Functional measurement methodology was used to assess children's attention to the total number of alternative outcomes as well as the number of target outcomes when making probability estimates. In Study 1, first-, third-, and fifth-grade children were given the task of estimating on a simple, continuous but nonnumeric scale the probability of drawing a particular color of jelly bean from a bag containing either 1, 2, or 3 jelly beans of that color, and either 6, 8, or 10 jelly beans total. In Study 2, first- through fifth-grade children were given the task of estimating the likelihood that a bug would fall on a pot containing a flower when presented displays of planters containing either 2, 3, 4, or 5 pots with flowers, and 6, 8, or 10 pots total. In both studies, the children were exposed to each of the combinations of numerator and denominator across 3 replications. The results indicate that all age groups attend to variations in the denominator as well as to variations in the numerator, and, furthermore, that they attend to the interaction between these variables. This finding contrasts sharply with research that requires children to choose which of 2 containers offers the greater chance of yielding a target item in a blind draw. It is suggested that children possess the skill to make accurate probability estimates, but they are unaware that these estimates should always be made and used when comparing the probability of an event across trials. The findings are discussed in relation to the broader issue of the limitations of the choice paradigm as a means of investigating children's thinking.
The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education