Product and Process Comparisons
7.4. Comparisons based on data from more than two processes
7.4.2. Are the means equal?
that describes the relationship between the response and the treatment
(between the dependent and independent variables)
Fixed and random effects
|The mathematical model that
describes the relationship between response and treatment for the one-way
ANOVA is given by
where Yij represents the j-th observation (j = 1, 2, ...ni) on the i-th treatment (i = 1, 2, ..., k levels). So, Y23 represents the third observation using level 2 of the factor. m is the common effect for the whole experiment, tirepresents the i-th treatment effect and eij represents the random error present in the j-th observation on the i-th treatment.
The errors eij are assumed to be normally and independently (NID) distributed, with mean zero and variance s2e . m is always a fixed parameter and t1, t2, ...tk are considered to be fixed parameters if the levels of treatment are fixed,and not a random sample from a population of possible levels. It is also assumed that m is chosen so that
S ti = 0 i = 1, ...k
holds. This is the fixed effects model.
Whether the levels are fixed or random depends on how these levels are
chosen in a given experiment