Table 2 Distribution of probability function of root diameter of Pinus seedlings at 68.3% distribution interval after Johnson function transformation.

From: A new method to optimize root order classification based on the diameter interval of fine root

Root order

Mean value

Standard deviation

Quartile of

Transformation formula of Johnson function

Y15.85%

Y84.15%

X15.85%

X84.15%

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

\

  1. Y15.85% − Y84.15% 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 X15.85% − X84.15% denotes the threshold value inverted from the threshold value of Y15.85% − Y84.15% distribution interval using Johnson function transformation formula corresponding to 68.3% distribution interval of distribution probability function. The same below.
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