Tables & Figures That Don't Lie

A good display earns its space: it shows a pattern faster than a sentence could, and it tells the truth about how big that pattern is. A bad one does the opposite: it dresses a tiny difference up as a landslide, or buries the real story under decoration. This lesson is about choosing between text, table, and figure, laying an APA table out correctly, and spotting the handful of tricks that make honest data look like a miracle.

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 earns its space 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. A picture beats a table when you want the pattern, not the digits.

And 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. A display nobody points to is a display nobody reads. 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 identical skeleton, which is about the most common formatting slip in a thesis built from an inherited 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.

That last rule is where sixth-edition habits show. Under APA 6 a figure's caption sat below the image while a table's title sat above it, so the two looked nothing alike; the seventh edition made them twins. A document with captions under its figures and titles over its tables was written half in each edition, and a marker who knows the difference will see it in a second. 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 not from fraud but from defaults left on, or flourishes added to "make it pop". The usual suspects:

• Truncated axis. Starting the y-axis at 45 instead of 0 turns a 10% gap into a cliff. This is the single most common way an honest number is oversold.
• 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, or you've hidden half the story.
• Unsorted or cherry-picked categories. Ordering bars by value (not alphabetically) makes honest comparison easy; hiding inconvenient categories makes it impossible.

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 durable piece of figure folklore, and it is wrong in both directions depending on which bar you drew. The arithmetic is small enough to do here. 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.

So where does .05 sit? Between them. 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 move with sample size (at n = 20 per group the touching-CI p is .007; in a huge sample it settles at .006), so they work as a reading habit rather than a calculation.

Three conditions come attached, and the last one bites hardest. The groups need similar sample sizes, they need similar spread, and they must be independent. In a within-subjects design the picture stops working altogether, because each condition's error bar carries the differences between people, which the paired test never looks at. 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

Here's 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 screams "Method C wins!" Turn the tricks off one at a time and watch the miracle shrink to what the data actually say, a difference of a few points.

Problem 42 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.