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Example data from Gleser, Cronbach and Rajaratnam (1965) to show basic principles of generalizability theory.

### Description

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.

### Usage

data(Gleser)

### Format

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

### Details

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.

### Source

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.

### References

Gleser, G., Cronbach, L., and Rajaratnam, N. (1965). Generalizability of scores influenced by multiple sources of variance. Psychometrika, 30(4):395-418.

### Examples

#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)