Acta Psychologica 60 (1985) 57-71 North-Holland 57 zyxwvutsrqponm INTUITIVE STATISTICAL INFERENCES ABOUT NORMALLY DISTRIBUTED DATA * J. St. B.T. EVANS and P. POLLARD P!~wouth Polytechnic, UK Accepted February 1985 Several experiments are reported in which subjects are asked to make intuitive judgements about normally distributed samples. Experiments 1 and 2 investigated judgements about population means as a function of the mean, size and variability of the samples. Trends to take account of all three factors, in the normative direction, were shown, but sample size was significant only when numerical displays were used (experiment 1) and variability only when graphical displays were used (experiment 2). In experiment 3a, subjects were asked to estimate variability of samples directly. and were found equally able to do so with either form of data display. Experiment 3b used a simplified procedure and clarified question, and also presented both numerical and graphical displays in the same experiment. Overall, subjects took significant (normative) account of all the relevant sample features. Interactions with form of presentation showed trends consistent with the findings of experiments 1 and 2 but failed to reach significance. A further presentation effect was shown in experiments 2 and 3b, in that subjects’ inferences about graphically displayed data appeared to differ somewhat between left and right centered distributions. Overall, subjects performed quite well as intuitive statisticians, though their probability estimates were typically very conservative. The evidence of trends for different modes of presenta- tion of data to induce differential attention to sample features was sufficient to encourage further research on this problem. Understanding people’s abilities to make intuitive judgements and inferences about statistical information is a topic of both practical importance and theoretical interest. Even trained professional users of statistics, such as experimental psychologists, rely on intuitive judge- ment for many aspects of the choice of research design and interpreta- tion of data, notwithstanding the use of formal procedures for testing * This research was supported, in part, by a grant from the Economic and Social Research Council (HR 6674). Mailing address: _I. St. B.T. Evans, Dept. of Psychology, Plymouth Polytechnic, Plymouth PL4 8AA, UK. OOOl-6918/85/$3.30 0 1985. Elsevier Science Publishers B.V. (North-Holland)