9.2 Descriptive Statistics for Patient Experience Data

9.2 Descriptive Statistics for Patient Experience Data

Quick Answer: Domain 2 of the CPXP Classification System names descriptive statistics as a required knowledge statement and applying descriptive statistics to analyze data as a required skill, and the official reference list includes a descriptive statistics text. You need four things cold: measures of center (mean, median, mode), measures of spread (range, interquartile range, variance, standard deviation), distribution shape (why experience data is negatively skewed), and the arithmetic of sampling (standard error, margin of error, confidence interval). Everything in Sections 9.3 and 9.4 rests on this.

The single most damaging habit in patient experience reporting is treating a small monthly sample as if it were a census: "we dropped four points last month" launches an improvement project against random noise, and the noise reverses next month, and the project takes credit.

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Measures of Center

Worked example — why this matters. Complaint resolution days for eight cases: 2, 2, 3, 3, 4, 5, 6, 47.

• Mean = 72 / 8 = 9.0 days
• Median = (3 + 4) / 2 = 3.5 days
• Mode = 2 and 3 (bimodal)

Reporting "average resolution 9 days" misrepresents typical performance for seven of eight cases. Report the median as typical performance and investigate the 47-day case as a defect, not as a data point to average away.

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Measures of Spread

• Range = maximum − minimum. Fast, but determined entirely by two extreme values.
• Interquartile range (IQR) = Q3 − Q1, the middle 50% of observations. Robust to outliers and the right companion to a median.
• Variance = the average squared deviation from the mean.
• Standard deviation (SD) = the square root of the variance, expressed in the original units. Roughly, how far a typical observation sits from the mean.

The rule the exam likes: report mean with standard deviation, or median with IQR. Mixing them — a median paired with a standard deviation — signals that the analyst does not know which question they are answering.

Standard deviation vs. standard error: not interchangeable

Because SEM shrinks with √n, precision improves slowly: quadrupling your sample only halves the margin of error. This is the central sampling fact in patient experience measurement.

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Distribution Shape: Why Experience Data Is Negatively Skewed

        TYPICAL PATIENT EXPERIENCE SCORE DISTRIBUTION

   frequency
      |                                        ####
      |                                     #########
      |                              ##################
      |            ______________#########################
      +------------------------------------------------------> score
        0                                                 100
        ^ long LEFT tail                    ^ dense pile at the TOP
        (few very negative)                 (most responses positive)

        NEGATIVELY (LEFT) SKEWED:  mean < median < mode

Most patients rate most encounters positively, so the bulk of responses pile up near the top of the scale with a thin tail of very negative responses. Three consequences follow directly:

1. The mean is dragged below the median by the negative tail, so the mean understates typical experience.
2. Small raw differences translate into large percentile swings — the compression effect covered in Section 9.3. Because hospitals cluster tightly at the top, a two-point top-box difference can move a hospital through many percentile ranks.
3. Top-box scoring is a deliberate response to the ceiling. When almost everyone answers positively, a mean loses discriminating power. Requiring the single most positive category restores variance where it matters.

Percentile vs. percentile rank — a distinction the exam tests:

• A percentile is a score value below which a given proportion falls. "The 90th percentile is 84.2% top-box."
• A percentile rank is a position. "Our 84.2% places us at the 90th percentile rank." Reporting "we are at the 90th percentile" without naming the comparison database is meaningless, because the peer group determines the rank entirely.

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Sampling Arithmetic: Telling Signal from Noise

Experience scores are usually proportions (percent top-box). The standard error of a proportion is:

$SE_p = \sqrt{\frac{p(1-p)}{n}}$

and the approximate 95% confidence interval is $p \pm 1.96 \times SE_p$.

Worked example. A unit reports 75% top-box on nurse communication from n = 30 responses.

• $SE_p = \sqrt{(0.75 \times 0.25) / 30} = \sqrt{0.00625} = 0.0791$
• Margin of error = $1.96 \times 0.0791 = 0.155$, about ±15.5 percentage points
• 95% CI ≈ 59.5% to 90.5%

Now suppose next month the same unit reports 68%. The confidence intervals overlap heavily. There is no evidence of a real decline. The correct report is: "Nurse communication is 68% (95% CI 51–85%, n = 28), not statistically distinguishable from last month."

The practical rule: at typical unit-level monthly volumes, only large movements are real. This is why credible experience reporting aggregates to rolling four-quarter windows for unit-level comparisons and uses run charts or control charts — which distinguish common-cause variation from special-cause signals — instead of month-over-month deltas. See Section 9.5.

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Six Errors That Recur in Experience Reporting

1. Comparing two small monthly samples without confidence intervals and declaring a trend.
2. Averaging percentages of unequal-sized groups. Combining a 90% top-box unit (n = 10) with a 60% unit (n = 200) gives 74% only if you weight by n; the unweighted mean of 75% is wrong.
3. Reporting a mean on skewed data such as wait time or resolution days, where the median is the honest statistic.
4. Confusing SD with SEM, producing intervals that are far too wide or too narrow.
5. Over-stratifying a small sample. Splitting 40 responses across six subgroups yields cells too small to interpret — a direct constraint on the equity analysis in Section 2.4.
6. Ignoring response rate and nonresponse bias. A 12% response rate does not invalidate the data, but the respondents may differ systematically from non-respondents; patient-mix adjustment corrects some of this, not all of it.

How to phrase it to leadership: "This looks like normal variation, not a change" is a complete, defensible, and professionally credible finding. Manufacturing a narrative from noise is the fastest way to lose the standing you need when a real signal does appear.