Table 2. Simulation results for the correlation estimation based on Kendall’s τ, biserial, polyserial, tetrachoric, or polychoric correlation.
The choice of correlation methods depends on the measurement scale. The values of ρ ranges from −0.9 to 0.9. The correlation estimates and standard deviations for various methods are calculated based on 10,000 replications.
| ρ | Continuous-Continuous | Continuous-Binary | Continuous-Ordinal | Binary-Binary | Binary-Ordinal | Ordinal-Ordinal |
|---|---|---|---|---|---|---|
| −0.9 | −0.8999 (0.0066) | −0.9003 (0.0112) | −0.9009 (0.0082) | −0.8999 (0.0159) | −0.9007 (0.0149) | −0.9004 (0.0120) |
| −0.8 | −0.7997 (0.0124) | −0.8002 (0.0185) | −0.8006 (0.0136) | −0.8000 (0.0249) | −0.8007 (0.0213) | −0.8008 (0.0160) |
| −0.7 | −0.6999 (0.0172) | −0.7004 (0.0238) | −0.7007 (0.0183) | −0.7000 (0.0315) | −0.7009 (0.0269) | −0.7008 (0.0206) |
| −0.6 | −0.6000 (0.0218) | −0.6004 (0.0287) | −0.6004 (0.0225) | −0.6002 (0.0374) | −0.6009 (0.0312) | −0.6008 (0.0252) |
| −0.5 | −0.4999 (0.0253) | −0.5001 (0.0324) | −0.5005 (0.0263) | −0.5000 (0.0418) | −0.5009 (0.0350) | −0.5006 (0.0287) |
| −0.4 | −0.4000 (0.0281) | −0.4005 (0.0351) | −0.4005 (0.0289) | −0.3998 (0.0453) | −0.4005 (0.0380) | −0.4005 (0.0311) |
| −0.3 | −0.3001 (0.0302) | −0.3004 (0.0371) | −0.3004 (0.0310) | −0.3003 (0.0477) | −0.3005 (0.0407) | −0.3005 (0.0333) |
| −0.2 | −0.2004 (0.0317) | −0.2010 (0.0388) | −0.2005 (0.0327) | −0.2010 (0.0493) | −0.2004 (0.0418) | −0.2009 (0.0352) |
| −0.1 | −0.1006 (0.0330) | −0.1008 (0.0398) | −0.1008 (0.0337) | −0.1008 (0.0509) | −0.1010 (0.0428) | −0.1011 (0.0359) |
| 0.0 | −0.0000 (0.0331) | 0.0002 (0.0397) | 0.0001 (0.0339) | −0.0001 (0.0506) | −0.0004 (0.0428) | 0.0002 (0.0364) |
| 0.1 | 0.0998 (0.0324) | 0.0999 (0.0392) | 0.0998 (0.0331) | 0.1000 (0.0499) | 0.0999 (0.0420) | 0.1000 (0.0354) |
| 0.2 | 0.1996 (0.0317) | 0.2003 (0.0390) | 0.1998 (0.0323) | 0.1997 (0.0494) | 0.1995 (0.0414) | 0.2000 (0.0348) |
| 0.3 | 0.2999 (0.0298) | 0.3002 (0.0370) | 0.3003 (0.0304) | 0.3001 (0.0477) | 0.3004 (0.0398) | 0.3006 (0.0326) |
| 0.4 | 0.3993 (0.0279) | 0.3996 (0.0352) | 0.4000 (0.0287) | 0.3994 (0.0449) | 0.4003 (0.0372) | 0.4003 (0.0311) |
| 0.5 | 0.4997 (0.0249) | 0.5004 (0.0319) | 0.5001 (0.0259) | 0.5001 (0.0416) | 0.5005 (0.0347) | 0.5006 (0.0284) |
| 0.6 | 0.6000 (0.0217) | 0.6006 (0.0285) | 0.6004 (0.0226) | 0.6000 (0.0377) | 0.6003 (0.0314) | 0.6009 (0.0249) |
| 0.7 | 0.6999 (0.0172) | 0.7004 (0.0237) | 0.7006 (0.0184) | 0.6999 (0.0317) | 0.7005 (0.0269) | 0.7008 (0.0206) |
| 0.8 | 0.8000 (0.0124) | 0.8004 (0.0184) | 0.8008 (0.0137) | 0.8003 (0.0250) | 0.8006 (0.0215) | 0.8011 (0.0162) |
| 0.9 | 0.8997 (0.0066) | 0.9001 (0.0113) | 0.9007 (0.0082) | 0.8996 (0.0160) | 0.9005 (0.0152) | 0.8997 (0.0112) |