The benefits and practical guidelines to log-transforming looking time data

• In Event: 2-151 - Step by Step: Improving best practices for research with children

Integrative Statement

Infant researchers often make use of both looking time (LT) data and inferential statistics in their experiments. However, parametric inferential statistics assume normality of the residuals in the analysis and LT data tends to have positively skewed distributions with a long tail of larger values, leading to inaccurate Type-I errors. Log-transforming LT data provides a solution by making the LT distributions less skewed. Thus, following the recommendations in Csibra et al. (2016), we encourage researchers to log-transform their LT datasets before statistical analysis.
In this talk, we will provide additional support for why it is better to log-transform LT data. First, in line with Csibra et al. (2016), we argue that LT data is multiplicative data by nature. In a typical within-subject experiment, when infants discriminate between a novel stimulus and a familiar stimulus, infants tend to increase their LT to the novel stimulus by percentages (e.g., 5%) instead of a fixed amount of LT (e.g., 5 sec). Logarithmic data directly tests for multiplicative, rather than additive, effects, and therefore provides a better analysis of the LT data.
Statistically, logarithmic transformations can also effectively maintain Type-I error control and improve the power of detecting statistically significant mean differences. We will present a simulation study to see how the Type-I error and statistical power of the same data set vary before and after logarithmic transformations. The parametric analysis in the simulation study was a paired t-test, as this is a typical test for within-subject comparison of infant LT data. Simulated population values were based on sample statistics from the in-house dataset used in Csibra et al (2016). We simulated 10000 data sets with a sample size of 20 each. The simulation revealed that the empirical Type-I error rate was closest to the nominal alpha of .05 in the logarithmic LT dataset (4.81%) in comparison to the raw LT dataset (4.29%). Importantly, we found that the Type-I error could be inflated to 7.01% if we applied the common practice of excluding outliers (i.e, excluding values farther than 2.5 S.D. from the mean). In addition, we found that the statistical power in the logarithmic LT dataset is higher (small effect: 11.28%, moderate effect: 43.94%) than that in the raw LT dataset (small effect: 9.08%, moderate effect: 33.83%).
Finally, we provide practical guidelines to researchers of how to interpret the log-transformed LT statistics. Although the inferential results with logarithmic LT data can be interpreted in a usual way, special interpretation is needed for reporting descriptive statistics. This is because the difference of log-transformed LT corresponds to a fractional difference on the original scale. We suggest two approaches here: (I) transform the logarithmic data to a symmetric percentage difference and interpret the data as percentages (Cole, 2000), or (II) back-transform the results by reversing the logarithmic values to the original scale and interpret the back-transformed values as geometric means (Olivier et al., 2008). We will use an example to illustrate these two approaches.

Authors

• Angeline Sin Mei Tsui, University of Ottawa
  Presenting Author

• Patricia Brosseau-Liard, University of Ottawa
  Non-Presenting Author