TY  - BOOK
AU  - Shaimaa Mohammed Ali Abdelhamid Yassin
AU  - Sayed Mesheal Elsayed , 
TI  - Analysis of covariance with pre-treatment in measurements randomized trials : : Comparison with different slopes and variances cases / 
PY  - 2016///
CY  - Cairo : 
PB  - Shaimaa Mohammed Ali Abdelhamid Yassin , 
KW  - ANCOVA
KW  - Covariance
KW  - Slopes and variances cases
N1  - Thesis (M.Sc.) - Cairo University - Institute of Statistical Studies and Research - Department of Applied Statistics and Econometrics; Issued also as CD
N2  - 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)
UR  - http://172.23.153.220/th.pdf
ER  -