Table 2.

Results for the BMI-PA data for different types of correlations

	$B{F}_{21}$	$P(H_1|Y_1,Y_2)$	$P(H_2|Y_1,Y_2)$	95%-LB	95%-UB	p values
Product–moment	4.353	.187	.813	$-0.587$	$-0.076$	.011
Polyserial	1.561	.391	.609	$-0.593$	$-0.010$	.009
Biserial	5.142	.163	.837	$-0.693$	$-0.100$	.009
Polychoric (I)	1.084	.480	.520	$-0.617$	0.030	.026
Polychoric (II)	1.724	.367	.633	$-0.817$	$-0.074$	.003
Tetrachoric	0.761	.568	.432	$-0.708$	0.139	.150

Note. BFs for the two-sided alternative ($H_2:\rho \ne 0$) against the ‘null’ hypothesis ($H_1:\rho =0$) and their respective posterior probabilities (assuming the hypotheses to be equally plausible a priori) when testing the correlation between physical activity ($Y_1$) and body mass index ($Y_2$) using different measurement levels. 95%-LB and 95%-UB refer to the lower and upper bounds of the 95% credible interval. Classical two-sided p values are based on the normal distributions except when testing the product–moment correlation, which is based on a t distribution with $n-2$ degrees of freedom