FREQUENCY EFFECTS IN DISTRIBUTIONS OF STIMULI
WITH OR WITHOUT STANDARDS
Marco Tommasi
Università degli Studi di Padova, Italy E-mail: marco.tommasi@unipd.it
Abstract
Category ratings of stimulus intensities are affected by the skewing of frequency distributions of stimuli. According to Parducci’s theory, frequency effects are due to the tendency of par-ticipants to use all the categories with the same frequency. According to Haubensak’s theory, these effects are due to the tendency of participants to use all categories during the initial presentations. Frequency effects should be reduced by the presentation of stimuli with ex-treme intensities as standards before each variable stimulus. In this experiment, participants rated brightnesses of squares or lengths of lines using integers from 1 to 5. Target stimuli were presented with or without standards and, for each of these two conditions, frequency distributions were negatively or positively skewed. Results show that the skewing of frequency distributions strongly affected subjective scales independently of the presence or absence of standards. This finding indicates that, in spite of the standards, participants used previous stimuli rather than the standards as a frame of reference for their judgments.
Absolute subjective judgments of stimulus intensities are affected by the way stimuli are presented to participants (Garner, 1954; Parducci & Marshall, 1961; Poulton, 1979). When participants rate perceptual magnitude produced by stimuli, the final subjective scales are bi-ased if some of the stimuli have a greater frequency of occurrence. Parducci (1963) proposed a theory about the effects of skewed distributions of stimuli on subjective scales. According to this theory, when a participant rates the magnitude of a perceptual attribute, his judgment is ruled by two principles of judgment. The first principle, called the range principle, is the as-signment of categories to each stimulus by dividing the range of stimuli into a number of equal subranges corresponding to the number of available categories. The second principle, called the frequency principle, is the assignment of categories in such a way that each cate-gory is used with the same frequency. In his experiments about frequency effect, Parducci (1982; Parducci & Perrett, 1971; Parducci & Wedell, 1986) had participants preview a set of stimuli selected so to be representative of the global range of stimuli used during the regular experimental sessions. That is, when the frequencies of stimuli were varied, also the preview stimuli were varied so to be as representative as possible of the regular series. This procedure could have facilitated participants to judge initial stimuli, because they could have used the stimuli of the preview as standards. It is also possible that participants forgot these standards during the experiment, and then began using the preceding stimuli of the regular series as a frame of reference, producing, as a consequence, biased subjective scales.
Haubensak (1990, 1992) proposed another theory of frequency effects on category ratings. Because more frequent stimuli more probably appear in the initial part of the stimulus series, participants center their scale on the restricted range of the most frequent stimuli, without changing it when, subsequently, the less frequent stimuli appear. Plausibly, this happens be-cause participants do not know the whole range of stimuli and, therefore, they use up all cate-gories during the initial presentations of stimuli, especially when the number of categories is small.
66
With standardsWithout standardsMean Rated Brightness54321
54321
SkewingNegativePositive01020
Figure 1. Mean ratings of brightness plotted against luminance of squares presented with or without standards. Open circles refer to frequency distributions with negative skewing and filled circles refer to frequency distributions with positive skewing.
How much are subjective scales biased when participants have the possibility to see the stimuli with the smallest and largest intensities every time before the target stimulus appears? If each target stimulus is preceded by the same pair of extreme stimuli, then participants have constant standards with which they can compare the sensory magnitude produced by the tar-get stimulus. Besides, standards should prevent participants from using up all categories in the initial presentations of stimuli. Consequently, participants should generate subjective scales that are slightly or not biased by the skewed frequency distributions of stimuli.
Method
Participants. Eighty University of Padova students participated in the experiment, all with normal or correct-to normal vision.
Stimuli. Stimuli were presented in the center of a 24 × 33 cm screen of a Sony Trinitron 200PS monitor controlled by a Power Macintosh G3 computer. Viewing distance was 80 cm. Stimuli were squares with side length of 16 mm and with luminances of 0.36, 1.1, 2.2, 5.6, 10.4, 17.9, 31.2 or 44.6 cd/m2, or were horizontal lines with lengths of 66, 69, 76, 91, 110, 126, 151 or 176 mm. To test the effect of standards on participants’ judgments, in one ex-perimental condition each stimulus was preceded by two standards, while in the other condi-tion each stimulus was presented without standards. For the squares, the standards had lumi-
304050/010202Luminance of Squares (cd/m )304050
nances of 0.2 or 54.5 cd/m2, and for the lines the standards had lengths of 63 or 189 mm. To test the effect of the skewing of distribution of stimulus frequencies on participants’ judg-ments, each series of stimuli was presented either with a positively or with a negatively skewed distribution. In the positive skewed distribution, the frequencies of the eight stimuli, from the smallest to the largest stimulus, were 12, 10, 8, 6, 4, 4, 2 and 2. In the negative skewed distribution the frequencies of the eight stimuli, from the smallest to the largest stimu-lus, were 2, 2, 4, 4, 6, 8, 10, and 12. The experiment was divided in eight sessions on the basis of the kind of stimuli (squares vs. lines), of the standards (presence or absence of standards) and of the kind of skewing (positive vs. negative skewing of frequency distribution).
66
With standardsWithout standardsMean Rated Length54321
54321
SkewingNegativePositive6080100
Figure 2. Mean ratings of perceived length plotted against physical length of lines presented with or without standards. Open circles refer to frequency distributions with negative skewing and filled circles refer to frequency distributions with positive skewing.
