![]() ![]() Not surprisingly, these plots have very similar shapes to the quantile difference plots we considered earlier. Related to quantile plots and Vincentile plots, delta plots show the difference between conditions, bin by bin (for each Vincentile) along the y-axis, as a function of the mean across conditions for each bin along the x-axis (De Jong et al., 1994). Group quantile and Vincentile plots can be created by averaging quantiles and Vincentiles across participants (Balota & Yap, 2011 Ratcliff, 1979). As expected from the way they are computed, quantile plots and Vincentile plots look very similar for our large samples from continuous variables. Below means were computed for 9 equi-populated bins. Then the mean is computed for each bin (Balota et al. To help with the group comparisons, I’ve also added plots of the quantile differences, which emphasise the different patterns of group differences.Īn alternative to quantiles are Vincentiles, which are computed by sorting the data and splitting them in equi-populated bins (there is the same number of observations in each bin). Because the quantiles are superimposed, they are easier to compare than in the previous scatterplots. If we remove the scatterplots and only show the quantiles, we obtain quantile plots, which provide a compact description of how distributions differ (please post a comment if you know of older references using quantile plots). This information would be lost if we only compared the medians. Comparing quantiles between groups give us a sense of the amount of relative compression/expansion on each side of the distributions. Medians are informative about the location of the bulk of the observations and comparing the lower to upper quantiles let us appreciate the amount of asymmetry within distributions. The deciles are represented by vertical black lines, with medians shown with thicker lines. To make the plots even more informative, I’ve superimposed quantiles – here deciles computed using the Harrell-Davis quantile estimator. Essentially, the function creates violin plots in which the constituent points are visible. Here we create scatterplots shaped by local density using the geom_quasirandom() function from the ggbeeswarm package. Scatterplots and kernel density plots can be combined by using beeswarm plots. Relative to scatterplots, I find that kernel density plots make the comparisons between groups much easier. With smaller sample sizes the evaluation of these graphs could be much more challenging. The main reason is probably that we need to estimate local densities of points in different regions and compare them between groups.įor the purpose of this exercise, each group (g1 and g2) is composed of 1,000 observations, so the differences in shapes are quite striking. The 1D scatterplots give us a good idea of how the groups differ but they’re not the easiest to read. Other approaches not covered here include explicit mathematical models of decision making and fitting functions to model the shape of the distributions (Balota & Yap, 2011).įor our current example, I made up data for 2 independent groups with four patterns of differences:įor our first visualisation, we use geom_jitter() from ggplot2. So unless the distributions are at least illustrated, this information is lost (which is typically the case when distributions are summarised using a single value like the mean). Reaction time distributions are also a rich source of information to constrain cognitive theories and models. As an example, we consider reaction time data, which are typically positively skewed and can differ in different ways. In this post I’m going to show you a few simple steps to illustrate continuous distributions. ![]()
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