Answer:
a. The resulting model will be a better fit of the data than the grand mean.
EXPLANATION:
The logic of ANOVA follows from what we already know about linear models:
• The simplest model we can fit to a set of data is the grand mean (the mean of the outcome variable). This basic
model represents ‘no effect’ or ‘no relationship between the predictor variable and the outcome’.
• We can fit a different model to the data collected that represents our hypotheses. If this model fits the data
well then it must be better than using the grand mean.
• The intercept and one or more parameters (b) describe the model.
• The parameters determine the shape of the model that we have fitted; therefore, the bigger the coefficients,
the greater the deviation between the model and the grand mean.
• In experimental research the parameters (b) represent the differences between group means. The bigger the
differences between group means, the greater the difference between the model and the grand mean.
• If the differences between group means are large enough, then the resulting model will be a better fit of the
data than the grand mean.
References:
Field, A. P. (2013). Discovering statistics using IBM SPSS Statistics: And sex and drugs and rock 'n' roll (4th ed.). London:
Sage.
Field, A. P. (2016). An adventure in statistics: the reality enigma. London: Sage.
Hawton, K. (1989). Sexual dysfunctions. In K. Hawton, P. M. Salkovskis, J. Kirk, & D. M. Clark (Eds.), Cognitive behaviour
therapy for psychiatric problems: a practical guide. (pp. 370-405). Oxford: Oxford University Press.
