Reparameterization and the conditional inverse of a balanced factorial experiment with three factors | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 13، شماره 1، خرداد 2022، صفحه 3733-3747 اصل مقاله (457.03 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.6150 | ||
| نویسندگان | ||
| Wisam Wadullah Saleem* 1؛ Asmaa GHalib Jaber2 | ||
| 1Department of Statistics and Informatics, Mosul University, Iraq University, Iraq | ||
| 2Department of Statistics, Baghdad University, Iraq | ||
| چکیده | ||
| In this research, a factorial experiment $2^3$ was studied through a balanced mathematical model applied in a complete random design (CRD) to show the effect of the main factors and the interactions between the factors through the use of the general linear model in which the design matrix $(X^{'}X)$ has less than full rank and thus the parameters vector $(\beta)$ is neither estimable nor testable. Therefore, the re-parameter method and conditional inverse were used to transform the design matrix $(X^{'}X)$ to a full-rank matrix, so that the parameters vector $(\beta)$ is capable of estimable and testable, after analyzing the experiment data and testing hypotheses it was found that the interactions ${(\alpha\beta\gamma)}_{ijk}^{*}$ and ${(\alpha\beta)}_{i j}^{*}$ are not significant, while the factors ${(\alpha)}_{i}^{*}$, ${(\beta)}_{j}^{*}$, ${(\gamma)}_{k}^{*}$ and the interactions ${(\alpha\gamma)}_{ik}^{*}$ and ${(\beta\gamma)}_{jk}^{*}$ have significant effects. | ||
| کلیدواژهها | ||
| Three factors؛ balanced؛ estimable؛ treatment؛ general linear model؛ testable؛ less than full rank؛ conditional inverse؛ ANOVA؛ full rank؛ test؛ statistic؛ generalization؛ reparameterization | ||
| مراجع | ||
|
| ||
|
آمار تعداد مشاهده مقاله: 16,493 تعداد دریافت فایل اصل مقاله: 9,804 |
||
| تعداد نشریات | 22 |
| تعداد شمارهها | 732 |
| تعداد مقالات | 10,558 |
| تعداد مشاهده مقاله | 73,789,406 |
| تعداد دریافت فایل اصل مقاله | 65,292,125 |