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The assumptions, including (1) identical, (2) independent, and (3) normally distributed errors are made to perform the ANOVA and the post-hoc analyses. Any statistical software, including MS Excel, provides output to check these assumptions.
Identically Distributed Error Term
Identically Distributed Error Term
The assumption of the identically distributed error term also implies that the error term is Homogenous and Constant, which is checked by the plot of residuals vs the fitted values. Figure 4 shows no obvious pattern indicating the residuals/errors are homogenous or constant or identically distributed.
Figure 4. Residuals vs Fitted Value
Independently Distributed Error Term
Independently Distributed Error Term
The residuals or errors are assumed to be uncorrelated with the observation time or order. The plot of residuals vs the observation order in Figure 5 does not show any obvious pattern. Therefore, the independence of error term with the observation order or time is not violated in this case.
Figure 5. Residuals vs Observation Order or Time
Normally Distributed Error Term
Normally Distributed Error Term
The normal probability plot (pp-plot) in Figure 6 shows that the points follow approximately a straight line, indicating the normal distribution of the residuals.
Figure 6. Normal Probability Plot (pp-plot) of the Residuals
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