Manova: Power Analysis of Models of Sudoku Square Designs

Abstract

<jats:p>This paper assesses the performance of multivariate treatment tests (Wilk’s Lambda, Hoteling-lawley, Roy’s largest root and Pillai) on multivariate Sudoku square design models in terms of power analysis. Monte carlo simulation was conducted to compare the power of these four tests for the four multivariate Sudoku square design models. This study used 0.062 as interval value for Power difference between two tests of the same sample size. The test is considered powerful or having advantage, if the difference between the powers of the tests is . The results of Power test show that Hoteling-lawley has advantage over three other tests at P=2 while at P=3 Wilk’s lambda test has power advantage over other tests in all the multivariate Sudoku models.</jats:p>

Analysis of Covariance of Models of Sudoku Squares with no Treatment Effects on Concomitant Variable

“…This extension can provide both more precise parameter estimates and better components identification. Several researchers have presented their works on Sudoku square design, authors like, Lorch, (2009), Subramani andPonnuswamy (2009), Subramani, (2012), Ramon et al (2012), Mahdian and Mahmoodian (2015), Danbaba and Dauran (2016), Shehu and Danbaba (2018), Shehu and Danbaba (2018a) and Shehu et al (2023). This study extends the work of Shehu and Danbaba (2018), the work showed the inclusion of concomitant variable into each of the four Sudoku square models, method of least square was used to derive the estimators for sum of squares and cross products.…”

“…Several researchers have presented their works on Sudoku square design, authors like, Lorch, (2009), Subramani andPonnuswamy (2009), Subramani, (2012), Ramon et al (2012), Mahdian and Mahmoodian (2015), Danbaba and Dauran (2016), Shehu and Danbaba (2018), Shehu and Danbaba (2018a) and Shehu et al (2023). This study extends the work of Shehu and Danbaba (2018), the work showed the inclusion of concomitant variable into each of the four Sudoku square models, method of least square was used to derive the estimators for sum of squares and cross products. The extension of the paper will be in area of analytical procedures of obtaining the least square estimates of the sums of squares and products, test of significance of the adjusted treatment effect, obtaining error mean squares for ANCOVA and ANOVA Sudoku square models, comparison of the two error mean squares and correlation coefficients between the concomitant variable and dependent variable.…”

“…We review the ANCOVA Sudoku square models proposed by Shehu and Danbaba (2018) In the study, we assume that 𝑒 𝑖𝑗𝑘 is normally identically, distributed with zero mean and constant variance 𝜎 2 , we also assume that there is linear relationship between 𝑦 𝑖𝑗𝑘 and 𝑥 𝑖𝑗𝑘 and regression coefficient for each treatment are identical, the treatment effect sum to zero and the concomitant variable is not affected by the treatment.…”

“…The sum of squares and cross-products for various effects have be derived for each of the proposed ANCOVA Sudoku square models (see Shehu and Danbaba, 2018 for details), analysis of covariance will be carried out and test of hypothesis will also be carried out on each of the models.…”

Estimation of Missing Value in Sudoku Square Design

“…Many authors like Subramani [13], Subramani and Ponnuswamy [14], Hui-Dong and Ru-Gen [15], Dauran et al [16], Shehu and Dauran [17], Danbaba and Shehu [18], Danbaba [19], Danbaba [20], Danbaba [21] and many others. These authors have written on the areas of analysis of variance (ANOVA), construction of models, Construction of graeco Sudoku square design, multivariate analysis and variance components of Sudoku square models.…”