Mean-sigma equating coefficients

Formula: the scale linking theta_R = A theta_F + B implies b_R = A b_F + B for the common items, so matching the first two moments of the difficulties gives A = sd(b_R) / sd(b_F) and B = mean(b_R) - A mean(b_F).

Usage

Eqms(y, b_R, b_F, ddof = 1)

Arguments

y

Scores on the Form F metric to place on the Form R metric.

b_R

Common-item difficulties on the Form R (reference) metric.

b_F

The same items' difficulties on the Form F metric.

ddof

Denominator correction for the standard deviations; 1 gives the sample sd, 0 the population sd.

Value

List with estimate, A, B, equated, n_items, n, method.

Details

Marco's method places the NEW form on the REFERENCE metric, the orientation implemented here (the same direction as eqmm).

References

Marco (1977), Journal of Educational Measurement 14(2):139-160, doi:10.1111/j.1745-3984.1977.tb00033.x.

Examples

Eqms(y = c(1, 2, 3, 4, 5, 6, 7, 8), b_R = c(1, 2, 3, 4, 5, 6, 7, 8),
  b_F = c(1, 2, 3, 4, 5, 6, 7, 8))
#> $estimate
#> [1] 1
#> 
#> $A
#> [1] 1
#> 
#> $B
#> [1] 0
#> 
#> $equated
#> [1] 1 2 3 4 5 6 7 8
#> 
#> $n_items
#> [1] 8
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "Mean-sigma equating coefficients"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"