Guttman-single-quote-s-Lambda: Guttman's Lambda

In SICSresearch/IRTpp_old: Estimating IRT parameters using the IRT Methodology

Description

Six Lower limits of reliability coefficients are presented.

Usage

gutt(test)

Arguments

test	a matrix or a Dataframe that holds the test response data

Details

Let S_j^2 the variances over persons of the n items in the test, and S_t^2 the variance over persons of the sum of the items. The firt estimate lambda_1 can be computed from L_1 = 1 - (sums_j^2/S_t^2) Let C_2 the sum of squares of the covariances between items, therefore is the sum of n(n-1)/2 terms. The bound lambda_2 is computed by L_2 = L_1 + (sqrtn/n-1 C_2/S_t^2) The third lower bound lambda_3 is a modification of lambda_1, it is computed from the L_3 = n/(n-1) L_1 Fourth lower bound lamda_4 has been interpreted as the greatest split half reliability, and requires that the test be scored as twohalves. It is calculated from L_4 = 2(1 - (s_a^2 + s_b^2)/s_t^2) where S_a^2 and S_b^2 are the respectives variances of the two parts for the single trial. For the fifth lower bound lambda_5, let C_2j be the sum of the squares of the covariances of item j with the remaining n-1 items, and let barC_2 be the largest of the C_2j. Then the coefficient can be computed from L_5 = L_1 + (2sqrtbarC_2)/S_t^2 The final bound is based on multiple correlation, let e_j^2 be the variance of the errors of estimate of item j from its linear multiple regression on the remaining n-1 items. Then lambda_6 can be computed from L_6 = 1 - (sume_j^2)/S_t^2

Value

The six coefficients Guttman for the test.

References

Guttman, L. (1945). A basis for analyzing test-retest reliability. Psychometrika, 10(4), 255-282.

SICSresearch/IRTpp_old documentation built on May 9, 2019, 11:12 a.m.