Abstract

Geometric squares, and rectangles (squares vertically elongated by 2%), were presented singly in a random sequence to three observers. By using the detectability-model parameter d′ as a measure, average discriminability was found to be 1.32. Two-, three-, and four-category response scales were shown to give equivalent discriminability data. Discriminability was not significantly affected by the inclusion of an extraneous stimulus (a square vertically elongated either 1% or 3%) interspersed randomly in the square-rectangle sequence without the observers’ knowledge. The data were interpreted as a favorable empirical test of detectability-theory assumptions applied to a visual discrimination task.

© 1962 Optical Society of America

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References

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  1. W. W. Peterson and T. G. Birdsall, “The Theory of Signal Detectability,” (1953).
  2. W. P. Tanner and T. G. Birdsall, J. Acoust. Soc. Am. 30, 922 (1958).
    [CrossRef]
  3. F. R. Clarke, T. G. Birdsall, and W. P. Tanner, J. Acoust. Soc. Am. 31, 629 (1959).
    [CrossRef]
  4. J. P. Egan, J. Acoust. Soc. Am. 29, 482 (1957).
    [CrossRef]
  5. W. P. Tanner and J. A. Swets, Psychol. Rev. 61, 401 (1954).
    [CrossRef] [PubMed]
  6. An inspection of Fig. 1(a) indicates that, as FAR and HR increase, the transformed values decrease. Such a standard-score transformation differs slightly from the transformation commonly employed. With respect to the literature cited as references, the axes in Figs. 2, 3, and 4 would have to be relabeled (1 − FAR) and (1 − HR). Alternately, if one inverts Figs. 2, 3, and 4 (thus locating the ROC curves primarily in the upper left quadrant), they become equivalent to the figures found in the signal-detection literature.
  7. J. P. Egan, A. I. Schulman, and G. Z. Greenberg, J. Acoust. Soc. Am. 31, 768 (1959).
    [CrossRef]
  8. R. B. Sleight and G. H. Mowbray, J. Psychol. 31, 121 (1951).
    [CrossRef]
  9. F. A. Veniar, J. Psychol. 26, 461 (1948).
    [CrossRef]
  10. J. A. Swets, Science 134, 168 (1961).
    [CrossRef] [PubMed]

1961 (1)

J. A. Swets, Science 134, 168 (1961).
[CrossRef] [PubMed]

1959 (2)

F. R. Clarke, T. G. Birdsall, and W. P. Tanner, J. Acoust. Soc. Am. 31, 629 (1959).
[CrossRef]

J. P. Egan, A. I. Schulman, and G. Z. Greenberg, J. Acoust. Soc. Am. 31, 768 (1959).
[CrossRef]

1958 (1)

W. P. Tanner and T. G. Birdsall, J. Acoust. Soc. Am. 30, 922 (1958).
[CrossRef]

1957 (1)

J. P. Egan, J. Acoust. Soc. Am. 29, 482 (1957).
[CrossRef]

1954 (1)

W. P. Tanner and J. A. Swets, Psychol. Rev. 61, 401 (1954).
[CrossRef] [PubMed]

1951 (1)

R. B. Sleight and G. H. Mowbray, J. Psychol. 31, 121 (1951).
[CrossRef]

1948 (1)

F. A. Veniar, J. Psychol. 26, 461 (1948).
[CrossRef]

Birdsall, T. G.

F. R. Clarke, T. G. Birdsall, and W. P. Tanner, J. Acoust. Soc. Am. 31, 629 (1959).
[CrossRef]

W. P. Tanner and T. G. Birdsall, J. Acoust. Soc. Am. 30, 922 (1958).
[CrossRef]

W. W. Peterson and T. G. Birdsall, “The Theory of Signal Detectability,” (1953).

Clarke, F. R.

F. R. Clarke, T. G. Birdsall, and W. P. Tanner, J. Acoust. Soc. Am. 31, 629 (1959).
[CrossRef]

Egan, J. P.

J. P. Egan, A. I. Schulman, and G. Z. Greenberg, J. Acoust. Soc. Am. 31, 768 (1959).
[CrossRef]

J. P. Egan, J. Acoust. Soc. Am. 29, 482 (1957).
[CrossRef]

Greenberg, G. Z.

