Describing data, reading charts and choosing the right statistical test
Types of data, normal and skewed distributions, mean vs median, SD vs SE, box-and-whisker plots, and a one-table method for choosing the statistical test in any study.
Reviewed and kept current
Last editorial review: 28 September 2026 · Next scheduled refresh: March 2027.
Clinical vignette
Begin with the patient. Read the case, weigh the options, then work through the unit.
Mrs H is being referred to an outpatient clinic. She asks how long she will wait.
The practice has recently audited the number of days from referral to first outpatient appointment for 240 patients. Most were seen within six weeks. A few waited more than a year. The audit summary reports only the mean wait.
Mrs H cares for her grandchildren three days a week. She wants to know whether to rearrange her plans for the next month or for the next year. She is planning her family commitments around your answer.
Options to weigh
- Quote the mean wait from the audit summary.
- Recognise that the waits are skewed by a few very long ones, and ask for the median and interquartile range instead.
- Tell her that most patients in the audit were seen within six weeks, but a few waited much longer.
- Give her a single expected date for her appointment.
Reflect
How would you describe the waiting times so that Mrs H can plan, and what would you be careful not to say?
What this unit covers
Pocket-sized and self-contained: three AKT-style questions, the answers explained, an expanded discussion with hyperlinked guidance, a decision algorithm and a certificate.
By the end of this unit you will be able to
Five steps, in order
Answer first, then learn. Each section unlocks as you progress, and your progress is saved in this browser.
1Three single best answer questions
Commit to an answer for all three single best answer questions, then submit. Sections 2–4 open on submission; your certificate opens at 2/3 or better.
Question 1 of 3
A practice audit records the number of days from referral to first outpatient appointment for 240 patients. A few patients waited more than a year, while most were seen within six weeks.
Which summary is most appropriate?
Question 2 of 3
An annual report presents HbA1c results for four practices as box-and-whisker plots.
What does the horizontal line inside each box represent?
Question 3 of 3
Investigators compare the proportion of current smokers among 300 patients with COPD registered at an urban practice and 280 registered at a rural practice.
Which statistical test is most appropriate?
2Answers explained
Question 1
Correct answer E. Median and interquartile range
Waiting times are positively (right) skewed: a long tail of very long waits drags the mean upwards. The median (the middle value) and interquartile range (25th to 75th centile) are resistant to outliers.
In positive skew, mean > median > mode. Mean and SD are for approximately normal data.
Question 2
Correct answer D. The median
In a box-and-whisker plot the box spans the interquartile range (25th–75th centile), the line inside is the median, and the whiskers usually extend to the most extreme values within 1.5 × IQR (or to the minimum and maximum), with outliers plotted as individual points.
If the median line sits off-centre in the box, or one whisker is much longer, the data are skewed.
Question 3
Correct answer B. Chi-squared test
The outcome (smoker / non-smoker) is categorical, and the two groups are independent. Proportions in independent groups are compared with the chi-squared (χ²) test (or Fisher’s exact test if expected cell counts are small, e.g. below 5).
- t-tests compare means of continuous, normally distributed data.
- Mann–Whitney U compares two independent groups of skewed or ordinal data.
- Pearson’s r measures linear association between two continuous variables.
3Expanded discussion, worked examples & guidance
1. Types of data
| Type | Definition | Examples | Summary |
|---|---|---|---|
| Nominal (categorical) | Named categories, no order | Blood group, ethnicity, smoker yes/no (binary) | Counts, proportions |
| Ordinal | Ordered categories, unequal gaps | NYHA class, pain score, CKD stage | Median, IQR; proportions |
| Discrete (numerical) | Whole-number counts | Number of asthma attacks | Median or mean |
| Continuous (numerical) | Any value in a range | BP, HbA1c, eGFR, weight | Mean ± SD if normal; median (IQR) if skewed |
2. Distributions
In a normal distribution the mean, median and mode coincide. About 68% of values lie within ±1 SD, 95% within ±1.96 (≈2) SD and 99.7% within ±3 SD. Laboratory reference ranges are usually the mean ± 2 SD, so about 5% of healthy people have an “abnormal” result.
Positive (right) skew: tail to the right; mean > median (e.g. income, waiting times, triglycerides). Negative (left) skew: tail to the left; mean < median (e.g. gestational age at birth).
Worked example 1 — reference ranges
Serum sodium in healthy adults is normally distributed with mean 140 mmol/L and SD 2 mmol/L. Within what range would about 95% of healthy adults lie?
- 95% ≈ mean ± 2 SD.
- 140 ± 4.
Answer. 136–144 mmol/L; 2.5% of healthy people would be below 136.
Worked example 2 — SE and a confidence interval
A sample of 100 patients has a mean systolic BP of 150 mmHg with SD 20 mmHg. Estimate the 95% CI for the population mean.
- SE = 20/√100 = 2.
- 95% CI = 150 ± 1.96 × 2 = 150 ± 3.9.
Answer. 146.1 to 153.9 mmHg.
3. Charts in the AKT
- Bar chart — categorical data (bars separated). Histogram — continuous data grouped into ranges (bars touching); shows shape and skew.
- Line chart — change over time (e.g. monthly antibiotic prescribing); look for trend, seasonality and step changes after an intervention.
- Box-and-whisker plot — median, IQR and range; ideal for comparing distributions between practices.
- Scatter plot — two continuous variables; add a regression line and r.
- Funnel plot (control chart) — practices or studies plotted against size with control limits; see Units 9 and 11.
4. Choosing a statistical test
Ask three questions: What type of outcome data? How many groups? Are the groups independent or paired?
| Outcome data | 2 independent groups | 2 paired groups | ≥3 groups | Association |
|---|---|---|---|---|
| Continuous, normal (parametric) | Unpaired t-test | Paired t-test | ANOVA | Pearson r; linear regression |
| Skewed or ordinal (non-parametric) | Mann–Whitney U | Wilcoxon signed-rank | Kruskal–Wallis | Spearman rank correlation |
| Categorical | Chi-squared / Fisher’s exact | McNemar | Chi-squared | Logistic regression |
| Time-to-event | Log-rank test; Cox proportional hazards regression | Hazard ratio | ||
Paired data are two measurements on the same people (before/after) or matched pairs.
5. Correlation vs regression
Correlation (r, from −1 to +1) measures the strength and direction of a linear association; r² is the proportion of variation in one variable explained by the other (r = 0.7 → r² = 0.49, 49%). Regression predicts one variable from another, giving an equation (y = a + bx). Correlation never proves causation.
- “Non-parametric” tests make no assumption of normality; they use ranks.
- An r of −0.9 is a stronger association than +0.5.
- Agreement between two observers on categories is measured by Cohen’s kappa, not by correlation.
References and further reading
Guidance checked at the last editorial review (28 September 2026). Always use the current version.
4Decision algorithm
Choosing the statistical test
Start
What is the outcome variable?
Decision
Is it time-to-event (e.g. time to death or admission)?
Decision
Is it categorical (yes/no, category)?
Decision
Is it normally distributed?
Outcome
Looking at the relationship between two continuous variables? Correlation (Pearson or Spearman) or regression.
Revision summary; apply clinical judgement and local pathways.
5Certificate of completion
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