![]() ![]() The statistical software SAS is widely used in this course and in previous lessons we came across outputs generated through SAS programs. In other words, errors that are near to each other in the sequence might be correlated with each other. The order related trend depicts a prototype situation where the errors are not independent. In figure (d), we are plotting residuals against the order of the observations. However the megaphone patterns in figure (c) suggests that variance is not constant. Using figure (c), we can depict that the linear model is appropriate as the central trend in data is a line. ![]() e ŷ 0 (a) e ŷ 0 (b) e ŷ 0 (c) e Order 0 (d)įigure (b) suggests that although the variance is constant, there are some trend in the response that is not explained by a linear model. within the horizontal bands) for all groups. The residuals are scattered randomly around mean zero and variability is constant (i.e. \(\underbrace\)).įigure (a) shows the prototype plot when the ANOVA model is appropriate for data. This partitioning of the deviations can be written mathematically as: In statistics, we call this the partitioning of variability (due to treatment and due to random variability in the measurements). In Lesson 2 we learned that ANOVA is based on testing the effect of the treatment relative to the amount of random error.
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