Description Usage Arguments Details Value References

Six Lower limits of reliability coefficients are presented.

1 |

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

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 *λ_1* can be computed from *L_1 = 1 - (sum{s_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 + (√{n/n-1 C_2}/S_t^2)*
The third lower bound *λ_3* is a modification of *λ_1*, it is computed
from the *L_3 = n/(n-1) L_1*
Fourth lower bound *λ_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 *\bar{C}_2* be the largest of
the

*C_{2j}*

. Then the coefficient can be computed from *L_5 = L_1 + (2√{bar{C}_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 - (∑{e_j^2})/S_t^2*

The six coefficients Guttman for the test.

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

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