Intuitive statistical inferences about normally distributed data |
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| Affiliation: | 1. Department of Medical Biology and Genetics, Faculty of Medicine, Gazi University, Besevler 06510, Ankara, Turkey;2. Department of Medical Biology, Faculty of Medicine, Duzce University, 81620 Duzce, Turkey;3. Department of Public Health, Faculty of Medicine, Gazi University, Besevler 06510, Ankara, Turkey;4. Department of Urology, Faculty of Medicine, Hacettepe University, Sıhhiye 06100, Ankara, Turkey;5. Department of Urology, Faculty of Medicine, Gazi University, Besevler 06510, Ankara, Turkey;1. AcSIR-Academy of Scientific and Innovative Research, Gaziabad, India;2. Medicinal, Aromatic and Economic Plants Group, Biological Science and Technology Division, CSIR-North East Institute of Science and Technology (NEIST), Jorhat, Assam, 785006, India;1. Scion, PO Box 29237, Fendalton, Christchurch, New Zealand;2. Scion, PO Box 3020, Rotorua, New Zealand;3. Indufor Asia-Pacific Ltd, PO Box 105039, Auckland, New Zealand;1. Advanced Analytics Institute, University of Technology, Sydney, Broadway New South Wales 2007, Sydney, Australia;2. The Tumour Bank, Children׳s Cancer Research Unit, The Children׳s Hospital at Westmead, Locked Bag 4001, Westmead New South Wales 2145, Sydney, Australia;3. Centre for Quantum Computation & Intelligent Systems, University of Technology, Sydney, Broadway New South Wales 2007, Sydney, Australia;1. Bolu Abant Izzet Baysal University Medical Faculty, Histology and Embryology Department, Bolu, Turkey;2. Bolu Abant Izzet Baysal University Medical Faculty, Biochemistry Department, Bolu, Turkey;1. Cambridge Centre for Sport and Exercise Sciences, Department of Life Sciences, Anglia Ruskin University, Science Building - 310, East Road, Cambridge CB1 1PT, United Kingdom;2. Department of Computing and Technology, Anglia Ruskin University, Cambridge, United Kingdom;3. Physiotherapy Department, South London and Maudsley NHS Foundation Trust, Denmark Hill, London SE5 8AZ, United Kingdom;4. Health Service and Population Research Department, Institute of Psychiatry, Psychology and Neuroscience, King''s College London, De Crespigny Park, London Box SE5 8AF, United Kingdom;5. Faculty of Health, Social Care and Education, Anglia Ruskin University, Chelmsford, United Kingdom;6. National Research Council, Neuroscience Institute, Aging Branch, Padova, Italy;7. Department of Sport and Health Sciences, University of Exeter, Exeter, United Kingdom |
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| Abstract: | 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 presentation of data to induce differential attention to sample features was sufficient to encourage further research on this problem. |
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