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Aspects of first year statistics students’ reasoning when performing intuitive analysis of variance: effects of within- and between-group variability

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Abstract

Making inferences about population differences based on samples of data, that is, performing intuitive analysis of variance (IANOVA), is common in everyday life. However, the intuitive reasoning of individuals when making such inferences (even following statistics instruction), often differs from the normative logic of formal statistics. The present study examined the reasoning used by several cohorts of first year statistics students when performing IANOVA. In general, participants perceived datasets representing larger but less reliable group differences as stronger evidence of a population effect than datasets representing smaller yet more reliable differences, across various data formats (Experiment 1) and datasets (Experiment 2). Qualitative results revealed several distinct patterns of reasoning between participants which was associated with performance. Implications for instruction are discussed.

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Notes

  1. When students perform an informal mental appraisal of the variability in datasets in IIR tasks such as those described above, they typically do not calculate variance in a strict sense (i.e., they do not determine the 2nd moment about the mean of the datasets). However, because such tasks were initially intended to get students to think informally about the logic underlying the formal procedure known as analysis of variance (ANOVA), I refer these tasks as intuitive analysis of variance (IANOVA), rather than analysis of variability.

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Acknowledgments

I would like to sincerely thank Judith Shedden and Steven Mewaldt for their assistance with data collection. Without them, this study would not have been possible. I would also like to thank Julie Corrigan for her assistance with data coding and for providing valuable feedback on the manuscript. As well, I would like to thank the anonymous reviewers of this article. The final version of the paper has benefited greatly from their input.

Experiment 1 of this paper was presented in a more limited scope at the 31st Annual Conference of the Cognitive Science Society.

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Authors and Affiliations

  1. University of Ottawa, Lamoureux Hall Room 430, 145 Jean-Jacques-Lussier Street, Ottawa, ON, K1N 6N5, Canada

    David L. Trumpower

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Correspondence to David L. Trumpower.

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Table 3 Hypothetical datasets presented to participants
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Trumpower, D.L. Aspects of first year statistics students’ reasoning when performing intuitive analysis of variance: effects of within- and between-group variability. Educ Stud Math 88, 115–136 (2015). https://doi.org/10.1007/s10649-014-9574-y

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