Using the random effects model, yij = μ + α i + ∈ ij , (i = 1, …, k; j = 1, …, ni ), where α i and ∈ ij are normal with means zero and variances σα 2 and σ i 2, this article considers eight methods of estimating σ i 2, σα 2, and thirteen corresponding procedures of estimating μ. Biases and mean squared errors (MSE's) of these procedures are examined for variations in the magnitudes of the unknown parameters, the sample sizes, and the number of groups.