Comparison of Type 1, 2 and 3 sums of squares in balanced and unbalanced factorial designs in terms of power of test

In this thesis study, in the balanced and unbalanced experiments in factorial order, it is planned to compare the power values of the test that will be formed as a result of the use of the sum of commonly used Type 1, type 2 and type 3 squares by creating combinations of different widths in terms of standart deviation between combinations of different sample widths, different distribution, different variance ratios and averages. The material of this thesis work consists of random numbers produced by using the IMSL library of Microsoft Developer Studio. 100 000 simulations for 4 different distributions were made (Z, Chi-Square) by using the sum of Type I-Type II and Type III squares according to 16 subgroup combinations with 2 factors with 3, 5, 10 and 20 observation numbers in balanced trials and each factor is 4 in the number of levels. (T and Beta). 100 000 simulation studies for 4 different distributions (Z, Ki- Kare, T and Beta) were made in the unbalanced test patterns, for the 16 subgroups with 2 factors and each level has 4 in the number of levels with different observation numbers, creating 8 different unbalanced trial patterns, using the sum of Type I-Type II and Type III squares. In the study, the sum of type 3 squares and the sum of type 2, type 1 squares give similar power values in balanced trials. In unbalanced test patterns, it is seen that the sum of type 3 squares gets higher power values. This situation explains the reason for using the sum of type 3 squares in package programs. However, in this study, it was observed that the sum of type 2 and type 1 squares received slightly higher power values in balanced trial patterns in curve distributions. In unbalanced trials, a general decrease in power was observed.