The Residual ANOVA Approach for Factorial Experiment with Confounding Having Simple Block Structure | ||||
| The Egyptian Statistical Journal | ||||
| Article 6, Volume 35, Issue 2, December 1991, Page 267-284 | ||||
| Document Type: Original Article | ||||
| DOI: 10.21608/esju.1991.315019 | ||||
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| Authors | ||||
| H.F. El-Laithy; Mohamed Ahmed El-Abd | ||||
| Abstract | ||||
| Nelder (1965) showed that all simple block structure can be characterized by a set of mutually orthogonal idempotent matrices which define the strata of the block structure. The ANOVA, the mean sums of squares are derivable using the degrees of freedom identities. In this paper, we derive the patterns of the design matrices in factorial experiments with confounding such that each treatment contrast lies within one stratum and hence the residual strata are uncorrelated. Therefore, the residual ANOVA approach may be applied. A simple straight forward procedure for deriving the projection operaters of the residual variance and the residual strata using the degrees of freedom identities is suggested for factorial experiments with confounding which have simple block structure. A numerical example is provided in order to examine the impact of confounding on the variances of confounded and unconfounded contrasts. | ||||
| Keywords | ||||
| Block Structure; Degrees of Freedom; Design Matrix; Factorial Experiments; Confounded Contrast; Residual Analysis of Variance Approach | ||||
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