A Bland-Altman plot is used to visualize the differences in measurements between two different instruments or two different measurement techniques.
It is often used to assess how similar a new instrument or technique is at measuring something compared to the instrument or technique currently being used.
The x-axis of the plot displays the average measurement of the two instruments and the y-axis displays the difference in measurements between the two instruments.
The following three lines are also shown in the plot:
- The average difference in measurements between the two instruments
- The upper limit of the 95% confidence interval for the average difference
- The lower limit of the 95% confidence interval for the average difference
This type of plot is useful for determining two things:
1. What is the average difference in measurements between the two instruments?
The horizontal line drawn in the middle of the chart shows the average difference in measurements between the two instruments. This value is often referred to as the “bias” between the instruments.
The further this value is from zero, the larger the average difference in measurements between the instruments.
2. What is the typical range of agreement between the two instruments?
The upper and lower confidence interval lines gives us an idea of the typical range of agreement between the two instruments. In general, 95% of the differences between the two instruments fall within these confidence limits.
The wider the confidence interval, the wider the range of differences in measurements between the two instruments.
The following step-by-step example shows how to create and interpret a Bland-Altman plot from scratch.
Note: A Bland-Altman plot is sometimes referred to as a Tukey mean-difference plot. These names are used interchangeably.
Step 1: Collect the Data
Suppose a biologist wants to know how similar two different instruments are at measuring the weight of frogs, in grams. He uses two instruments (A and B) to weight the same set of 20 frogs.
The weight of the frogs, as measured by each instrument, is shown in the following table:
Step 2: Calculate the Average Measurement & Difference in Measurements
Next, we will calculate the average measurement ( (A+B)/2 ) and the difference in measurements (A-B) for each frog:
Step 3: Calculate the Mean Difference & Confidence Interval
The average of the values in the Difference column turns out to be 0.5.
The standard deviation of values in the Difference column turns out to be 1.235.
The upper and lower limits of the confidence interval for the average difference can be calculated as:
Upper Limit: + 1.96*s = 0.5 + 1.96*1.235 = 2.92
Lower Limit: – 1.96*s = 0.5 – 1.96*1.235 = -1.92
Here’s how to interpret these values:
- On average, instrument A weighs frogs to be 0.5 grams heavier than instrument B.
- 95% of the differences in weight between the two instruments are expected to fall in the range of -1.92 grams and 2.92 grams.
Next, we’ll create a Bland-Altman plot to visualize these values.
Step 4: Create the Plot
Next, we can create the following plot that shows the average measurement of the two instruments on the x-axis and the difference between measurements on the y-axis.
We can also add a horizontal line at the mean difference between the measurements (0.5) along with an upper confidence limit (2.92) and a lower confidence limit (-1.92) that we calculated in the previous step: