New paper alert! Now published in @SageQJEP with @LlewMills, Brett Hayes, and Evan Livesey.

Something that I've been thinking about for YEARS - is there a better way to analyse generalisation gradients? Decide for yourself :)

Download here: https://jessicaleephd.wordpress.com/publications/ 

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In #AssociativeLearning, researchers often want to know whether a particular effect is present in their data (e.g., peak shift) or whether an experimental manipulation changes the breadth or shape of the generalisation gradient (group differences).

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For peak shift, it's typical to conduct two sets of tests to show a significant "rise" and "fall" in the dependent variable.

For group differences, it's typical to report group interactions with linear and/or quadratic trend.

Simple, right?

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Well, one issue with assessing peak shift in this way is that you can't quantify how much/far the peak has shifted, only how reliably the gradient goes up and down.

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There's also questions about whether you should be correcting for multiple comparisons by selecting the peak stimulus after observing the data.

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Human data often display a high amount of individual variability, making it hard to detect effects statistically, and we can't really say much when we get a null effect. Boo...

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Enter the augmented Gaussian - a function with 4 parameters (mean, height, and 2 width parameters that allow the function to be asymmetrical) that each have an intuitive interpretation wrt generalisation.

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In this method, we fit an augmented Gaussian function to individual gradients in a hierarchical Bayesian framework and estimate each of the 4 parameters at the subject- and group-level.

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Check out the paper for re-analyses of data using this method and a demonstration of how to infer the presence of peak shift, area shift, and group differences using the posteriors of the augmented Gaussian.

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Special thanks to 4 reviewers for a bunch of helpful suggestions that dramatically improved the paper, including @ajwills72 and @joaquinmoris

Github repo: https://github.com/jessica-c-lee/bayesian-curve-fitting

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