IMPLICIT INTUITIVE STATISTICAL DESCRIPTION: PERCEPTIONS THAT MAY IMPEDE OR FACILITATE STATISTICAL INSTRUCTION

摘要

Statistical properties to which people intuitively pay attention were inferred from experiments in which subjects made similarity judgments about collections.;Each collection comprised 10 goldfish, identical except for their sizes. Five distinct sizes were used. The distribution of sizes varied from collection to collection.;In one experiment, children and adults sorted drawings of goldfish tanks, then pictorial histograms. Most subjects produced sorts that were independent of the positions of the fish in the stimuli. Nearly all subjects produced sorts apparently based wholly or partly on some measure of location (overall bigness or smallness) of the fish sizes in a stimulus; an appreciable minority produced sorts apparently based wholly or partly on some measure of dispersion of sizes. The mathematical sorting criterion that subjects most often expressed was the number of largest-size fish.;In another experiment, second-grade children, fifth-grade children, and adults judged tank stimuli, then histogram stimuli, in triads tests. The children and some adults saw stimuli like those of the first experiment. For other adults, the goldfish in each tank stimulus were arranged from smallest to largest. For the remaining adults, tank and histogram stimuli displayed numerals instead of goldfish.;Nonmetric multidimensional scaling of the size distributions was performed; the INDSCAL procedure of Carroll and Chang was used to analyze differences among the groups of responses marked by different combinations of age and stimulus representation. Two dimensions were identified: a location dimension, well described by a weighted sum of the numbers of largest- and second-largest-size fish in a stimulus, and a dispersion dimension, well described by the coefficient of variation. Dimension weights were more variable among groups of responses to tank stimuli than among groups of responses to histogram stimuli, with second-grade children's responses to tank stimuli most heavily weighted on the location dimension.;A separate analysis of differences among subjects suggested that (a) many subjects could be classified as attentive primarily to location or primarily to dispersion and (b) children were most diverse in their patterns of response to histograms.;Implications of these judgments for statistical instruction are discussed.