. 2018 Feb 13;8:2960. doi: 10.1038/s41598-018-21248-6

Table 2.

Distribution of probability function of root diameter of Pinus seedlings at 68.3% distribution interval after Johnson function transformation.

Root order	Mean value	Standard deviation	Quartile of				Transformation formula of Johnson function
Root order	Mean value	Standard deviation	Y_15.85%	Y_84.15%	X_15.85%	X_84.15%	Transformation formula of Johnson function
I	−0.007	1.018	−1.026	1.012	0.344	0.474	Yi = −3.90828 + 3.62112 * Ln((Xi + 0.502049)/(0.724921 − Xi))
II	0.011	1.008	−0.997	1.020	0.484	0.753	Yi = 2.82472 + 2.52664 * Ln(Xi − 0.263610)
III	0.923	0.160	0.763	1.084	0.763	1.084	\
IV	0.035	0.998	−0.964	1.033	1.084	1.486	Yi = 1.81605 + 1.43391 * Ln((Xi − 0.873319)/(2.54309 − Xi))
V	1.674	0.184	1.489	1.858	1.489	1.858	\

Y_15.85% − Y_84.15% denotes a threshold value of the 68.3% distribution interval of distribution probability function of the diameter of Pinus tabuliformis seedlings after Johnson function transformation, and X_15.85% − X_84.15% denotes the threshold value inverted from the threshold value of Y_15.85% − Y_84.15% distribution interval using Johnson function transformation formula corresponding to 68.3% distribution interval of distribution probability function. The same below.