Checking violation of assumptions underlying the analysis of variance [electronic resource].

Includes reference.

The strategy for checking any violations of the analysis of variance assumptions has rarely been adopted among researchers and data analysts especially with models that contain more than one error term. The objective of this work is to set out steps to check these assumptions of a split-plot design. Analysis of variance assumptions have been checked for a field experiment laid out in a split-plot design. Three whole-plot (WP) nitrogen fertilizer rates were laid out in four randomized blocks. and maize (Zea mays L.) cultivars were in four split plots (SP). To fulfill this objective a five-stage strategy was followed. These checking stages were for: fit of the model, outliers, independence of the error variable. equality of error variances, and finally normality assumption. This strategy depends mainly on calculating the residual values of both the main-and the sub-plot factors. In addition, the coefficients of multiple detennioation, R,2, were calculated for whole- and sub-plots as measures of madellack offit, Some assumptions seemed to be violated during the two years of the study. In Year 1, the pattern of residuals of the three N levels resembled a funnel-like shape; this warrants a possible violation of equality of error variance assumption. In Year 2, plotting of residuals indicates the presence of an extreme residual point at 2.72078 standard units that lies within Block 2 with both N Levelland Cultivar 2. Regarding the independence issue, the residual spatial pattern, represented here by spatial arrangement (block factor), did not seem to exhibit apparent problems in both years. Based on the residuals associated with only subplots (SP), in Year I, the variations in residuals within Cultivars 2 and 4 were more pronounced compared to those within Cultivars 1 and 3. In Year 2, a relatively more spread exists within Cultivars 4. Coefficients of determination were about 9.0 and 25.0 % for WP and SP in Year 1, and were quite improved in Year 2 to become 39.0 and 58.0 0/0, respectively. For the WP sub designs in both year, the extremely low coefficient values indicate that a small proportion of the variability in the datais contributed by the WP nitrogen fertilizer factor included in the model, whereas these values were relatively higher for SP sub designs. The WP N factor should not be replaced. but this warrants more attention bepaid when applying nitrogen fertilizer rates to main plots. Nearly all non significant effects had extremely small «1.0) F ratios. These <1.0 values, however, may indicate violations of one or more of ANOVA assumptions. Both error variance equality and normality assumptions seemed not to be violated in both years.

Summary in Arabic.

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