How do I enter paired data?

Put one number per line in each column, with corresponding measurements on the same row. The columns must contain the same number of rows, from 2 to 10,000 pairs. Decimal and scientific notation are accepted. Interior blank rows, nonfinite values and extra text are reported with the column and row; no invalid row is silently dropped.

How do I make a Bland-Altman plot here?

Enter the two aligned columns, choose A minus B or B minus A, and select Create plot. The starting example is ready to calculate. The chart and paired-values table appear after a successful calculation. Changing any input clears the result, so select Create plot again before downloading the current chart or data.

What is a Bland-Altman plot, and what does each point show?

The horizontal position is the pair mean, (A + B) / 2. The vertical position is the signed difference, either A minus B or B minus A. For A = 1, 2, 3 and B = 2, 2, 4, the pair means are 1.5, 2 and 3.5, and the A-minus-B differences are -1, 0 and -1.

How are bias and limits of agreement calculated?

The mean difference, sometimes called bias, is the average of the signed differences. Sample standard deviation uses the sum of squared deviations divided by n minus 1. The two reference lines are the mean difference minus and plus 1.96 times that sample standard deviation. These are often called normal-approximation limits of agreement; the chart labels them reference lines. In the three-pair example, the mean is -2/3 and the sample SD is the square root of 1/3.

How do I read and interpret the plot?

Start with the chosen difference direction. With A minus B, a negative mean difference means A is lower on average; a positive mean means A is higher on average. The vertical spread shows how much the individual differences vary around that mean. Inspect the paired-values table for individual observations. The normal approximation is most informative when independent pairs have approximately normally distributed differences with similar spread across the measurement range; the lines do not guarantee that 95% of this sample falls between them.

What can proportional bias look like on the plot?

An upward or downward pattern in the differences as pair means increase can suggest that the difference depends on measurement size, often called proportional bias. A widening vertical spread is a different pattern: variability changes with size. This chart supports visual inspection but does not fit a regression line, estimate a slope or test proportional bias.

How does a Bland-Altman plot differ from correlation?

Correlation describes how two columns vary together. A Bland-Altman plot displays their signed differences across the measurement range. Two columns separated by a constant nonzero offset can rise together perfectly while every difference remains nonzero. This tool plots those differences and does not calculate a correlation coefficient.

Do the reference lines show whether two methods are interchangeable?

No. These are descriptive normal-approximation reference lines for the recorded differences. They do not establish acceptable error, clinical agreement, quality certification or interchangeability. The tool does not provide an acceptability verdict or confidence intervals for the reference lines.

What changes when I reverse the difference direction?

Switching from A minus B to B minus A negates every difference and the mean difference. The pair means and sample SD stay the same. The lower and upper reference lines become the negated previous upper and lower lines. Create the plot again after changing direction so every output uses the current settings.

What happens with identical columns or extreme numbers?

Identical columns produce zero differences, zero mean difference and zero sample SD, so all three lines coincide. Constant plot values receive display padding. Scaled and compensated calculations reduce avoidable numeric overflow, but values or reference lines that cannot be represented in browser numeric precision produce an explicit request to rescale the measurements.

What do the SVG, PNG and CSV downloads contain?

SVG and PNG contain the complete chart, labels, pair count, numerical summary and descriptive caveat. CSV contains every original pair, pair mean and signed difference with unrounded numeric values. Display precision affects chart and table text, not the calculations or CSV numbers. The visible table is paged in groups of 100 rows. If PNG preparation fails, the SVG remains available.

Are my measurements uploaded or saved?

The calculations and exports run in your browser. Measurements stay in memory and are not uploaded or written to local storage. Edited column labels, direction and display precision may be remembered in this browser. Restoring those preferences does not run an analysis.

Bland–Altman Plot

Turn two paired numerical columns into a difference plot, with every pair available in a table. Choose the difference direction, label the columns and inspect the mean difference, sample standard deviation and 1.96 SD reference lines before exporting the chart or paired data.

Means and differencesDescriptive paired-data analysis · up to 10,000 pairs

Paired numerical columnsOne value per line

Column AColumn B

Column A labelColumn B label

Difference directionDisplay decimal places0 to 10; calculations keep full precision.

Use 2 to 10,000 paired finite numbers. Interior blank rows are errors. Measurements stay in memory; only display preferences are saved after edits.

Difference plotAwaiting analysis

See the difference between pairsEnter aligned measurements and create a plot. Each dot will show a pair's mean and signed difference.

Reference lines describe the sample.
They are not acceptable-error thresholds or evidence that two methods are interchangeable.

Example pairs are ready. Choose Create plot to calculate them.

