Recent work with the full 4-card selection task supports the picture presented by Margolis and, moreover, fills out further details. The 4-card task is difficult, not because subjects cannot reason accurately, but because they misunderstand the rule they are asked to verify. The RAST is easier because the absence of the 'P' and '¬P' cards provides an implicit hint what that rule means.
2. Subjects were given six successive selection problems without feedback. They were asked to physically turn the cards over, but only as few as were necessary, and ascertain whether the rule was true or false. A majority of subjects (18/30 in Gebauer & Laming, 1997; 78/96 in Osman & Laming, 2001) made selections which were in complete logical consistency with some particular (mis)understanding of the rule. If subjects who made one false selection only are included, or who changed their minds just once, the proportions rise to 26/30 and 91/96 respectively.
3. The possibility that such consistent performance was achieved simply by repetition of previous card selections can be discounted. Of those subjects who responded consistently throughout, none in Gebauer & Laming, 1997 and only 4 out of 78 in Osman & Laming, 2001 made any mistake at all in declaring the rule 'true' or 'false'. So, the great difficulty of Wason's 4-card selection task subsists in misunderstanding the rule that is to be verified.
4. Two errors of understanding are particularly prevalent: (a) reading "top/underneath" for "one side/other side" and (b) replacing the simple conditional with a bi-conditional ("if and only if"). These component misunderstandings occur independently as the following table shows (X2 = 0.001 with 1 d.f).
Component Correct Top/underneath Bi-conditional Top/underneath
& bi-conditional
Gebauer &
Laming, 1997 1 4 2 11
Osman &
Laming, 2001 10 13 19 22
Totals
error 11 17 21 33
5. This analysis applies to the RAST task discussed by Margolis in this manner. Envisage a subject who misunderstands "top/bottom" for "one side/other side", but does not mistake the simple conditional for a bi-conditional (17 subjects in the table above). Such a subject will select 'P' only from the full 4-card task. Now remove 'P' and '¬P'; there is now no relevant card left for this subject to select, and that of itself points up the misunderstanding. It provides an implicit hint that "top/bottom" is wrong. Correcting that error means replacing "top/bottom" with "one side/other side" and those 17 subjects will then get the RAST task correct.
6. The resultant proportion of correct responses might appear a little low in relation to the claims made in Margolis' article (4). I comment that the proportions of correct responses can be manipulated by rephrasing the rule in such a way as to protect against specific misunderstandings (Platt & Griggs, 1993, 'P explication, standard rule' condition; Gebauer & Laming, 1997, Expt 2, Rule III; Baker, unpublished MS). Moreover, the effects of such manipulations are large, so that the comparison between the incidences of specific component misunderstandings in different experiments is not reliable. In addition, showing the subjects a sample set of cards to handle and turn over in the course of preliminary instruction appears to reduce the incidence of the "top/bottom" misunderstanding (as one might readily expect; Baker, unpublished MS).
7. Turning now to specific comments on the target article:
(a) The 'category' idea (5) is incorrect-but perhaps what Margolis
really means is the "top/bottom" error, but has failed to express
it clearly. Note that the misreading of "one side/other side" for
"top/bottom" in 5 is put the wrong way round.
(b) There is no evidence that the bi-conditional error (6) has
anything to do with the relative ease of the RAST. The removal of
'P' and '¬P' still leaves the bi-conditional subject with 'Q' and
'¬Q' to examine and provides no hint that '¬Q' alone is correct.
(c) Matching bias (the selection of 'P' & 'Q'; Evans, 1998) results
from the combination of both component errors (32 out of 82
subjects in the table above). The "top/bottom" error removes '¬Q'
as a relevant card and the bi-conditional error adds 'Q'.
(d) Margolis (10) presents yet another example of how dramatically
card selections in the full 4-card task can be influenced simply by
rephrasing the rule, the same rule. This example, and the other
cases listed above, work by constraining the ways in which subjects
might understand what they are to do.
(e) The 'cognitive illusion' (13) is really a simple
misunderstanding, but to place it at 'the stage of interpreting the
task' is exactly correct. In fact, Wason's selection task involves
no reasoning at all until subjects are actually asked to say
whether the rule is true or false (see Osman & Laming, 2001); it is
all about (mis)understanding.
Baker, H. Misunderstandings in Wason's selection task. Unpublished student project report.
Evans, J.St.B.T. (1998 Matching bias in conditional reasoning: Do we understand it after 25 years. Thinking and Reasoning, 4, 45-82.
Gebauer, G., & Laming, D. (1997) Rational choices in Wason's selection task. Psychological Research, 60, 284-293.
Margolis, H. (2000) Wason's Selection Task With Reduced Array. PSYCOLOQUY 11(005) ftp://ftp.princeton.edu/pub/harnad/Psycoloquy/2000.volume.11/ psyc.00.11.005.reduced-wason-task.1.margolis http://www.cogsci.soton.ac.uk/psyc-bin/newpsy?11.005
Osman, M. & Laming, D. (2001). Misinterpretation of conditional statements in Wason's selection task.. Psychological Research, in press.
Platt, D.P. & Griggs, R.A. (1993) Facilitation in the abstract selection task: The effects of attentional and instructional factors. Quarterly Journal of Experimental Psychology, 46A, 591-613.