Abstract: For three normal populations with unknown means and variances, assume that there is a treeorder restriction between ratios of means and standard deviations. According to the ideas of the PAVA algorithm, when sample numbers of three normal populations are different, a procedure of obtaining the maximum likelihood estimators of means and standard deviations under tree order restrictions is proposed.

Key words: semiorder restriction, tree order restriction, max imum likelihood estimation, likelihood function, PAVA algorithm