Introduction to Mixed Modelling: Beyond Regression and Analysis of Variance, 2nd Edition

3.11 Comparison of a variance component estimate with its standard error

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

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can be rejected. If H₀ is true, the ratio

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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

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(For an account of the normal ...