It is a widely held belief that an anchor test used in equating should be a miniature version (or "minitest") of the tests to be equated; that is, the anchor test should be proportionally representative of the two tests in content and statistical characteristics. This paper examines the scientific foundation of this belief, especially regarding statistical characteristics. In particular, we study, through several simulation studies and a real data example, the correlation of the raw score of the total test with several anchor tests, including those having statistical characteristics that differ from those of the total test. Anchor tests with spread of item difficulties less than that of a total test are shown to consistently have higher correlations than a minitest. Because of the general view that higher correlations of the scores of an anchor test and the total test lead to better equating, our results suggest that requiring an anchor test to mimic the statistical characteristics of the total test may be too restrictive and may not be optimal.