Variables (X, Y)

ANSUR Male

(4082)

ANSUR Female

(1986)

Simulation

(4000)

rho = 0.4716

Simulation

(2000)

rho = 0.5387

(I) $\frac{H-{\mu }_H}{{\sigma }_H},\frac{W-{\mu }_W}{{\sigma }_W}$

Mean dCor

0.4725

0.5004

0.4428

0.5099

SE dCor

0.0259

0.0285

0.0231

0.0243

Pearson $\rho$

0.4689

0.5335

0.4584

0.5359

Theoretical dCor

0.4248

0.4860

0.4150

0.4883

(II) $\frac{\ln H-m_H}{s_H},\frac{\ln W-m_W}{s_W}$

Mean dCor

0.4856

0.5027

0.4443

0.5032

SE dCor

0.0272

0.0292

0.0228

0.1186

Pearson r

0.4716

0.5387

0.4604

0.5030

Theoretical dCor

0.4273

0.4910

0.4169

0.4570

(III) $\frac{\ln H-m_H}{s_H},\frac{\ln W-m_W}{s_W}-r\left(\frac{\ln H-m_H}{s_H}\right)$

Simulation

(4000)

rho = 0

Simulation

(2000)

rho = 0

A. Repeated Sampling of Total Population (Sample Size 50)

Mean dCor

0.2475

0.2454

0.2275

0.2382

SE dCor

0.0119

0.0104

0.0081

0.0112

Pearson Corr Coeff

−4.1118 × 10⁻¹¹

−4.1011×10⁻¹¹

0.0171

0.0124

Theoretical dCor

0

0

0.0152

0.0110

B. Single Sample of Sub Population (Sample Size 1000)

Mean dCor

0.0611

0.0676

-

0.0599

Pearson Corr Coeff

−0.0263

−0.0219

-

0.0213

Theoretical dCor

0.0234

0.0195

-

0.0190