Figures and graphs

Graphs reveal distributions, comparisons, relationships and change. Their form, scale, labels and supporting text determine which features of the data a reader can see and interpret.

Exploring and explaining data

Summary statistics can conceal different data patterns: Anscombe's quartet contains four datasets with matching x and y means, variances and correlations, yet plotting reveals a scattered linear pattern, a curve and patterns dominated by outliers. ^{1, 2, 3} Exploratory visualisation examines the whole dataset before a main message has been identified; explanatory visualisation communicates a particular finding after analysis, often using selected data in a report's results section. ^{4, 5}

A graph should answer a question and convey one main message rather than act as a store for everything collected. ^{6, 7} Two or three simple figures can communicate more effectively than one complicated display. ^{8, 9} Preparation should establish three things: ^{10, 8, 9, 11}

1. Identify the audience, the detail it needs and the chart forms it can readily interpret.
2. Identify the main message.
3. Identify the medium: a slide needs immediate comprehension, while a report can accommodate more detail.

^{10, 8, 9, 11}

A hand-drawn sketch helps organise ideas and agree the strategy before software work; a polished slide draft can draw feedback towards colours, font sizes and fit instead. ^{11, 12} Unfamiliar chart forms may meet resistance among clinicians and researchers, and even experienced audiences may not spend time deciphering a complex graph. ^{13, 14}

Encoding and choice of form

Graphs encode values through visual attributes: bars use length or height, while scatter plots use position. ¹⁵ The intended question, message and variable type guide the choice of representation. ^{6, 16} A country variable does not automatically require a map, and percentages summing to 100 do not automatically require a pie chart. ^{17, 18}

For example, a chart of migrants arriving in Greece in 2016 could use a pie to show that nearly half came from Syria, with Syria highlighted against all other countries; bars would better compare individual countries, and a map would serve a question about geographic patterns. ^{19, 20, 21, 18} The same data can therefore need different displays for different questions. ¹⁷

Common alternatives by purpose include: ²²

Purpose	Options
Change over time	Line graph; column graph; calendar heat map; circle timeline
Comparison	Paired column graph; proportional symbol; radar graph; parallel coordinates
Part-to-whole relation	Pie chart; stacked column graph; grid plot; tree map
Correlation	Scatter plot; line-plus-column graph; bubble chart

²²

Bars and lines

Bar charts compare values across categories, and sorting them ascending or descending can make ranking easier, depending on the intended comparison. ^{23, 24, 25} Grouped columns can compare populations or reveal subgroup patterns that an aggregate series conceals. ^{26, 27} Stacked segments that do not share a baseline are harder to compare than grouped columns. ²⁸

Line graphs commonly show continuous variation over time. ^{25, 23, 29} Advice differs on using columns for time trends: a clinical-writing guide allows bars for trends, while a scientific-writing guide recommends arithmetic line graphs instead of columns for that purpose. ^{29, 26}

Pie charts

A pie chart readily conveys parts of a whole but makes similar slices difficult to compare because readers must judge areas and angles. ^{30, 21, 23, 14} Its categories should be mutually exclusive proportions summing to 100%; overlapping categories can make that representation false. ^{30, 24}

Recommendations differ on whether to use pies at all. ^{30, 31} A scientific-writing guide recommends generally avoiding pie and three-dimensional charts unless they add value, while the AMA Manual of Style, 11th edition, recommends against pies as often uninformative or misleading and illustrates replacing a complicated pie with a divided bar chart. ^{31, 32} Publication requirements also differ, so the destination's instructions matter. ²⁹

A data-presentation checklist from the 2021 AMWA conference recommends: ²⁸

• Make axis labels clear, accurate and legible.
• Make the finished figure large enough for its details to be visible.
• Keep graphs simple so differences remain discernible; excess non-data ink can mislead.
• For line graphs, use continuous variables, keep each line easy to follow and use a trend line to improve clarity.
• For bars or columns, replace stacked bars with grouped columns and a total column if needed; avoid grey shades or striping vulnerable to print quality; use a table if exact numbers would otherwise be added above bars.
• For pies, use percentages summing to 100 and a message carried by one or two clear segments; start at 12 o'clock, use suitable colours or shades, and identify segments with clear labels or a key.
• Avoid multiple pies because they are difficult to compare.
• Avoid three-dimensional graphs, which can create optical illusions and hide points.

