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Chapter 16: One-Way Analysis of Variance
We can now generalize this example if we have any amount of treatment
levels for any single factor.
Figure 16-22
shows the generalization of the
data collected for a one-way ANOVA.
Figure 16-22:
Generalization of Recorded Values in a
One-Way ANOVA
Note that the Yij observation corresponds to the i
th
observation (row) for the
j
th
treatment level (column) of the data display. The contributions to this
value can be written in terms of a
common effect for the whole experiment
;
the
effect of the treatment on this value
; and the
error incurred in the
measuring of the observed response value
. We mathematically can combine
these contributions to give the value for Yij. The resulting equation will
represent the model for the one-way ANOVA experiment.
Mathematical Model for a One-Way ANOVA
The mathematical model is given next.