Normalization of timed measures in bilingualism research

The time it takes an individual to respond to a probe (e.g., a word, picture, or question) or to read a word or phrase provides useful insights into cognitive processes. Consequently, timed measures are a staple in bilingualism research. However, timed measures usually violate assumptions of linear models, one being normal distribution of the residuals. Power transformations are a common solution but which of the many possible transformations to apply is often guesswork. Box and Cox (1964)Box, G. E. P., & Cox, D. R. (1964). An analysis of transformations. Journal of the Royal Statistical Society. Series B (Methodological), 261, 211–252. developed a procedure to estimate the best-fitting normalizing transformation, coefficient lambda (λ), that is easy to run using standard R packages. This practical primer demonstrates how to perform the Box-Cox transformation in R using as a testbed the distractor items from a recent eye-tracking study on sentence reading in speakers of Spanish as a majority and a heritage language. The analyses show (a) that the exponents selected via the Box-Cox procedure reduce positive skewness as well as or better than the natural log; (b) that the best-fitting value of λ varies based on factors such as group and, in the case of eye-movement data, the measure of interest; and (c) that the choice of transformation sometimes impacts p values for model estimates.