Procedure. There were ten different participants for each experimental session. Before start-ing the experiment, each participant was presented written instructions on the monitor screen, which described their task. Each target stimulus was preceded by the presentation of a white cross, with arms 13 mm long, in the center of the monitor screen to indicate the fixation point. Subsequently, two different procedures for showing each stimulus were used accordingly to the presence or absence of standards. When standards were presented, 1 sec after the appear-ance of the white cross the following stimuli and crosses appeared for 1 sec: first the standard, then the white cross, then the second standard, then the white cross and, finally, the target stimulus to be judged. Each stimulus was presented twice and the order of presentation of standards was counterbalanced. When there was no standard, only the white cross preceded the target stimulus. Verbally each participant rated stimulus brightnesses or stimulus lengths using integers from 1 to 5. The standards–the stimuli with the smaller and larger value–were labeled with the numbers 0 and 6 (14 pt. in size), respectively, which appeared 2.2 cm above the standard. Participants were told to use the standards as points of reference for their judg-ments and that all stimuli they would have seen could never be larger or smaller than the standards. For each participant, the order of presentation of stimuli was randomized and the total number of presentations was 96.
120140160180 100 6080Length of Lines (mm)120140160180
Results
Figure 1 shows the results for the rating of brightness and Figure 2 shows the results for the rating of length. Error bars indicate one standard error above and one below the corre-sponding mean. Figure 3 shows the subjective scales of brightness and length for stimuli pre-sented with or without standards.
5BrightnessLength5
Mean Ratings44
33
22
1123456
Figure 3. Comparison between the brightness and length scales for stimuli with ({) or with-out (z) standards. Ratings are plotted against the eight different stimuli.
A three-way 2 (Kind of Stimulus) × 2 (Standards) × 2 (Kind of Skewing) ANOVA showed that all the main effects were significant (F1,625 = 10.3 with p < .01; F1,625 = 20.6 with p < .01; F1,625 = 257 with p < .001, respectively). The interaction between Kind of Stimulus and Stan-dards was significant (F1,625 = 37.1, p < .001). Figure 4 shows that brightness scales were rela-tively unaffected by the presence or absence of standards, while length scales were strongly affected.
Discussion
The results clearly show that the presence of standards does no reduce the effect of the skewed frequency distributions on subjective scales. In particular, when stimuli are squares with different luminances, the only effect of standards seems to increase slightly the ratings for dark gray squares. When stimuli are horizontal lines, with the standards present, partici-pants use all of the available categories, while, with no standards, participants reduce the range of possible categories. Probably, this effect is due to the tendency of participants to avoid considering the 66 mm long line as the lowest extreme of the range of lines, because they expect to see shorter lines. Thus, ratings of small lines are increased. This means that participants, when they do not know precisely how many stimuli they will see, tend to seek a
7812Stimulus Number
3456781
frame of reference in their prior knowledge, in this case, probably, the metric scale for meas-uring lengths.
Petzold and Haubensak (in press) assert that in category rating people use two kinds of frames of reference: a long term memory frame, consisting of the extreme stimuli and a short
3.6term memory frame, consisting of the
two stimuli which have preceded the 3.5current stimulus. If the current stimulus 3.4is between the two previous stimuli, 3.3participants use the previous stimuli as 3.2standards. Otherwise, if the current
stimulus is smaller or greater than the 3.1two previous stimuli, then participants 3.0use the small or large extreme stimulus 2.9and the nearest previous stimulus as
Present Absentstandards. However, the stimuli stored
Standardsin memory and used as standards are
not all equally important for the partici-Figure 4. Interaction between kind of stimuluspants, when they rate stimulus intensi-[gray squares ({) vs. horizontal lines ()] andties. The empirical results of the present standards.
experiment show that participants prefer selecting the previous stimuli as stan-dards rather than the extreme stimuli, because they are more concerned for keeping a good accord between their present and previous responses rather than for evaluating consistently the distances between stimulus intensities, especially when a correct evaluation of stimulus intensities involves a radical shift of their responses.
Parducci explained the frequency effect on the basis of the frequency principle. However, only four participants used category „1“ for the shortest line both in the series of lines with positive and negative skewed frequency distributions and without standards. This result in-validates Parducci’s frequency principle. Probably, this principle was confirmed in Parducci’s experiments because of the use of previews composed by sets of stimuli similar to those used in the regular stimulus series. The fundamental difference between the performance of Par-ducci’s participants and that of the participants of the present experiment is that Parducci’s participants always had the possibility to know from the beginning the range of variation of stimulus intensities, and, consequently, they knew which were the stimuli with the lowest and the highest category, while in the present experiment, when standards were not shown, par-ticipants did not have this possibility.
These results strengthen Haubensak’s concept that participants set their scales during the first few presentations of stimuli and keep their current judgments coherent with those of the initial presentations. Because more frequent stimuli have greater probability to appear in the initial presentations, subjective scales tend to shift upward or downward when the more fre-quent stimuli are large or small, respectively. Plausibly, the fact that participants are forced to use only five categories makes them think that there will be a number of stimuli which is not greater than the number of available categories. For this reason, they easily use up all the categories in the initial presentations, thus causing the shift of the subjective scales. If partici-pants had been told to use a greater number of categories, then they would not have finished all the categories in the initial presentations, because they would have expected to see more different stimuli. Indeed, Parducci’s experiments show that contextual effects are reduced considerably when participants can use a great range of categories for their judgments (Par-ducci 1982; Parducci & Wedell, 1986).
Mean Rating
References
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