1. BlandAltman plot
Worked example
Blood pressure by two methods (mm Hg) 
Method 1 
Method 2 
Method 1 
Method 2 
85 82 87 88 90 95 97 101 103 115 
89 97 93 101 105 105 117 106 120 130 
120 122 131 134 140 156 162 170 190 201 
132 129 141 149 145 171 182 179 195 221 
These are data from a study on blood pressure of dogs using two methods of measurement. The first of these (method 1) is the current accepted standard, but is an invasive procedure which carries risks. The second method is a new technique which must be validated against the current standard.
As before, the first step is to plot the practical variable (method 2) against the criterion variable (method 1). In this case the variability does not increase with the mean so no transformation is required. The line of equality is drawn in.

You can see from the graph below that results from the two methods are closely correlated, but method 2 always gives a somewhat higher reading than method 1.
{Fig. 3}
This bias is quantified by plotting for each pair of observations the difference between the two methods against the mean of the two methods, as shown in the second graph above. The mean bias is +11.9 mm Hg  in other words on average method 2 gives a reading 11.9 mm Hg greater than method 1.
The 'limits of agreement' are estimated by multiplying the standard deviation of the differences (5.39) by ±1.96 which gives ±10.6. Hence the lower and upper limits of agreement are 1.3 and 22.5. Providing the differences are normally distributed, and randomly obtained, on average these limits would include 95% of observations.


2. Validating a proxy measure
Worked example
Numbers trapped from populations of known size 
Popn. size 
No. trapped 
Popn. size 
No. trapped 
12 12 12 12 12 35 35 35 35 35 56 56 56 
3 5 3 4 3 8 10 6 9 7 14 18 9 
56 56 79 79 79 79 79 98 98 98 98 98 
12 11 25 15 14 20 22 25 32 17 19 23 
These are data from a study seeking to validate relative population estimates of a small mammal (field mouse) against absolute population size. Live traps are used to sample the mice in artificially established populations of known size.
The first step is to plot the practical variable (numbers trapped) against the criterion variable (population size). The figure below shows clearly that variability increases with mean so each variable is log transformed. The effect of this is shown in the second figure. 
{Fig. 2}
A regression line is then fitted to the data using the standard methods (see popup on graph). If you wish to estimate population size from the trap catch, you would then obtain the calibration equation by rearranging the regression equation, namely:
Population size = [0.44 × trap catch] / 0.891
Obtaining a confidence interval for the estimated population size is slightly problematic since one is using the equation to estimate X from Y rather than vice versa. However, we provide a method to do this in Unit 12

