Since the range of differences between the new and old measurements is pretty high (i.e. Whether we accept the new measurement instrument or not depends on the level of precision that is needed in a particular domain. We add these horizontal lines to the scatter diagram by adding three series to the scatter diagram data, as described in Limits of Agreement for Bland-Altman Plot. Note that the x values for the scatter plot in Figure 2 range from 30 to 80, and so we specify in range V2:Y3 of Figure 4 the endpoints for the three horizontal lines (for the mean and lower and upper limits) shown in Figure 2. We calculate the standard error shown in cells W7 and W8 by the formula The standard error in cell W6 is calculated by the formula =Q5/SQRT(Q3). We see from Figure 4 that = 1.515 (cell Q4) and the limits of agreement are -6.36352 (cell Q7) and 9.393515 (cell Q8). The calculation of the mean and limits of agreement is shown on the left side of Figure 4.įigure 4 – Calculation of Mean and Limits of Agreement the difference values) to check that the normality assumption does indeed hold, as shown in Figure 3.įigure 3 – Shapiro-Wilk and QQ Plot tests for normalityĪs we can see from Figure 2, only one out of the 20 points lies outside the limits of agreement, with the points scattered within the limits of agreement. For this example, we can use the Real Statistics Descriptive Statistics and Normality data analysis tool on the data in range F4:F23 (i.e. That the differences are normally distributed is actually quite likely. Assuming the differences are normally distributed, this would result in a 95% prediction intervalĬalled the limits of agreement, where, as usual, = AVERAGE(F4:F23), s d = STDEV.S(F4:F23) and 1.96 = NORM.S.INV(.975). If there is agreement, we would expect the values in Figure 2 to cluster around the mean of the differences (called the bias), and certainly within 2 standard deviations of the mean. Highlighting range E4:F23, we then select Insert > Chart|Scatter to create the scatter plot shown on the right side of Figure 2. We will explain the horizontal lines shown on the Bland-Altman Plot shortly. We obtain the values in columns E and F by inserting the formula =(A4+B4)/2 in cell E4 and inserting =A4-B4 in cell F4, and highlighting the range E4:F23 and pressing Ctrl-D. This is called a Bland-Altman Plot, and is shown in Figure 2. In order to more readily see the difference between the two measurement instruments, it is useful to plot the means of each pair of measurements ( x value) versus the difference between the measurements (y value). 90, but we would clearly not have agreement between the two measurements. In fact, if we double the data values in column B, the correlation would remain at. 903678.īut, it is important to note that correlation is not the same as agreement. In fact, using the worksheet formula =CORREL(A4:A23,B4:B23), we see that the correlation coefficient is. They do this by taking the measurements of 20 rods using both methods, as shown in Figure 1.įigure 1 – Comparison of two measurement instrumentsĪs we can see from the scatter diagram on the right side of Figure 1, there is a high degree of correlation between the two methods. The management team would like to implement a more cost-effective method (New), but first, they want to make sure there is agreement between the measurements done by these two methods. ExampleĮxample 1: A nuclear power plant has been using a fairly expensive method (Old) for measuring the strength of the rods in the nuclear reactor. it is less expensive or safer to use) over an existing measurement technique. This is especially important if you are trying to introduce a new measurement capability that has some advantages (e.g. Bland-Altman is a method for comparing two measurements of the same variable.
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