Glucose measurement, answer 9

Question 9: For glucose, are these assumptions met? What would be the consequences of any failure to meet the assumptions here?

Suggested answer:

The assumptions are not met.

The plot of difference against the average of the two measurements shows quite clearly that the mean difference changes, being positive for small glucose and negative for large glucose. The spread of the differences may also increase, but it is difficult to tell.

The distribution of the differences is not Normal. There are a lot of fairly small positive differences and a few large negative differences. The distribution is clearly left or negatively skew.

The effect is to invalidate the limits of agreement. They should not be the same for all magnitudes of glucose. If we estimated limits of agreement which depended on the magnitude of glucose, they would be narrower than those given and the limits would get smaller (i.e. more negative) as the magnitude increased. (There is a method to do this.)

The number of observations outside the limits is 4 out of 88, which is 4.5%, close enough to the 5% we want. The limits are not completely wrong, but we could do better.

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