Table 1.
Proportion of 1000 confusion matrices in which violations were detected by marginal and probit analyses in simulated data with known violations.
| Known violation | Analysis:(M)arginals or (P)robits | Violations detected (proportion) | |||||
|---|---|---|---|---|---|---|---|
| PI in (1,1) | PI in (2,1) | PI in (1,2) | PI in (2,2) | PS | DS | ||
| None | M | 0.000 | 0.000 | 0.000 | 0.000 | 0.028 | 0.028 |
| P | 0.019 | 0.016 | 0.009 | 0.013 | 0.002 | 0.000 | |
| PI in (1,1) correlation = −0.25 | M | 0.000 | 0.000 | 0.000 | 0.000 | 0.025 | 0.022 |
| P | 0.226 | 0.023 | 0.014 | 0.025 | 0.001 | 0.000 | |
| PI in (1,1) correlation = +0.25 | M | 0.000 | 0.000 | 0.000 | 0.000 | 0.024 | 0.025 |
| P | 0.305 | 0.024 | 0.027 | 0.027 | 0.002 | 0.000 | |
| PI in (1,1) correlation = −0.5 | M | 0.000 | 0.000 | 0.000 | 0.000 | 0.031 | 0.022 |
| P | 0.802 | 0.016 | 0.019 | 0.016 | 0.002 | 0.000 | |
| PI in (1,1) correlation = +0.5 | M | 0.000 | 0.000 | 0.000 | 0.000 | 0.024 | 0.029 |
| P | 0.929 | 0.013 | 0.015 | 0.027 | 0.002 | 0.000 | |
| PI in all distributions: | M | 0.000 | 0.000 | 0.000 | 0.000 | 0.023 | 0.017 |
| correlation = −0.25 | P | 0.236 | 0.301 | 0.281 | 0.230 | 0.002 | 0.000 |
| PI in all distributions: | M | 0.000 | 0.000 | 0.000 | 0.000 | 0.026 | 0.021 |
| correlation = +0.25 | P | 0.309 | 0.208 | 0.238 | 0.274 | 0.004 | 0.000 |
| PI in all distributions: | M | 0.000 | 0.000 | 0.000 | 0.000 | 0.019 | 0.022 |
| correlation = −0.5 | P | 0.744 | 0.938 | 0.934 | 0.709 | 0.001 | 0.000 |
| PI in all distributions: | M | 0.000 | 0.000 | 0.000 | 0.000 | 0.027 | 0.028 |
| correlation = +0.5 | P | 0.927 | 0.726 | 0.774 | 0.935 | 0.002 | 0.000 |
| PS: d ′ = 2 versus d ′ = 2.5 | M | 0.000 | 0.000 | 0.000 | 0.000 | 0.578 | 0.234 |
| P | 0.020 | 0.014 | 0.023 | 0.008 | 0.347 | 0.019 | |
| PS: d ′ = 2 versus d ′ = 3 | M | 0.000 | 0.000 | 0.000 | 0.000 | 0.984 | 0.016 |
| P | 0.015 | 0.012 | 0.011 | 0.030 | 0.964 | 0.099 | |
| DS with a continuous decision | M | 0.000 | 0.000 | 0.000 | 0.000 | 0.021 | 0.609 |
| bound: c = 0 versus c = 0.25 | P | 0.240 | 0.255 | 0.250 | 0.349 | 0.001 | 0.138 |
| DS with a continuous decision | M | 0.000 | 0.000 | 0.000 | 0.000 | 0.024 | 0.973 |
| bound: c = 0 versus c = 0.5 | P | 0.771 | 0.765 | 0.762 | 0.984 | 0.000 | 0.944 |
| DS with a piecewise decision | M | 0.000 | 0.000 | 0.000 | 0.000 | 0.027 | 0.621 |
| bound: c = 0 versus c = 0.25 | P | 0.020 | 0.014 | 0.018 | 0.018 | 0.000 | 0.144 |
| DS with a piecewise decision | M | 0.000 | 0.000 | 0.000 | 0.000 | 0.024 | 0.976 |
| bound: c = 0 versus c = 0.5 | P | 0.013 | 0.009 | 0.009 | 0.011 | 0.001 | 0.942 |
Due to space limitations, results are reported for single violations and for d ′ = 2 only, although results for d ′ = 1 are similar. Inferential errors are shown in bold. Perceptual independence (PI); perceptual separability (PS); decisional separability (DS).