Calculate or wait: Is man an eager or a lazy intuitive statistician?

Abstract

Research on people's ability to act as intuitive statisticians has mainly focused on the accuracy of estimates of central tendency and variability. In this paper, we investigate two hypothesised cognitive processes by which people make judgements of distribution shape. The first claims that people spontaneously induce abstract representations of distribution properties from experience, including about distribution shape. The second process claims that people construct beliefs about distribution properties post hoc by retrieval from long-term memory of small samples from the distribution, implying format dependence with accuracy that differs depending on judgement format. Results from two experiments confirm the predicted format dependence, suggesting that people are often constrained by the post hoc assessment of distribution properties by sampling from long-term memory. The results, however, also suggest that, although post hoc sampling from memory seems to be the default process, under certain predictable circumstances people do induce abstract representations of distribution shape.

Keywords:

• Intuitive statistics
• Numerical cognition
• Sampling model

This research was sponsored by the Swedish Research Council and the Bank of Sweden Tercentenary Foundation. We are indebted to Håkan Nilsson, Ebba Elwin and Maria Henriksson for reading and commenting on earlier drafts of the manuscript and to Anja Löfgren for help with the data collection.

This research was sponsored by the Swedish Research Council and the Bank of Sweden Tercentenary Foundation. We are indebted to Håkan Nilsson, Ebba Elwin and Maria Henriksson for reading and commenting on earlier drafts of the manuscript and to Anja Löfgren for help with the data collection.

Notes

¹ Whereas the MR measure was created to standardise performance in the two tasks against random performance, it is possible that our model of random judgement will have affected the outcome of the analyses. To investigate the robustness of our results, we therefore reran all analyses with two separate changes in the assumptions. First, in the identification task we assume that there is an equal probability of any graph being chosen by a naive participant. However, a naive participant might choose an uninformative graph (i.e. the uniform graph) rather than any of the graphs with equal probability. We therefore changed MAE_R in the identification task to equate the choice of the uniform distribution and reran all analyses of main effects and interactions in both experiments. These analyses revealed qualitatively equivalent results in both experiments. However, the format by order interaction in Experiment 1 was now only marginally significant. Thus, even when choosing a model of random judgement that suggests an uninformative rather than random response the results are similar. Second, and making an even stronger test of the robustness, we reran all analyses whereas assuming that both tasks were equally difficult under random performance. The results were similar to the original results with similar qualitative conclusions. However, in Experiment 2 the main effect of format did not reach significance. Thus, even under unrealistic assumptions, when equating the two tasks under random performance, we find comparable results suggesting that our results are fairly robust to the choice of dependent measure.

² Whereas the standardisation is undertaken to allow use of ANOVAs by adherence to the homogeneity of variance assumption underlying the test, we verified that this standardisation procedure does not itself affect the conclusions of the analyses.