Pairs: Not analyzed

Mean difference: Awaiting result

Sample SD: Awaiting result

Direction: A minus B

Worked examples

Three pairsA: 1, 2, 3; B: 2, 2, 4
Means: 1.5, 2, 3.5. Differences: −1, 0, −1. Mean difference −2/3; sample SD √(1/3).
Reverse directionB minus A for the same pairs
Mean difference +2/3; pair means and sample SD stay the same.
Identical columnsA: 1, 2; B: 1, 2
Mean difference 0; sample SD 0. All three reference lines coincide.

Accuracy. Descriptive statistics only. Reference lines are normal-approximation summaries, not acceptable-error thresholds or evidence that methods are interchangeable. No medical or quality-certification verdicts.

Common questions

How do I enter paired data?: Put one number per line in each column, with corresponding measurements on the same row. The columns must contain the same number of rows, from 2 to 10,000 pairs. Decimal and scientific notation are accepted. Interior blank rows, nonfinite values and extra text are reported with the column and row; no invalid row is silently dropped.
How do I make a Bland-Altman plot here?: Enter the two aligned columns, choose A minus B or B minus A, and select Create plot. The starting example is ready to calculate. The chart and paired-values table appear after a successful calculation. Changing any input clears the result, so select Create plot again before downloading the current chart or data.
What is a Bland-Altman plot, and what does each point show?: The horizontal position is the pair mean, (A + B) / 2. The vertical position is the signed difference, either A minus B or B minus A. For A = 1, 2, 3 and B = 2, 2, 4, the pair means are 1.5, 2 and 3.5, and the A-minus-B differences are -1, 0 and -1.
How are bias and limits of agreement calculated?: The mean difference, sometimes called bias, is the average of the signed differences. Sample standard deviation uses the sum of squared deviations divided by n minus 1. The two reference lines are the mean difference minus and plus 1.96 times that sample standard deviation. These are often called normal-approximation limits of agreement; the chart labels them reference lines. In the three-pair example, the mean is -2/3 and the sample SD is the square root of 1/3.
How do I read and interpret the plot?: Start with the chosen difference direction. With A minus B, a negative mean difference means A is lower on average; a positive mean means A is higher on average. The vertical spread shows how much the individual differences vary around that mean. Inspect the paired-values table for individual observations. The normal approximation is most informative when independent pairs have approximately normally distributed differences with similar spread across the measurement range; the lines do not guarantee that 95% of this sample falls between them.
What can proportional bias look like on the plot?: An upward or downward pattern in the differences as pair means increase can suggest that the difference depends on measurement size, often called proportional bias. A widening vertical spread is a different pattern: variability changes with size. This chart supports visual inspection but does not fit a regression line, estimate a slope or test proportional bias.
How does a Bland-Altman plot differ from correlation?: Correlation describes how two columns vary together. A Bland-Altman plot displays their signed differences across the measurement range. Two columns separated by a constant nonzero offset can rise together perfectly while every difference remains nonzero. This tool plots those differences and does not calculate a correlation coefficient.
Do the reference lines show whether two methods are interchangeable?: No. These are descriptive normal-approximation reference lines for the recorded differences. They do not establish acceptable error, clinical agreement, quality certification or interchangeability. The tool does not provide an acceptability verdict or confidence intervals for the reference lines.
What changes when I reverse the difference direction?: Switching from A minus B to B minus A negates every difference and the mean difference. The pair means and sample SD stay the same. The lower and upper reference lines become the negated previous upper and lower lines. Create the plot again after changing direction so every output uses the current settings.
What happens with identical columns or extreme numbers?: Identical columns produce zero differences, zero mean difference and zero sample SD, so all three lines coincide. Constant plot values receive display padding. Scaled and compensated calculations reduce avoidable numeric overflow, but values or reference lines that cannot be represented in browser numeric precision produce an explicit request to rescale the measurements.
What do the SVG, PNG and CSV downloads contain?: SVG and PNG contain the complete chart, labels, pair count, numerical summary and descriptive caveat. CSV contains every original pair, pair mean and signed difference with unrounded numeric values. Display precision affects chart and table text, not the calculations or CSV numbers. The visible table is paged in groups of 100 rows. If PNG preparation fails, the SVG remains available.
Are my measurements uploaded or saved?: The calculations and exports run in your browser. Measurements stay in memory and are not uploaded or written to local storage. Edited column labels, direction and display precision may be remembered in this browser. Restoring those preferences does not run an analysis.

Descriptive statistics only. Reference lines are normal-approximation summaries, not acceptable-error thresholds or evidence that methods are interchangeable. No medical or quality-certification verdicts.