From observed laterality to latent hemispheric differences: Revisiting the inference problem

Figures & data

Figure 1. Probability of being left or non-left hemispheric dominant given a single measurement of perceptual laterality. [To view this figure in color, please see the online version of this journal.]

Figure 2. The boxplots show the distribution of dichotic listening scores for left dominant, unclassified, and right dominant subjects, according to the Bayesian classification, for the example in Section “Empirical data example”. [To view this figure in color, please see the online version of this journal.]

Table 1. Comparison between classifical classification with a cut-off at zero and classification based on the Bayesian model developed in this paper.

	Classical classification
Bayesian classification	Left	Unclassified	Right
Left	2,075	196	246
Unclassified	0	0	233
Right	0	0	105

Figure 3. If a first measurement with value given by the x-axis has been obtained for a right-handed subject, the curves show the value of the final probability of left hemispheric dominance after a second measurement has been obtained with value given by the colour legend. The dashed black line shows the same probabilities in the case where only a single measurement has been obtained. [To view this figure in color, please see the online version of this journal.]

Table 2. The table shows the probability of left brain asymmetry after obtaining one, two, three, or four measurements of the same magnitude for a right-handed subject.

	Measurements
Perceptual laterality measure	1	2	3	4
−40.00	0.09	0.00	0.00	0.00
−30.00	0.25	0.02	0.00	0.00
−20.00	0.54	0.17	0.03	0.01
−10.00	0.80	0.71	0.60	0.48
−5.00	0.88	0.90	0.91	0.92
0.00	0.93	0.97	0.98	0.99
5.00	0.96	0.99	1.00	1.00
10.00	0.98	1.00	1.00	1.00
20.00	0.99	1.00	1.00	1.00
30.00	1.00	1.00	1.00	1.00
40.00	1.00	1.00	1.00	1.00

Table 3. The table shows how the number of classification with 80% probability or higher depends on the number of measurements for left-handers and right-handers.

	Right-handers			Left-handers
n	Left	Non-left	Undecided	Left	Non-left	Undecided
1	431 (88.9%)	17 (3.5%)	37 (7.6%)	267 (69.2%)	15 (3.9%)	104 (26.9%)
2	440 (90.7%)	21 (4.3%)	24 (4.9%)	287 (74.4%)	19 (4.9%)	80 (20.7%)
3	443 (91.3%)	23 (4.7%)	19 (3.9%)	287 (74.4%)	20 (5.2%)	79 (20.5%)

Figure 4. How an individual subject's probability of being left dominant (black lines) changes by successively entering 1, 2, 3, and 4 laterality measures into the prediction. [To view this figure in color, please see the online version of this journal.]

Table 4. The table shows how the number of classification with 95% probability or higher depends on the number of measurements for the Bless App data.

n	Left	Non-left	Undecided
1	28 (84.8%)	1 (3%)	4 (12.1%)
2	30 (90.9%)	1 (3%)	2 (6.1%)
3	29 (87.9%)	2 (6.1%)	2 (6.1%)
4	28 (84.8%)	3 (9.1%)	2 (6.1%)

Figure 5. Results of the simulation experiment described in Section “Simulation experiment.” The figures show the proportion of subjects classified correctly, incorrectly, or undecided at an 80% threshold. Shaded regions represent 95% confidence bands. [To view this figure in color, please see the online version of this journal.]

Figure 6. Proportion correctly classified, incorrectly classified and undecided subjects as a function of the chosen probability threshold for classification. [To view this figure in color, please see the online version of this journal.]

Table A1. Satz's model for right-handers, using updated prior information.

	Left dominance	Non-left dominance	Total
Left ear adv.	0.21	0.12	0.33
Right ear adv.	0.66	0.01	0.67
Total	0.87	0.13	1.00

Table A2. Satz's model for left-handers, using updated prior information.

	Left dominance	Non-left dominance	Total
Left ear adv.	0.22	0.29	0.51
Right ear adv.	0.43	0.06	0.49
Total	0.65	0.35	1.00

Table A3. Probabilities of left or right brain dominance in Satz's model, using updated prior information.

Handedness	Ear advantage	P(Left dom.)	P(Right dom.)
Left	Left	$0.22/0.29=0.43$	$0.29/0.22=0.57$
Left	Right	$0.43/0.06=0.88$	$0.06/0.43=0.12$
Right	Left	$0.21/0.12=0.64$	$0.12/0.21=0.36$
Right	Right	$0.66/0.01=0.98$	$0.01/0.66=0.02$

Data availability statement

R scripts for reproduction of all numerical examples and simulation results, including figures and tables, are available at the Open Science Framework, https://osf.io/mkwcr. The data from Bless et al. (2013) analysed in Section “Empirical data example” is also available at https://osf.io/mkwcr. We cannot share the data from Hugdahl et al. (2009) and Bless et al. (2015) analysed in Section “Empirical data example” nor the data from Karlsson et al. (2019) analysed in “Empirical data example .”