What this answers

This calculator answers "do these two methods agree closely enough to be used interchangeably, and is there a systematic bias where one method consistently reads higher or lower than the other?" A high correlation between two methods can mask a large but consistent offset that correlation alone would never reveal.

How it is calculated

For each pair of measurements, this calculator computes the average of the two values and the difference between them (Method A minus Method B). The bias is the mean of all those differences, showing any systematic offset between methods. The 95% limits of agreement are the bias plus and minus 1.96 times the standard deviation of the differences, the range within which about 95% of the differences between the two methods are expected to fall.

Worked example

For Method A reading consistently 1 unit higher than Method B across every pair, the bias is exactly 1, and because every difference is identical, the standard deviation of the differences is 0, giving zero-width limits of agreement, correctly reflecting a perfectly consistent (if biased) relationship between the two methods.

Assumption audit

Calculated from your data: every pair's average and difference, the overall bias, and the 95% limits of agreement.

Evidence to review: whether the differences look roughly constant across the full range of measured values, or whether they grow or shrink as the measured quantity gets larger; a Bland-Altman plot (built from this calculator's output points) makes that pattern, if present, immediately visible.

You must verify: that both methods measured the exact same underlying quantity on the exact same subjects or samples, and that neither method is being treated silently as a "gold standard" unless it genuinely is one.

What this result does not mean

Limits of agreement describe the expected spread of disagreement between methods; they are not a formal pass/fail validation threshold on their own. Whether a given bias and spread are "acceptable" depends entirely on the practical consequences of that much disagreement in your specific application, a judgment this calculator cannot make for you.

Limitations

This calculator assumes the differences are reasonably normally distributed and do not systematically change in magnitude across the measured range; a visibly increasing or decreasing spread in the plotted differences typically calls for reporting proportional (percentage-based) limits instead of a single fixed-width limit.