Standardised adjusted expectations

 

We standardise each adjusted expectation to have expectation zero and variance unity, and evaluate these standardised quantities as follows:

How do we interpret such values? For the change in expectation is about 0.93 standard deviations upward, a change that doesn't trouble us greatly. However, the change for is fractionally over two standard deviations, and so is somewhat larger than we would have expected: for a reduction in variance of only about 5%, we saw a relatively large change in expectation.

These standardised values serve as diagnostic flags. Here we have seen a value larger than expected, and we should consider the following possibilities:

• the data are more variable than expected, as is further from than expected;
• the resolved variation is smaller than would be consistent with such a change in expectation, implying that the prior variance is too tight.