Data
Quick Answer: Use the mean for symmetric data and the median for skewed data such as length of stay. Standard deviation measures spread. On a run chart, 6+ points on one side of the median = shift and 5+ consecutively rising or falling = trend. On a control chart, points inside the control limits are common-cause variation; points outside are special-cause.
The blueprint asks candidates to use basic statistical techniques to describe, analyze, and interpret data and to assist with preparing and presenting findings in a format relevant to the audience. These are two halves of one skill: summarizing a distribution correctly, then displaying it so the right people act.
Measures of Central Tendency
| Measure | Definition | Use when |
|---|---|---|
| Mean | Arithmetic average: sum ÷ count | Data are roughly symmetric with no extreme outliers |
| Median | The middle value when data are ordered | Data are skewed — length of stay, time to antibiotic, cost |
| Mode | The most frequently occurring value | Describing the most common category (e.g., most common organism) |
Worked example. Post-operative length of stay for seven patients: 3, 3, 4, 4, 5, 6, 45 days (one patient had a prolonged complication).
- Mean = 70 ÷ 7 = 10 days
- Median = 4 days
The mean says the typical patient stays ten days. No patient stayed ten days. One outlier dragged the mean past every observation but one. This is why hospital length-of-stay, time-to-treatment, and cost data are reported as medians.
Measures of Dispersion
| Measure | What it tells you |
|---|---|
| Range | Maximum minus minimum — simple, but hostage to one outlier |
| Standard deviation (SD) | Average distance of observations from the mean |
| Variance | SD squared |
| Interquartile range (IQR) | Middle 50% of the data (25th to 75th percentile) — the companion to the median |
In an approximately normal distribution:
That last figure is why control charts place limits at ±3 SD: only about 3 observations in 1,000 fall outside by chance alone, so a point beyond the limit is worth investigating.
Exam Tip: Two units can share an identical mean hand hygiene compliance of 80% while one ranges 78–82% and the other 40–100%. The mean is the same; the SD tells you which unit has a process problem.
Choosing the Right Display
| Display | Best for |
|---|---|
| Line list | Case-level detail during an investigation — one row per case, columns for time, place, person, exposures |
| Epidemic curve (histogram) | Case counts by onset date — reveals point-source vs. propagated patterns |
| Run chart | A single measure over time against a median centerline |
| Control chart (SPC) | A measure over time with a mean centerline and ±3 SD control limits |
| Bar chart | Comparing discrete categories (infections by unit, by organism) |
| Pareto chart | Ranked bars with a cumulative line — isolates the vital few causes |
| Histogram | Distribution of a continuous variable |
| Scatter plot | Relationship between two continuous variables (e.g., DUR vs. infection rate) |
Reading a run chart
A run chart is the workhorse of unit-level feedback because it needs no statistical software. Non-random signals:
- Shift — six or more consecutive points entirely above or entirely below the median
- Trend — five or more consecutive points all increasing or all decreasing
- Too few or too many runs — indicates a non-random pattern
- Astronomical point — an obviously extreme value
Reading a control chart
Control charts distinguish two kinds of variation:
- Common-cause variation — the inherent noise of a stable process. Points fall inside the control limits. Do not react to individual points; to improve, redesign the process.
- Special-cause variation — something changed. A point beyond a control limit, or a run pattern, warrants investigation.
Chart type follows data type: p-charts for proportions (percent compliance), u-charts for rates with varying denominators (infections per 1,000 device days), and c-charts for simple counts with a constant opportunity.
Exam Tip: The most common management error in IPC is treating common-cause variation as special cause — convening a task force because CLABSI went from 1 to 2 cases in a month. A control chart exists to prevent exactly that reaction.
The Small-Denominator Problem
Rates are unstable when the denominator is small. A unit with 200 catheter days and one infection reports 5.0 per 1,000 catheter days; a single additional case doubles the rate to 10.0. Nothing about care necessarily changed.
Practical rules:
- Report the numerator and denominator alongside the rate, always
- Aggregate small units over longer periods (quarterly rather than monthly)
- Prefer the standardized infection ratio with its confidence interval, which explicitly signals imprecision when predicted infections are few
- Resist ranking units by rate when denominators differ by an order of magnitude
Matching the Format to the Audience
| Audience | What they need | Format |
|---|---|---|
| Bedside staff on a unit | Their own unit, current, actionable | One-page run chart posted on the unit, days-since-last-infection counter, specific practice asks |
| Unit managers | Comparison to peer units and to goal | Trended rates with numerator/denominator and process measure compliance |
| Infection Prevention Committee | Facility-wide picture with context | SIRs vs. national benchmark, control charts, action plans by owner and due date |
| Executive leadership / board | Risk, regulatory standing, resources | Short dashboard: goal, current, trend arrow, financial and regulatory exposure, the specific ask |
| Public health | Case-level reportable data | Line lists and required reporting formats |
Universal presentation discipline: start the y-axis at zero unless there is a stated reason not to (a truncated axis manufactures dramatic-looking change), annotate interventions directly on the chart so viewers can see what happened when, label axes with units and denominators, and state the time period explicitly.
An infection preventionist reports post-operative length of stay for a surgical service. Most patients stay 3 to 5 days, but two patients with complications stayed 40 and 52 days. Which measure of central tendency best represents the typical patient?
On a run chart of monthly hand hygiene compliance, seven consecutive points fall above the median. What does this indicate?
A control chart of monthly CLABSI rates shows all points within the upper and lower control limits, fluctuating month to month. Leadership requests a root cause analysis because this month's rate is higher than last month's. What is the most appropriate response?
A 6-bed specialty unit reports 200 catheter days and 1 CAUTI this quarter, yielding a rate of 5.0 per 1,000 catheter days. What is the most appropriate way to present this to the Infection Prevention Committee?