Generalizability coefficient for the crossed p x i design

The random-effects ANOVA of a persons-by-items score matrix gives the three variance components; the generalizability coefficient is for relative decisions and the index of dependability for absolute ones. For this design the generalizability coefficient is algebraically identical to coefficient alpha.

Usage

Genvxt(X, facets = NULL)

Arguments

X

Persons-by-items score matrix.

facets

Optional number of items to project onto.

Value

List with estimate, e_rho2, phi, var_p, var_i, var_pi, ms_p, ms_i, ms_pi, n_p, n_i, method.

Details

Formula: var_p = (MS_p - MS_pi)/n_i, var_i = (MS_i - MS_pi)/n_p, var_pi = MS_pi; E rho^2 = var_p / (var_p + var_pi/n_i); Phi = var_p / (var_p + (var_i + var_pi)/n_i).

References

Cronbach, Gleser, Nanda and Rajaratnam (1972), The Dependability of Behavioral Measurements, Wiley; Brennan (2001), Generalizability Theory, Springer, ch. 2.

Examples

M <- matrix(c(1, 2, 3, 4, 5, 6), nrow = 2)
Genvxt(M)
#> $estimate
#> [1] 1
#> 
#> $e_rho2
#> [1] 1
#> 
#> $phi
#> [1] 0.2727273
#> 
#> $var_p
#> [1] 0.5
#> 
#> $var_i
#> [1] 4
#> 
#> $var_pi
#> [1] 0
#> 
#> $ms_p
#> [1] 1.5
#> 
#> $ms_i
#> [1] 8
#> 
#> $ms_pi
#> [1] 0
#> 
#> $n_p
#> [1] 2
#> 
#> $n_i
#> [1] 3
#> 
#> $method
#> [1] "random-effects ANOVA components, Cronbach et al. (1972); Brennan (2001) ch. 2"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"