J. P. Egan, A. I. Schulman, and G. Z. Greenberg, J. Acoust. Soc. Am. 31, 768 (1959).
[CrossRef]

Mowbray, G. H.

R. B. Sleight and G. H. Mowbray, J. Psychol. 31, 121 (1951).
[CrossRef]

Peterson, W. W.

W. W. Peterson and T. G. Birdsall, “The Theory of Signal Detectability,” (1953).

Schulman, A. I.

J. P. Egan, A. I. Schulman, and G. Z. Greenberg, J. Acoust. Soc. Am. 31, 768 (1959).
[CrossRef]

Sleight, R. B.

R. B. Sleight and G. H. Mowbray, J. Psychol. 31, 121 (1951).
[CrossRef]

Swets, J. A.

J. A. Swets, Science 134, 168 (1961).
[CrossRef] [PubMed]

W. P. Tanner and J. A. Swets, Psychol. Rev. 61, 401 (1954).
[CrossRef] [PubMed]

Tanner, W. P.

F. R. Clarke, T. G. Birdsall, and W. P. Tanner, J. Acoust. Soc. Am. 31, 629 (1959).
[CrossRef]

W. P. Tanner and T. G. Birdsall, J. Acoust. Soc. Am. 30, 922 (1958).
[CrossRef]

W. P. Tanner and J. A. Swets, Psychol. Rev. 61, 401 (1954).
[CrossRef] [PubMed]

Veniar, F. A.

F. A. Veniar, J. Psychol. 26, 461 (1948).
[CrossRef]

J. Acoust. Soc. Am. (4)

W. P. Tanner and T. G. Birdsall, J. Acoust. Soc. Am. 30, 922 (1958).
[CrossRef]

F. R. Clarke, T. G. Birdsall, and W. P. Tanner, J. Acoust. Soc. Am. 31, 629 (1959).
[CrossRef]

J. P. Egan, J. Acoust. Soc. Am. 29, 482 (1957).
[CrossRef]

J. P. Egan, A. I. Schulman, and G. Z. Greenberg, J. Acoust. Soc. Am. 31, 768 (1959).
[CrossRef]

J. Psychol. (2)

R. B. Sleight and G. H. Mowbray, J. Psychol. 31, 121 (1951).
[CrossRef]

F. A. Veniar, J. Psychol. 26, 461 (1948).
[CrossRef]

Psychol. Rev. (1)

W. P. Tanner and J. A. Swets, Psychol. Rev. 61, 401 (1954).
[CrossRef] [PubMed]

Science (1)

J. A. Swets, Science 134, 168 (1961).
[CrossRef] [PubMed]

Other (2)

An inspection of Fig. 1(a) indicates that, as FAR and HR increase, the transformed values decrease. Such a standard-score transformation differs slightly from the transformation commonly employed. With respect to the literature cited as references, the axes in Figs. 2, 3, and 4 would have to be relabeled (1 − FAR) and (1 − HR). Alternately, if one inverts Figs. 2, 3, and 4 (thus locating the ROC curves primarily in the upper left quadrant), they become equivalent to the figures found in the signal-detection literature.

W. W. Peterson and T. G. Birdsall, “The Theory of Signal Detectability,” (1953).

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Figures (4)

Fig. 1
Fig. 1

(a) The basic distributions assumed by detectability theory. (b), (c) The addition of a third stimulus provides an additional distribution.

Fig. 2
Fig. 2

The z-score plot for subject BG showing the ROC curve for Δh=0.4 mm. (See footnote 6.)

Fig. 3
Fig. 3

The z-score plot for subject AM showing the ROC curve for Δh=0.4 mm. (See footnote 6.)

Fig. 4
Fig. 4

The z-score plot for subject PF showing the ROC curve for Δh=0.4 mm. (See footnote 6.)

Tables (1)

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Table I Analysis of variance using standard score values.a

Equations (2)

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d = [ ( μ r - μ s ) / σ s ] .
FAR = i = 1 k P ( R i S ) ,             HR = i = 1 k P ( R i R ) .