Example data from Gleser, Cronbach and Rajaratnam (1965) to show basic principles of generalizability theory.
Gleser, Cronbach and Rajaratnam (1965) discuss the estimation of variance components and their ratios as part of their introduction to generalizability theory. This is a adaptation of their "illustrative data for a completely matched G study" (Table 3). 12 patients are rated on 6 symptoms by two judges. Components of variance are derived from the ANOVA.
data(Gleser)
A data frame with 12 observations on the following 12 variables. J item by judge:
J11
a numeric vector
J12
a numeric vector
J21
a numeric vector
J22
a numeric vector
J31
a numeric vector
J32
a numeric vector
J41
a numeric vector
J42
a numeric vector
J51
a numeric vector
J52
a numeric vector
J61
a numeric vector
J62
a numeric vector
Generalizability theory is the application of a components of variance approach to the analysis of reliability. Given a G study (generalizability) the components are estimated and then may be used in a D study (Decision). Different ratios are formed as appropriate for the particular D study.
Gleser, G., Cronbach, L., and Rajaratnam, N. (1965). Generalizability of scores influenced by multiple sources of variance. Psychometrika, 30(4):395-418. (Table 3, rearranged to show increasing patient severity and increasing item severity.
Gleser, G., Cronbach, L., and Rajaratnam, N. (1965). Generalizability of scores influenced by multiple sources of variance. Psychometrika, 30(4):395-418.
#Find the MS for each component: #First, stack the data data(Gleser) stack.g <- stack(Gleser) st.gc.df <- data.frame(stack.g,Persons=rep(letters[1:12],12), Items=rep(letters[1:6],each=24),Judges=rep(letters[1:2],each=12)) #now do the ANOVA anov <- aov(values ~ (Persons*Judges*Items),data=st.gc.df) summary(anov)
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