  Methods for random-effects meta-analysis require an estimate of the
between-study variance, $\tau^2$. The performance of estimators of $\tau^2$
(measured by bias and coverage) affects their usefulness in assessing
heterogeneity of study-level effects, and also the performance of related
estimators of the overall effect. For the effect measure mean difference (MD),
we review five point estimators of $\tau^2$ (the popular methods of
DerSimonian-Laird, restricted maximum likelihood, and Mandel and Paule (MP);
the less-familiar method of Jackson; and a new method (WT) based on the
improved approximation to the distribution of the $Q$ statistic by
\cite{kulinskaya2004welch}), five interval estimators for $\tau^2$ (profile
likelihood, Q-profile, Biggerstaff and Jackson, Jackson, and the new WT
method), six point estimators of the overall effect (the five related to the
point estimators of $\tau^2$ and an estimator whose weights use only
study-level sample sizes), and eight interval estimators for the overall effect
(five based on the point estimators for $\tau^2$, the
Hartung-Knapp-Sidik-Jonkman (HKSJ) interval, a modification of HKSJ, and an
interval based on the sample-size-weighted estimator). We obtain empirical
evidence from extensive simulations and an example.
