Subjects
A total of 188 undergraduates (81% were education majors) at a large mid-western university participated in the 1992 study. Of those subjects, 33 (18%) were male and 155 (82%) were female; their age ranged from 18 to 44 years old with 96% falling into the traditional student range of 18-22 years old. Approximately 65% indicated that they intended to teach at the elementary school level. Over 70% of subjects were sophomores.
In the 1998 study, the sample was composed of 100 undergraduates who enrolled in education courses in the Spring of 1998 at the same university. The proportion of the two genders was exactly the same as that from the 1992 study (18% males versus 82% females). There was 10% more education majors in the 1998 sample (93%) than in the 1992 sample (81%). The age range was smaller in this study (from 18 to 28 years old) with 98% falling into the traditional student range of 18-22 years old. Eighty-three percent of them planned to teach at the elementary school level (about 20% more than those in the 1992 study). The percentage of sophomores was about the same as the one in the 1992 study (over 70%). Thus, in general, the data collected in 1998 were more homogeneous than the 1992 data in terms of subjects' major, age, and intended teaching level in grade schools. All subjects volunteered to become involved in both studies, though a simple token of appreciation was awarded upon completion of the experiment.
Instrument
An interactive computer program developed by Peng and Bolte (1992) was used in both studies for stimulus presentation and data recording. Three tasks were administered by the computer in the sequence of (1) the expectation task, (2) the paired comparison task, and (3) the probability restatement task. When the instrument was administered, the order of presentation of stimuli within each task was randomized by the computer program. In general, subjects were able to complete all tasks in less than 20 minutes.
Procedure
The first (expectation) task asked subjects to indicate their expectations regarding the reported percentage in 21 educationally related statements which were extracted from reputable references (e.g. education textbooks, journal articles, research reports, etc). A complete list of these statements is given in the Appendix. Each statement contained a numeric percent which was near one of the medians (7%, 22%, 36%, 50%, 64%, 79%, and 93%) for 7 intervals that equally divided percentages from 0 to 100. The numeric percentage in each statement has been judged to be equal to, higher than, or lower than what was expected by the majority of the subjects in the pilot study. Thus, in each of the 7 probability intervals, three statements were presumed to carry different expectation information. For example, in the interval of 28.7% to 42.9% (the median is 36%), the percentage in the statement, "Of adolescent girls who become pregnant, 37% do so in the first three months of sexual activity," was judged to be equal to what was expected. The percentage in the statement, "Of those children who are homeless, 38% attend school on a regular basis," was judged to be higher than what was expected. The percentage in the statement, "In a national poll, 36% of the parents said they would not like their child to take up teaching as a career," was judged to be lower than what was expected. In all three statements, the percentage was controlled to be sufficiently close to the median value.
In the second (paired comparison) task, each of 11 most commonly used probability expressions was paired with the remaining 10; subjects were asked to choose, in each pair, an expression which implies a greater likelihood of occurrence for an event. The 11 probability expressions were chosen because they covered the 0%-100% range well and were the most common terms used across studies (Reagan et al., 1989). The point- and interval-estimates of the medians from Reagan et al. (1989) for these terms were: "almost impossible" (2%, 0%-5%), "very unlikely" (10%, 2%-15%), "improbable" (15%,10%-20%), "unlikely" (15%, 10%-25%), "possible" (40%, 40%-70%), "an even chance" (50%, 45%-55%), "probable" (70%, 60%-75%), "likely" (70%, 65%-85%), "very probable" (80%, 75%-90%), "very likely" (85%, 80%-90%), and "almost certain" (90%, 90%-100%). Since these estimates were consistent across time and various studies (Mosteller & Youtz, 1990; Reagan et al., 1989), we chose to include their corresponding probability terms as references with which to compare our results.
The third (probability restatement) task asked subjects to select one probability expression (out of the 11 listed above) which best conveyed the meaning of the percentage (numeric probability) embedded in each of the 21 educational statements. In this task, about a third of the subjects were presented the 21 statements without any fractional restatement (i.e. exactly the same as the 21 statements used in the expectation task). For example, "In a national poll, 36% of the parents said they would not like their child to take up teaching as a career." Another one third were presented the statements with fractional restatements using 100 as the denominator. For example, "In a national poll, 36% of the parents - or 36 of every 100 - said they would not like their child to take up teaching as a career." The remaining one third were presented the statements with fractional restatements using 100,000 as the denominator. For example, "In a national poll, 36% of the parents - or 36000 of every 100000 - said they would not like their child to take up teaching as a career."