Bland–Altman Plot Maker

How to Use the Bland–Altman Plot Maker

1. 1. Paste the pairs. Two columns, one subject per row: the reading from method A, then from method B. Copy from a spreadsheet or type with tabs, commas or spaces. A header row names the axes.
2. 2. Choose what to plot. Raw differences suit most data. If the scatter widens as measurements grow, switch to percentage differences or to ratios on the log scale.
3. 3. Set your criterion (optional). Enter the largest difference you would accept clinically or scientifically — decided before seeing the data — and the page judges the limits against it.
4. 4. Read and download. The plot shows the bias, the limits of agreement and shaded confidence intervals. Download it as SVG or PNG, or copy the results line.

What a Bland–Altman Plot Shows

Two methods can correlate almost perfectly and still disagree: a thermometer that reads 2 degrees high correlates perfectly with a correct one. Bland and Altman (1986) therefore plot each pair's difference against the pair's mean. The average difference d̄ is the bias, and the interval d̄ ± 1.96 s, where s is the standard deviation of the differences, is the 95% limits of agreement: if the differences are roughly normal, about 95% of future differences between the two methods should fall inside it. The 1986 paper rounds 1.96 to 2.

The mean of the pair goes on the x-axis, not either single method, because the difference is mathematically correlated with each method alone; plotting against one of them manufactures a trend. Whether the limits are good enough is a judgement about the measurement, not a statistic — which is why the optional acceptable-difference box exists.

Confidence Intervals for the Bias and the Limits

The limits are estimates too. Bland and Altman (1999) give approximate intervals: the bias is d̄ ± t · s/√n, and each limit is L ± t · s · √(1/n + 1.96²/(2(n − 1))), with t from the t distribution on n − 1 degrees of freedom. With 20 pairs a limit is uncertain by about ±0.81 standard deviations; with 100 pairs, ±0.34. If the outer ends of those intervals are still inside your acceptable difference, agreement is acceptable; if the limits themselves exceed it, it is not; in between, you need more data.

Proportional Bias, Percentages and Ratios

A single bias and fixed limits assume the disagreement is the same across the measurement range. The page regresses the differences on the means: a slope that differs clearly from zero means one method reads progressively higher or lower as values grow. When the spread widens with size, plot percentage differences, or take natural logs and report a ratio (back-transformed bias and limits, such as "A reads 0.99 times B, limits 0.78 to 1.26"). Bland and Altman (1999, section 4) also describe regression-based limits that bend with the mean, which you can draw here.

Worked Example: Two Peak-Flow Meters

Click Load example for the 17 pairs of peak expiratory flow readings (l/min) from the Wright and mini Wright meters in Bland and Altman's 1986 paper. The mean difference is −2.1 and the SD of the differences 38.8, matching the published values.

One of the 17 differences falls outside the limits. The slope has p = 0.749, so there is no sign of proportional bias. The wide intervals around the limits show how little 17 pairs can say: the upper limit alone could plausibly lie anywhere from 39 to 109 l/min, and whether that matters is a clinical question. On the percentage scale the bias is −1.2% with limits of −24.9% to 22.6%; on the ratio scale the geometric mean ratio is 0.988 with limits of 0.778 to 1.255.

• Reporting only the correlation or a paired t-test. Neither measures agreement: a non-significant t-test only says the bias is not clearly nonzero.
• Omitting the confidence intervals. The limits from a small sample are imprecise; show how much.
• Using the method for repeated measures of the same subject without care. Several readings per subject are not independent; the plain formulas here need one pair per subject.
• Ignoring non-normal differences. If the differences are skewed or have outliers, the ±1.96 s interval is a poor guide; look at the plot and consider a transformation.

Frequently Asked Questions

What are the limits of agreement in a Bland–Altman plot?

They are the interval within which about 95% of differences between the two methods are expected to lie, calculated as the mean difference plus and minus 1.96 times the standard deviation of the differences. They describe how far apart two measurements of the same subject by the two methods are likely to be.

How do I interpret a Bland–Altman plot?

Look at the bias (is the middle line away from zero?), the width of the limits (are they narrow enough for your purpose?), and any pattern in the points (a slope, or a funnel that widens at larger means). Then compare the limits, with their confidence intervals, to the largest difference you would accept.

What is a good bias or limit of agreement?

There is no universal value. Bland and Altman stress that acceptable agreement is defined in advance from clinical or scientific requirements, such as the smallest difference that would change a decision. The statistic only estimates the limits.

How many pairs do I need?

There is no fixed minimum, but the precision of the limits depends on n. The interval around each limit is roughly ±0.81 SD with 20 pairs and ±0.34 SD with 100 pairs, so a few dozen pairs is a practical floor and a few hundred makes the limits stable.

When should I use percentage differences or ratios?

When the spread of differences grows with the size of the measurement — common for concentrations and other positive quantities. Percentage differences divide by the mean of the pair. The ratio scale takes logs, then back-transforms the bias and limits, so they read as multiplicative differences; it needs every value above zero.

Is a Bland–Altman plot better than correlation or a t-test?

For agreement, yes. A correlation coefficient measures association, which can be perfect even with a large systematic offset, and a paired t-test only tests whether the average difference is zero. The Bland–Altman plot shows the size and pattern of the differences, which is what agreement means.