Question

"If the differences between group means are large enough, then:

Answer 1

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.