الفهرس 
Analysis of covariance with pre-treatment in measurements randomized trials
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Abstract
This study presents a new proposed method used for ANCOVA to deal with four different cases ;(i) equal slope with equal variances, (ii) unequal slope with unequal variances, (iii) equal slope with unequal variances, and (iv)unequal slope with equal variances. A comparison among three methods: ordinary least square, generalized least square and modified maximum likelihood (new method) was made under each case. Starting with the largest sample size (n= 13), results show that under equal slope with equal variances case, all estimators of parameter Ý(Ý₃, Ý₄, Ý₅) are greater than 1. The new method has a RE greater than 1with largest bias. Under equal slope with unequal variances case, the OLS shows the largest bias in negative values of Ý₂ = {u2212}27.29179, the GLS showsÝ₁ = {u2212}0.0994,and the MML shows(Ý₃ = {u2212}27.29129). The relative efficiency ofthese methods are less than 1 .Results also show that under the unequal slopes with unequal variances with (n₁ = 10, n₂ = 15, n₃ = 20), the relative efficiency of the modified maximum likelihood is the largest (Ý₃ = 795.836) compared to the ordinary least square and generalized least square which is less than 1. The biased value of these two methods are (Ý₅= -0.01543 and -0.01033) while of the modified maximum likelihood is(Ý₃ = -1.96704). Finally, under case of unequal slope with equal variance, the relative efficiency of modified maximum likelihood is the largest (Ý₁ = 518.5873) where as the ordinary least square and generalized least square are less than 1 and the bias of the three methods are (Ý₃= -27,27859 , -27,2913 and -4.417179)