²⁸

Individual observations and summaries

Overlapping points can hide repeated values; spreading them horizontally can reveal their frequency while preserving their measured vertical values. ³³ Individual-point plots suit small datasets, while mean-and-standard-deviation (SD) displays or box plots can summarise larger datasets. ³³ Box plots show the median and quartile distribution, but whiskers can follow different conventions, including full ranges or extreme non-outlying values with outliers drawn separately. ^{33, 34}

A worked concentration dataset illustrates the distinction: 5, 8, 10, 11, 12, 15, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 18, 22, 23 and 27 mg/L had mean 15.5 mg/L, SD 5.0 mg/L and median 16 mg/L. ³³ Dividing the ordered values into lower and upper halves gives a lower-half median of 13.5 mg/L; the box shows the central two quartiles and the remaining quarters extend outside it. ³³

Plots of paired observations can connect each person's before and after measurements to show the direction and variation of change. ^{35, 36} Group means can also conceal individual variation: a dose–Cmax example produced R² = 0.9872 when plotted as means but R² = 0.154 for individual observations. ²⁷ Selecting a more pleasing display should not conceal the spread of the observations. ²⁷

Error bars should represent the quantity intended. ²⁷ Using the smaller standard error does not show the variability that an SD display would show. ²⁷

Axes, scales and definitions

A scatter plot can place a predictor on the horizontal axis and an outcome on the vertical axis, with a fitted line describing their relationship. ³⁷ A straight-line approximation over the middle of a log-concentration–effect curve excludes its near-zero and near-maximal regions. ³⁷

Arithmetic scales show absolute numerical differences, whereas logarithmic scales show proportional change. ³⁸ In a hypothetical first-order elimination curve, successive halvings from 100 to 50, 25 and 12.5 produce a curved arithmetic trajectory and a straight logarithmic one. ³⁸ A log scale can clarify proportional relationships while making large absolute differences appear smaller. ^{38, 27}

Restricting an axis to a narrow range can exaggerate a difference: responder rates displayed on an 80–90% axis appear much further apart than on a 0–100% axis. ²⁷ Other misleading practices include combining different studies in one graph, extrapolating beyond observed data, omitting unfavourable data and leaving axes without parameters or units. ³⁹

Definitions belong beside the visual when ordinary language could mislead. ^{40, 19} In a Florida student-homelessness visualisation, counts included children without a permanent home who moved among relatives' homes, rather than only children living on the street; maps without that definition could suggest the narrower meaning. ^{41, 42, 43, 19}

A four-country quality-of-life display aligned each country’s general-population mean at zero, allowing treatment-response series with different national reference means to be viewed together. ^{44, 45}

Visual contrast and captions

Unnecessary borders, grid lines and frames can be removed to reduce clutter; useful grid lines should remain light. ^{46, 47, 48} Non-data lines can be thin and pale, data lines heavier and darker, and white space can replace rules; distracting bar patterns reduce clarity. ⁴⁸ Tufte-based design advice favours lighter shades and simple patterns over distracting fills, with a white control bar giving that group less visual emphasis. ⁴⁸ These choices increase the data-ink ratio while preserving visual contrast that makes the data apparent. ⁴⁸

Labelling series directly on the lines, in matching colours, avoids repeated movement between a separate legend and the plot. ^{47, 49, 50} A graph and its caption should make sense without searching the surrounding text, with axes, units and symbols explained and formatting consistent across the document. ^{51, 52, 53} Captions normally stay close to the figure, although manuscript submission conventions may collect them separately. ⁵⁴ Caption position follows the target journal or in-house style and should be consistent within the document. ⁵⁵

Proportional-chart captions can state the total, period and source, distinguish actual from budget figures, explain rounding and itemise an “other” category. ^{56, 57, 58, 59} For example, AMWA's 2006–2007 income chart explicitly noted percentages below 100 because of rounding, while the following year's budget chart noted percentages above 100 for the same reason. ^{56, 57}