Teaching intuitive statistics I: Estimating means and variances

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Abstract
Previous studies have shown that man is only fairly efficient as an intuitive statistician. It is proposed that users of statistics, for example, should be trained to become better intuitive statisticians to enable them to appreciate and make inferences in numerically determined environments. To this end, an experiment was performed which investigated the training of subjects to estimate means and variances using immediate knowledge of results. Initial analyses showed that subjects seemed to be good at estimating means but that they were influenced by the variance of the numbers when estimating the mean, although the difference between the high and low variance conditions was small. When estimating variances subjects were less accurate than when estimating means, and were influenced by the size of the variance of the numbers. Further analyses of the variance estimate data showed that subjects’ performance improves over trials when they are estimating low variances but not high variances, i.e. they can learn to estimate low but not high variances. These analyses also showed that subjects were sometimes using the range to help them with their estimates, particularly for low variance estimates, but that they were not using immediately preceding feedback in a direct way.

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