Although unbiasedness is a basic property of a good test, many tests on vector parameters or scalar parameters against two-sided alternatives are not finite-sample unbiased. This was already noticed ...

Jun Shao, Hansheng Wang, Sample Correlation Coefficients Based on Survey Data under Regression Imputation, Journal of the American Statistical Association, Vol. 97, No. 458 (Jun., 2002), pp. 544-552 ...