EFFECT OF SPEED AND ACCURACY INSTRUCTIONS ON CONFIDENCE JUDGMENTS FOR MAGNITUDE ESTIMATES *

Accuracy and speed instructions have been recently and successfully used to determine the locus of confidence judgments for detection and discrimination tasks (Baranski & Petrusic, 1998; Petrusic & Baranski, 2000). No such research has been done using magnitude estimation. This paper studies, using an absolute magnitude estimation task and four experimental conditions, the effects of speed and accuracy instructions on responses, proportion of correct responses, decisional response times, confidence judgments and confidence response times. The proportion of correct responses used has been previously defined in Garriga-Trillo (1996). Results show greater effects for the accuracy condition than for the speed one in all the five dependent variables considered. It seems that subjects not only apply both instructions to estimate magnitudes but also to estimate confidence. When confidence is demanded, either under accuracy or speed conditions, mean decisional response times are significantly longer than for the nonconfidence condition. Confidence judgments could be, to a certain extent, processed with the response. Magnitude estimation involves a detection and a discrimination phase, previous to giving a numerical response to quantify stimulus magnitude. Subjects first have to detect the stimulus, then discriminate between stimuli and, finally assign a number to the perceived stimulus magnitude. Following this inclusion mechanism and although recognizing a more complex undertaking, studying aspects from detection and discrimination tasks can shed light on magnitude estimations. This approach has been taken by Garriga-Trill o, Vill arino, GonzálezLabra & Arnau (1993, 1994) to begin studying confidence judgments of magnitude estimates concerning the underconfidence-overconfidence effect and considering studies with detection and discrimination tasks. Díaz & Serrano (2000) and Serrano & Díaz (2000) have considered issues from previous research done with discrimination tasks to study the same effect with a magnitude estimation task. Very recently, according to Petrusic and Baranski (2000), theories trying to explain the basis for confidence judgments, within a general framework of detection and discrimination, have been developed. Balakrishnam & MacDonald (2000) mention that confidence judgments may be the result of an information accumulation process or a derivative of such a process produced after the discrimination decision is made. Although most models present the locus of confidence after the decisional process is attained (its locus is then post-decisional) researchers like Baranski & Petrusic (1998) present evidence of a pre-decisional locus under some conditions and a postdecisional locus under other conditions. These conditions were mainly related to accuracy and speed instructions. Although their work, and that of others, concern detection and discrimination tasks, as we stated at the beginning, it is useful to implement their ideas to continue studying confidence judgments of magnitude estimates. This work pretends to study the effects of accuracy and speed instructions on confidence judgments of magnitude estimates using a sensory task, the estimation of rectangles areas, having in mind a future search for a possible locus of confidence judgments of magnitude estimates. METHOD Subjects. Sixty-four volunteer subjects (14 males and 50 females; mean age = 23.4 years; age range = 18-55 years) participated in the experiment. All the subjects had normal or corrected-tonormal vision and were naive to the nature and aims of the experiment. All participants were tested individually. Apparatus. The stimuli were presented on a 14-inch screen monitor, which had a resolution capabilit y of 800 pixels horizontally by 600 pixels vertically. A Pentium II PC was used and a specific programmed software (Serrano, 1999) controlled instructions, event sequencing, randomisation, and the recording of responses, response times, confidence ratings and confidence response times. The computer keyboard was used as an input device. Stimuli. Eight rectangles of different areas were displayed centred on the computer screen. They appeared in white on a black background and were generated making their length 1 cm longer than their width both within the rectangles and between them. For the experiment, the areas considered were 2, 6, 12, 20, 30, 42, 56 and 72 squared centimetres. Another four stimuli were used for the practice trial session, but using a 2 centimetre difference between length and width. Their areas were 3, 15, 35 and 63 squared centimetres. All stimuli were randomised within blocks. The display was presented at eye level and at a viewing distance of approximately 50 cm. Previous to the rectangles’ display, a white circle appeared on the centre of the screen to focus the subjects’ attention. Procedure. Four experimental conditions were defined considering four different sets of instructions (accuracy-confidence, speed-confidence, accuracy-no confidence, speed-no confidence). Subjects were randomly assigned to one of the four groups. The instructions were presented on the screen. All groups had to estimate the rectangleś areas using the absolute magnitude estimation technique both in the trial session and in the three experimental blocks. The speed instructions encouraged observers to respond immediately after the rectangles disappeared from the screen. In the accuracy instructions observers were instructed to be accurate in their estimations of the rectangleś areas. The confidence groups were required to give a confidence rating, from 1 to 100, for their magnitude responses. A confidence value of 100 indicated absolute certainty, and 1 indicated no certainty at all . When the participant had read and understood the instructions, s/he pressed the “Enter” key and the experiment began. The white circle appeared on the centre of the screen to focus the subjectś attention. Then, the first rectangle appeared centred on the screen. When the subject was ready to estimate its area s/he pressed the “Enter” key and the primary decision time was recorded. This primary decision time is then the time measured from stimulus onset to pressing the “Enter” key. The screen was cleared and a question asking for the area of the rectangle then appeared on the screen. Observers indicated their estimated area by moving the index finger of their preferred hand from the “Enter” key to the number response keys. This secondary decision time (the time measured from starting with the number keys to ending giving the numerical answer) and the number given were also recorded. The program also recorded the sum of both primary and secondary decision times, the decisional response time (Decisional RT). If a confidence rating was demanded from the subject, observers pressed the “Enter” key and moved the same finger from the “Enter” key to the numerical keys to express their confidence by pressing their response using the same numerical keys. Thus the time from the depression of the “Enter” key to the depression of the last number from the numeri cal keys was the time to deter mine confidence, or confidence response time (Confidence RT). The confidence judgment and the confidence RT were also recorded. All RTs were measured in seconds. RESULTS and DISCUSSION Our data has been analyzed both descriptively and inferentially . Figures 1-5 show plots in which accuracy and speed are one of the independen t variables considered. The other independen t variable is either stimulus magnitude or blocks. A new independen t variable is considered in Figure 6: confidence and no confidence conditions . The dependent variables were response, proportion (or percentage ) of correct responses, decisional RT, confidence ratings and confidence RT. The proportion of correct response s (or its percentage ) was calculated as defined in Garriga-Trill o (1996) using an index s imilar to Kendall ́s Tau. Figure 1. Mean respons e for each stimulus magnitude under accuracy-spee d conditions. Figure 2. Proportion of correct responses for each block under four experimental conditions. In Figure 1 we can observe an ascending trend in response as s timulus magnitude increases . There are si gnificant differences between responses , F(7,1528)=134, p<0.0001, Power=1. Subject s discriminate between stimuli. Also mean response s (each point represent s 192 judgments) are significantly greater in the accurac y condition than in the speed one, F(1,1534)=6.55, p<0.01, Power=0. 73. The interaction between the independen t variables was not significant. Figure 2 consider s four conditions and three blocks as independen t variables. The differences in proportion of correct responses between blocks is not significant, F(2,189)=0.19, p>0.83, Power=0. 08. No learni ng effect is det ected. The differences in percentage of correct response s between the four conditions is si gnificant, F(3, 188)=3.6, p<0.01, Power=0. 79, although all the percentage s are high. This may mean that the task was easy. The highest percentages are obtained in confidence-accurac y (mean=90.4) and the smallest ones in confidence-sp eed (mean=84.9). The mean difference, using the Tamhane statistic, is significant for p<0.03. The other differences between conditions are not significant. The interacti on between the two independen t variables was not significant. Α Confidence-Accuracy Β No Confidence-Accuracy Χ Confidence-Speed ∆ No Confidence-Speed Experimental Conditions Block 1 Block 2 Block 3 Blocks 84 86 88 90 92 P r o p o r t i o n o f c o r r e c t r e s p o n s e s