Table 8.

Obuchowski-Rockette split-plot (cases nested within test) analysis of Kundel et al [9] data for soft-copy computed radiographs and screen-film radiographs using trapezoid AUC estimation and jackknife covariance estimation for t = 2 tests, r = 4 readers. The images were from different patients for each type of radiograph, with 95 images in each group (soft-copy computed radiograph: 66 nondiseased, 29 diseased; screen-film radiograph: 68 nondiseased, 27 diseased).

Trapezoid AUCs: Test 1 (Soft-copy computed radiograph) 2 (Screen-film) Reader (j) θ̂1j θ̂2j 1 0.815 0.818 2 0.767 0.836 3 0.831 0.828 4 0.803 0.834 θ̂1· = .804 θ̂2· = .829 ANOVA table: Source df Sum of squares Mean square T 1 0.00125969 0.00125969 R 4 0.00076530 0.00025510 T*R 4 0.00164974 0.00054991 Fixed-reader covariance estimates computed from jackknife covariance matrix: ${\hat{\sigma }}_{\epsilon }^2=0.0023651313,{\widehat{\text{Cov}}}_2=0.0008800774$ $$F_{\text{OR}}=\frac{\mathrm{M}\mathrm{S}(T)}{\mathrm{M}\mathrm{S}(T*R)+\text{max}(r{\widehat{\text{Cov}}}_2,0)}=0.31$$ Denominator degrees of freedom: $$\mathrm{d}{\mathrm{f}}_2=\frac{{[\mathrm{M}\mathrm{S}(T*R)+\text{max}(r{\widehat{\text{Cov}}}_2,0\left)\right]}^2}{\frac{{[\mathrm{M}\mathrm{S}(T*R)]}^2}{(t-1)(r-1)}}=164.4$$ P-value for H0: θ1 = θ2: p = Pr (F(t−1), df2 ≥ FOR) = 0.579 95% CI for θ2 − θ1: ${\hat{\theta }}_{2·}-{\hat{\theta }}_{1·}\pm t_{\mathrm{d}{\mathrm{f}}_2}\sqrt{\frac{2}{r}\{\mathrm{M}\mathrm{S}(t*R)+r\text{max}({\widehat{\text{Cov}}}_2,0\left)\right\}}=(-0.064,0.114)$ Single test 95% confidence intervals using only corresponding data. Note: ${\text{StdErr}}^{(i)}=\sqrt{\frac{1}{r}\{\mathrm{M}\mathrm{S}{(R)}^{(i)}+r*\text{max}({\widehat{\text{Cov}}}_2^{(i)},0\left)\right\}}$ i θ̂i ${\widehat{\text{Cov}}}_2^{(i)}$ MS(R)(i) StdErr(i) ${\mathrm{d}\mathrm{f}}_2^{(i)}$ 95% CI 1(Soft-copy) 0.804 0.000880 0.000735 0.0326 100.4 0.739, 0.867 2(Screen-film) 0.829 0.000881 0.000070 0.0300 7997.2 0.770, 0.888