Fig 1.
Examples of univariate relative density plots.
The plots compare the distribution of white men’s earnings in 1977 to those in 1967 (data from the annual U.S. Current Population Survey). Panel (a) plots the overall relative density (RD) against the quantiles of the 1967 distribution. Panels (b) and (c) decompose the overall difference into the specific effects of location and shape shifts. Reproduced with modifications from [5].
Fig 2.
Example of a relative density cloud.
The figure compares the performance changes of 2,667 participants who underwent an online cognitive training (T) with that of 2,378 control participants, on a battery of seven neuropsychological tests (data from [11]). Positive scores indicate increased performance between pre- and post-test; negative scores indicate decreased performance. The plots are based on 7,429 probes, with densities estimated from k = 52 nearest neighbors. AR = arithmetic reasoning. GR = grammatical reasoning. PM = progressive matrices. MS = memory span. RMS = reverse memory span. TTS = two-target search. GNG = go/no go.
Fig 3.
The plot compares the distribution of relative densities in Fig 2 (purple line) with the distribution obtained from a random split of the data, with equal numbers of cases from the two groups in each randomized half (gray line).
Fig 4.
Relative density cloud of sex differences in personality.
The figure compares the male (M) and female (F) distributions of the Big Five personality traits (total N = 100,000, 50% females). The plots are based on 8,000 probes, with densities estimated from k = 224 nearest neighbors. A = Agreeableness. C = Conscientiousness. N = Neuroticism (emotional instability). E = Extraversion. O = Openness to experience.
Fig 5.
Example of decomposition into location and shape.
The relative density clouds show the decomposition of the overall relative densities in Fig 4 into (a) a location component and (b) and shape component adjusted for sex differences in centroids. Note: transparency is referenced to the global maximum across Figs 4–7.
Fig 6.
Example of decomposition into scale and residual shape.
The relative density clouds show the decomposition of the shape component of Fig 5b into (a) a scale component and (b) a residual shape component adjusted for sex differences in centroids and variances. Note: transparency is referenced to the global maximum across Figs 4–7.
Fig 7.
Example of decomposition into covariation and residual shape.
The relative density clouds show the decomposition of the residual shape component of Fig 6b into (a) a covariation component and (b) a residual shape component adjusted for sex differences in centroids, variances, and correlations. Note: transparency is referenced to the global maximum across Figs 4–7.
Fig 8.
Example of transparency referenced to the local maximum.
This is the same relative density cloud of Fig 7a (covariation component of sex differences in Big Five personality traits), with transparency referenced to the local maximum to improve the legibility of the plots.
Fig 9.
Example of bivariate relative densities.
The figure shows the relative density cloud for sex differences in traits Agreeableness (A) and Conscientiousness (C), plotted from the same dataset used for Figs 4–8. The plots are based on 11,000 probes, with densities estimated from k = 224 nearest neighbors.
Fig 10.
Multivariate interpretation of regions in the cloud.
The cloud compares the male (M) and female (F) distributions of cognitive performance on four tasks of the ASVAB battery. The data are from the 1997 National Longitudinal Survey of Youth and comprise 3,582 males and 3,494 females (complete cases only). The plots are based on 8,500 probes, with densities estimated from k = 60 nearest neighbors. Black rectangles in the scatterplots identify regions with scores < 1 SD below the mean on both tasks. Gray bands identify regions with scores < 1 SD below the mean on a single task.