August 2023
Volume 23, Issue 9
Open Access
Vision Sciences Society Annual Meeting Abstract  |   August 2023
Stop pretending your trials are independent: Learn more from your data with asymptotic regression
Author Affiliations & Notes
  • Alasdair Clarke
    Department of Psychology, University of Essex
  • Amelia Hunt
    School of Psychology, University of Aberdeen
  • Footnotes
    Acknowledgements  This research was funded by the Economic and Social Research Council grant number ES/S016120/1 to A.D.F.C. and A.R.H.
Journal of Vision August 2023, Vol.23, 5997. doi:https://doi.org/10.1167/jov.23.9.5997
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      Alasdair Clarke, Amelia Hunt; Stop pretending your trials are independent: Learn more from your data with asymptotic regression. Journal of Vision 2023;23(9):5997. https://doi.org/10.1167/jov.23.9.5997.

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      © ARVO (1962-2015); The Authors (2016-present)

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Abstract

Typical experiments in vision science include a brief set of practise trials to ensure participants understand the task, and then a series of trials that repeat a set of conditions multiple times. The unit of analysis is typically a measure of central tendency taken from all the trials within a given condition/participant, which represents an estimate of performance in that condition that can be compared to other conditions. But inherent in any set of repeated trials is the way performance changes; for example, stimulus-response mappings get faster and less error-prone, and participants tune their attention to pick up information from the appropriate locations and start to anticipate sequences of events and their timing with more precision. We throw all this information away when we express performance as an average. Multi-level models (LMM) are an increasingly popular approach, but these assume that all trials are statistically independent and identically distributed. Here we advocate for applying a straightforward asymptotic regression (Stevens, 1951) to repeated-measures performance data and show how it provides a richer and more accurate measure of the effects of different manipulations on performance. Methods based on "average performance" (whether using aggregate statistics or a multi-level framework) tend to result in statistics that are biased by the early trials. We demonstrate the utility of asymptotic regression using data from classic paradigms such as visual search and show the extent to which established effects are driven by a) performance in early trials b) differences in the stable performance asymptote and c) how the learning rate varies between conditions. We think asymptotic regression should become a standard tool applied to repeated measures data to provide a richer picture of the dynamic changes in performance inherent in experiments with repeated measures.

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