As before (Section 3.4), each variance component in the output of the
REML statement is accompanied by an SE: for example, the variation among breeding lines is estimated to be ± 6242. This SE provides an indication of the precision with which the variance component is estimated. It may also provide a tentative indication of whether any variation is really accounted for by the term under consideration: that is, whether the null hypothesis
can be rejected. If H0 is true, the ratio
is expected to have a value of about ±1, on average. In the present case,
This is considerably larger than the expected value, suggesting that H0 is false.
If were an observation of a normally distributed variable, this ratio could be made the basis for a formal significance test. z would then be approximately an observation of a standard normal variable: that is, of a variable Z such that
(For an account of the normal ...