Computes adjusted Wald confidence intervals for a G-index of agreement for all pairs of raters in a 3-rater design with a dichotomous rating, and computes adjusted Wald confidence intervals for differences of all pairs of G agreement. An adjusted Wald confidence interval for unanimous G agreement among the three raters also is computed. In the three-rater design, unanimous G agreement is equal to the average of all pairs of G agreement.

ci.agree.3rater(alpha, f)

Arguments

alpha

alpha level for 1-alpha confidence

f

vector of frequency counts from 2x2x2 table where f = [f111, f112, f121, f122, f211, f212, f221, f222] first subscript represents rating of rater 1, second subscript represents rating of rater 2, third subscript represents rating of rater 3

Value

Returns a 3-row matrix. The rows are:

  • G1,2: G-index for raters 1 and 2

  • G1,3: G-index for raters 1 and 3

  • G2,3: G-index for raters 2 and 3

  • G1,2-1,3: difference in G1,2 and G1,3

  • G1,2-2,3: difference in G1,2 and G2,3

  • G2,3-1,3: difference in G2,3 and G1,3

  • G(3): G-index of unanimous agreement for all three raters

The columns are:

  • Estimate - estimate of G-index (two-rater, difference, or unanimous)

  • LL - lower limit of confidence interval

  • UL - upper limit of confidence interval

References

Bonett DG (2022). “Statistical inference for G-indices of agreement.” Journal of Educational and Behavioral Statistics, 47(4), 438--458. ISSN 1076-9986, doi:10.3102/10769986221088561 .

Examples

f <- c(100, 6, 4, 40, 20, 1, 9, 120)
ci.agree.3rater(.05, f)
#>                  Estimate          LL         UL
#> G{1,2}         0.56666667  0.46601839  0.6524027
#> G{1,3}         0.50000000  0.39564646  0.5911956
#> G{2,3}         0.86666667  0.79701213  0.9135142
#> G{1,2}–G{1,3}  0.06666667  0.00580397  0.1266464
#> G{1,2}–G{2,3} -0.30000000 -0.40683919 -0.1891873
#> G{2,3}–G{1,3} -0.36666667 -0.46222023 -0.2662566
#> G(3)           0.64444444  0.57382971  0.7068720

# Should return:
#                  Estimate          LL         UL
# G{1,2}         0.56666667  0.46601839  0.6524027
# G{1,3}         0.50000000  0.39564646  0.5911956
# G{2,3}         0.86666667  0.79701213  0.9135142
# G{1,2}-{1,3}  0.06666667  0.00580397  0.1266464
# G{1,2}-{2,3} -0.30000000 -0.40683919 -0.1891873
# G{2,3}-{1,3} -0.36666667 -0.46222023 -0.2662566
# G(3)           0.64444444  0.57382971  0.7068720