Because the critical manipulation (of block type) regarded the type of lures that could occur, we restricted our analyses to lure trials. Generalized linear mixed-effects models (GLMMs) with a binomial distribution were used to analyses the percentage false alarms (FAs), and linear mixed-effects models (LMMs) to analyses reaction times (RTs) (correct rejection trials only) in a procedure similar to the approach described in
Helbing, Draschkow, and Võ (2020) and
Draschkow and Võ (2017). Trials in which the response times were faster than 200 ms or greater than 3 standard deviations from the participant's mean were discarded from the analysis. This resulted in an average loss of 1.4% ± 0.19% (
m ± standard error of the mean [
SEM]) of trials. These analyses were run using the lme4 package (version 1.1-17;
Bates et al., 2015). We used mixed-effects models because they hold multiple benefits over a more traditional approach to analysis of variance. Importantly for the current study, these approaches are more reliable in unbalanced designs when different conditions have different trial numbers—for example, common versus rare lures (
Baayen, Davidson, & Bates, 2008). All GLMMs and LMMs were fitted with the maximum likelihood criterion. For the GLMMs, where we report regression coefficients
β with the z statistic and use a two-tailed 5% error criterion for significance, the
p values for the binary accuracy variable are based on asymptotic Wald tests. For the LMMs, we report
β with the
t statistic and apply a two-tailed criterion corresponding to a 5% error criterion for significance. The
p values were calculated with Satterthwaite's degrees of freedom method using the lmerTest package (version 3.1-0;
Kuznetsova, Brockhoff, & Christensen, 2017). Pairwise tests after significant interactions were further investigated using the lsmeans package (
Lenth, 2016) with Tukey post-hoc correction.
In this experiment there were two main independent variables of interest: lure type (common vs. rare) and, block type (color-distinguishing and tilt-distinguishing). The comparisons were modelled using sum contrasts, in which the grand mean of the dependent measure served as the intercept. For binary responses such as FAs in the GLMM approach, the coefficients are represented by logits. We began each model with a maximal random-effects structure (
Barr, Levy, Scheepers, & Tily, 2013) that included intercepts for each participant, as well as by-participant slopes for the effects of lure type and block type. Full models such as these often fail to converge or lead to overparameterization (
Bates, Kliegl, Vasishth, & Baayen, 2015). Therefore we used a principal component analysis (PCA) of the random-effects variance-covariance estimates to identify overparameterization for each fitted model and removed random slopes that were not supported by the PCA (i.e., did not explain significant variance in the model) and did not contribute significantly to the goodness of fit in a likelihood ratio (LR) test (
Bates, Kliegl, et al., 2015). For both the GLMM and LMMs, this resulted in the removal of the by-subject slopes for lure type from the random effects, and therefore the random-effects structures for the optimal models included the subject intercepts, as well as by-subject slopes for block type. Further details regarding the models and model comparisons can be found in the analysis script. Analysis scripts and data can be found here,
https://osf.io/x7u4q/.
To make sure the results did not depend on the chosen approach, we also conducted traditional repeated-measures analyses of variance for both FA and RT. These showed equivalent results and can also be found in the analysis script provided on OSF on acceptance. The ggplot2 package (version 3.1.0;
Wickham, 2009) was used for plotting results. Furthermore, where relevant, the within-subject standard error of the mean was calculated from normalized data using the approach from
Morey (2008).