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Method Comparison (Bland-Altman)

Analyze → Scale → Bland-Altman. For two methods that measure the same quantity — a new blood-pressure device against the reference sphygmomanometer, a portable meter against the laboratory assay — the question is not whether the methods correlate but whether they agree: can one replace the other without changing the clinical or scientific conclusion? A correlation near 1 cannot answer that — two methods can correlate almost perfectly while one reads consistently 20 units higher, or drifts apart at high values. The Bland-Altman analysis answers the agreement question directly: how far apart are the two methods on the same subject, and how far apart can they be expected to get?

The analysis works on the per-subject differences (method 1 − method 2):

  • the bias — the mean difference, the systematic offset between methods;
  • the limits of agreement — bias ± 1.96 × SD of the differences, the interval expected to cover about 95% of individual differences;
  • the mean-vs-difference plot — each subject's difference against the pair mean, with the bias and limit lines drawn on it.

Whether the limits are acceptable is a subject-matter judgment, made in the measurement's own units and ideally declared before looking: a ±74 l/min disagreement between peak-flow meters means something to a respiratory clinician, not to the statistics.

The data layout

One row per subject, one numeric column per method — the same wide layout as a paired t test. Only rows complete on both methods enter; the output's note counts the complete pairs. (Repeated measurements per subject are a different design — see the scope note below.)

The dialog

Pick Method 1 and Method 2 — the differences are method 1 − method 2, and every table names that direction, so choose the order you want to read (convention: the new or test method first, the reference second; a positive bias then means the new method reads higher). The confidence interval dropdown (90/95/99%) sets the level of the confidence intervals only — the limits of agreement themselves always use 1.96. Plot mean vs difference (on by default) draws the plot.

Reading the output

  • Bland-Altman Statistics — one row per quantity, each with its confidence interval:
    • Bias (Mean Difference) — the systematic offset. Its CI answers "is the bias distinguishable from zero?" — but a tiny, certain bias can matter less than wide limits, so read on.
    • Std. Deviation of Differences — the spread the limits are built from.
    • Lower / Upper Limit of Agreement — bias ± 1.96 × SD: roughly 95% of individual differences are expected to fall between them. These, not the bias, are the agreement verdict — compare them against the difference you could tolerate clinically or scientifically. Their CIs (t-based, using Bland & Altman's 1999 exact variance) show how precisely the limits themselves are estimated — with few subjects the limits are themselves uncertain, and the CI says by how much.
    • The note carries the complete-pair count and the exact conventions.
  • Proportional Bias — a regression of the differences on the pair means. A slope distinguishable from zero means the disagreement changes with the size of the measurement (e.g. the methods agree at low values and drift apart at high ones); the level bias line and limits then average over a trend, so read the plot and consider whether a single pair of limits is a fair summary. With a near-zero slope, the intercept simply restates the bias.
  • Bland-Altman Points — the plot's own (mean, difference) coordinates, printed so the figure's data exports like any table.
  • The plot — the points with a solid line at the bias and dashed lines at both limits, each labelled with its value. What to look for: points scattered evenly in a level band (good — the limits summarize fairly); a fan or slope (proportional bias — see the table above); isolated far points (subjects the methods genuinely disagree on — investigate them, don't delete them).

Worked reading (the 1986 peak-flow data)

On Bland & Altman's own peak-flow data (a Wright meter against the Mini Wright, 17 subjects), the bias is −2.1 l/min — essentially no systematic offset — but the limits of agreement run from −78 to +74 l/min: for an individual patient the two meters can disagree by over 70 l/min in either direction, far more than a clinician would accept, and the near-zero bias (and a correlation of 0.94) would never have revealed it. That is the method's whole point.

Relation to the other agreement tools

  • Intraclass Correlation — agreement of two or more raters as a single relative index (0–1), scale-free. Bland-Altman instead states agreement between two methods in the measurement's own units — preferred when "how many l/min apart?" is the question that matters.
  • Cohen's kappa (in Crosstabs) — agreement on categorical ratings.

Scope (v1). The classic single-measurement design: the limits use the literal 1.96, differences are raw (no percentage or ratio variant), and repeated measurements per subject are not covered — the repeated-measures Bland-Altman (within-subject variance components) is a recorded follow-up. A frequency weight (Weight Cases) is honored as case replication; a declared survey design is not covered and the output says so.