The Regular-Random Numerosity Illusion Rediscovered: A Rejoinder to Alam, Luccio, and Vardabasso
Norman Ginsburg · Perceptual and Motor Skills · 1987
The author welcomes replication by Alam, et al. (1) of his finding (2, 3, 4, 5. 6 ) that of dots are perceived as more numerous than random sets. The similarity of findings is hardly surprising, given similariry of stimuli and procedure. Ginsburg ( 3 ) and Alam, et al. ( 1 ) both used method of constant stimuli, with standards of 37 dots arranged either regularly or randomly and variables of 10 stimuli ranging from 28 to 46 docs. In Exp. 2, however, using direct estimation, Alam, et al. claim that there is no apparent effect of regularity of patterns on estimation (1, p. 887) . This statement is surprising in that, in their Table 2, 17 of 20 comparisons show estimates to be greater than irregular. Furthermore, if we collapse data across number and duration, mean estimate for was 38.2 and that for irregular was 35.3. These values can be compared to 37, average number of dots presented. This relationship between and irregular, both to each other and to actual number of dots, is exactly that reported by Ginsburg (4 , 5 ) , using direct estimation. In their conclusion, Alam, et al. (1) make some very misleading statements: Our results concur with previous ones which we find in literamre with regard . . . to regularity of patterns . . . but a point must be made with regard to a notable exception. Ginsburg (3, 4 ) found opposite results (relative overestimation of irregular patterns) (p. 888) . First of all, it is not clear whether they refer to their results in Exp. 1 (regular greater than irregular) or Exp. 2 (no difference between and irregular). Second, to which literature do they refer? W e assume they include a paper by Taves ( 7 ) mentioned in their inuoduction. Taves ( 7 ) , comparing dots arranged randomly with dots arranged in a configuration, stated the data . . . indicated definitely that placing dots in a coofiguration reduces numerousness (p. 194) . For further discussion of Taves results, reader should consult Ginsburg ( 3 ) . Finally, Ginsburg reported that regular patterns appeared significantly more numerous than random arrays (3, p. 663) , and regular sea were overestimated . . . while random were underestimated ( 4 , p. 267).