Tables & Figures That Don't Lie

A good table or figure shows a pattern faster than a sentence could, and it shows accurately how big that pattern is. A bad one makes a tiny difference look huge, or hides the main result under decoration. This lesson covers choosing between text, table, and figure, laying out an APA table correctly, and spotting the common tricks that make ordinary data look dramatic.

Text, table, or figure?

Pick the lightest tool that does the job. Two or three values belong in a sentence ("recall rose from 24.1 to 28.4"), not a table with two rows. A table is the right choice when the reader needs the exact values, or many of them: several groups × several measures, model coefficients, descriptive summaries. A figure is right when the shape of the data is the point, as with a trend, a distribution or an interaction.

Every table and figure must be referred to in the text ("as Figure 1 shows…") and be understandable on its own, through its title and notes. Once you've settled on a figure, the chart chooser narrows which kind, and names the classic mistake that goes with each.

APA table anatomy

APA tables are deliberately spare. The rules that trip students up:

• No vertical lines, ever. Only horizontal rules: one under the title row, one under the column headers, one at the bottom. White space separates the columns.
• A numbered title above the table (Table 1, then an italicized descriptive caption on the next line).
• Decimals aligned, with a consistent number of decimal places down each column.
• Notes underneath for abbreviations, the meaning of the error term, and significance markers.

Figures have that same anatomy now

APA 7 gave figures the same structure as tables, and getting this wrong is one of the most common formatting slips in a thesis built from an older template. Above the image: the figure number in bold on its own line (Figure 1), then the title in italics on the next. Below the image: the note, opening with an italicized Note. and a period. Nothing else goes under a figure.

Sixth-edition habits show up here. Under APA 6 a figure's caption went below the image while a table's title went above it, so the two looked different. The seventh edition made them match. A document with captions under its figures and titles above its tables mixes the two editions, and a marker who knows the rules will notice at once. One related detail: the legend naming your bars or lines belongs inside the figure frame, not down in the note.

Figures that lie

Most misleading charts come from software defaults or from decoration added to "make it pop", not from fraud. The common problems:

• Truncated axis. Starting the y-axis at 45 instead of 0 turns a 10% gap into a cliff. This is the most common way a correct number is made to look bigger than it is.
• Dual axes. Two different y-scales on one plot can manufacture a "relationship" between any two lines by sliding the scales around.
• 3-D and chartjunk. Fake depth, gradients, drop shadows, and rainbow palettes add ink but no information, and 3-D actively distorts which bar looks taller.
• No error bars. Bare bars imply the numbers are exact. Show the uncertainty, so the reader can judge the difference against it.
• Unsorted or cherry-picked categories. Ordering bars by value (not alphabetically) makes comparison easy. Hiding inconvenient categories misleads the reader.

Say what the error bars show

An error bar is meaningless until you say what it represents, because three common choices look identical but mean very different things:

• SD shows how spread out the individual data points are. It doesn't shrink with sample size.
• SE shows how uncertain the mean is (SD ÷ √n). Smaller with more data.
• 95% CI gives a plausible range for the true mean (≈ ±1.96 SE), and is the most reader-friendly. See Confidence Intervals.

Always state the choice in the caption ("error bars show 95% CIs"). Bars without a definition can't be interpreted at all.

What overlapping bars actually mean

"Overlapping error bars mean no significant difference" is a common belief, and it is wrong in both directions, depending on which kind of bar you drew. The arithmetic is short. Take two independent groups of 30 with similar spread, and call one group's standard error SE. The difference between the two means has a standard error of SE√2, and everything else follows from that one factor.

±1 SE bars that just touch put the means 2 SE apart, giving t = 1.41 and p = .16, so bars that barely fail to overlap are nowhere near significant. 95% CI bars that just touch put the means 4.00 SE apart, giving t = 2.83 and p = .006. Insisting on a visible gap between two confidence intervals is a far harsher test than α = .05.

The .05 threshold falls between these two cases. Two 95% CIs can overlap by 59% of one arm and still give p = .05, and two ±1 SE bars need a gap of about 0.83 SE, roughly four-fifths of one bar's length. Those proportions hardly change with sample size: at n = 20 per group the touching-CI p is .007, and in a huge sample it settles at .006. So you can use them as a rule of thumb when you read a figure.

Three conditions apply, and the third matters most. The groups need similar sample sizes, they need similar spread, and they must be independent. In a within-subjects design the rule fails completely, because each condition's error bar includes the differences between people, which the paired test removes. Twenty people scoring 50 in one condition and 54 in the other, with a between-person SD of 12, produce 95% CIs of [44.4, 55.6] and [48.4, 59.6]: almost total overlap. The paired test on those same numbers returns t(19) = 4.47, p = .0003. So if your design is repeated measures, plot the differences instead, or say in the caption that the bars are between-subject and can't be read against each other.

Fix this chart

Below is a chart of exam scores under three teaching methods, drawn with every trick switched on: a chopped axis, fake 3-D, chartjunk, no error bars, and bars in no useful order. It suggests that Method C wins by a lot. Turn the tricks off one at a time and the difference shrinks to what the data show: a few points.

Problem 99 of the practice problems asks whether a client should spend two million on the strength of one 3-D bar chart with a truncated axis.