A survey of 300 households reports “average monthly income of 2,500”. A closer look at the data shows a median of about 1,200: a handful of very high earners doubled the mean. The statement is arithmetically correct and still gives readers the wrong picture of a typical household.
Descriptive statistics are often treated as the easy part, dashed off before the “real” analysis. In fact they are where reviewers first check whether authors understand their own data. A poorly presented Table 1 means every later analysis is read with suspicion.
Look before you calculate
Before computing anything, draw a histogram or boxplot for every continuous variable. Answer three questions:
- Is the distribution clearly skewed? Income, length of hospital stay, citation counts and many biochemical measures are typically right-skewed.
- Are there outliers, and are they errors or real values? An age of 250 is an error; a very high income may be genuine.
- Do values pile up somewhere? Lots of zeros, or bunching at the top of a scale (a ceiling effect).
Ten minutes with plots often reveals problems that ten pages of tables hide.
Mean or median?
| Situation | Centre | Spread |
|---|---|---|
| Roughly symmetric, no extreme values | Mean | Standard deviation (SD) |
| Clearly skewed or with extreme values | Median | Interquartile range (IQR, 25th to 75th percentile) |
| Ordinal scale with few levels, such as a single 5-point Likert item | Median or frequency distribution | IQR or percentage at each level |
| Very small sample | Median, with minimum and maximum | Range |
A quick check: for a variable that cannot be negative, such as time or cost, an SD larger than about half the mean almost always signals skew. A mean hospital stay of 6 days with an SD of 9 days cannot come from a symmetric distribution without negative values. Report the median and IQR.
SD and SE are not interchangeable
The standard deviation (SD) describes how individuals in the sample vary around the mean. The standard error of the mean (SE) describes how the estimate of the mean would vary across repeated samples. SE = SD / √n.
Example: 100 students have a mean score of 70 with an SD of 10. SE = 10 / 10 = 1. Writing “70 ± 1” suggests the students scored almost identically, when in fact most fall between roughly 60 and 80.
The rule: use SD to describe your sample, and use confidence intervals to express the precision of an estimate, which are easier to interpret than the SE. Always state whether the figure after ± is an SD or SE; journals regularly send papers back over this alone.
Categorical variables: always show the denominator
- Report n (%) with both count and percentage, for example 84 (42%).
- With missing data, show the denominator, “84/196 (43%)”, or add a “missing” row. A percentage of 200 and of 196 are different numbers.
- For multiple-response questions, percentages can exceed 100%; say so in a footnote.
- Never report a percentage for a tiny group without the count: “50%” of four people is two people.
Decimal places: false precision is an error
Reporting a mean age of 34.5271 years does not make a study more precise; it just makes the table harder to read. As a general guide, give means and SDs one decimal place beyond the precision of measurement; percentages from samples of a few hundred rarely need decimals; give p values to two or three decimals and write “p < 0.001” when very small. Use a decimal point in English and be consistent throughout.
Table 1: describing your sample
Table 1 describes who is in the study. The usual layout is one row per variable, with columns for the whole sample and each comparison group. Points experienced reviewers look for:
- State the format in the column heading or a footnote: “mean (SD), median [IQR] or n (%)”.
- In randomised trials, do not test baseline differences with p values. If randomisation worked, any baseline differences are due to chance by definition, and CONSORT advises against such tests. Look at the size of differences instead.
- In observational studies, consider reporting standardised differences to show how far groups diverge.
- Order variables logically: demographics first, then clinical or academic characteristics, then exposures.
In practice: a descriptive statistics checklist
- Every continuous variable has been plotted.
- Outliers have been checked and the handling documented.
- Skewed variables are reported as median [IQR], symmetric ones as mean (SD).
- Every ± is labelled as SD.
- Categorical variables show n and %, with denominators where data are missing.
- Decimal places are sensible and consistent.
- Table 1 has a format footnote and no baseline p values if the study is randomised.
- Numbers in the text match numbers in the tables.
The last item sounds obvious but is one of the errors reviewers catch most often, usually after a table has been updated and the text has not.
Next step: open your dataset, plot a histogram for every continuous variable before calculating anything, and flag which ones need medians. Getting the description right from the start means every analysis that follows is read with confidence.
Câu hỏi thường gặp
When should I use the median instead of the mean?
When the distribution is clearly skewed or has extreme values, as with income, costs or length of stay. Report the median with the interquartile range.
What is the difference between SD and SE?
The SD describes how individuals vary around the mean. The SE describes the precision of the estimated mean and equals the SD divided by the square root of the sample size. Use the SD to describe a sample.
Should Table 1 include p values?
Not in randomised trials, where baseline differences are due to chance and CONSORT advises against testing them. In observational studies, standardised differences are often more informative than p values.
How many decimal places should I report?
Means and SDs usually take one decimal place beyond the measurement precision, and percentages from modest samples rarely need decimals. Consistency across the paper matters most.
Should Likert data be reported as mean or median?
For single Likert items with few levels, the median or a frequency distribution represents the data more honestly. For summed scale scores, the mean and SD are generally accepted.
