Akira Tagaya (2019) Tetrachoric correlation of bilateral nonmetric traits: a defect in the conventional procedure and a proposal for two alternative estimation methods. Anthropological Science, 127(1): 39–45.

doi:10.1537/ase.190227e

I would like to notify two kinds of errors involving descriptions and results of statistical procedures in the original publication. First, for items 1, 2, 5, 6, and 9 listed below, the degrees of freedom of the chi-square values for model fit exceeded the correct value by one degree. Second, for items 1, 3, 4, and 6 listed below, the confidence interval for the correlation coefficient of the interindividual component of liability between traits should have been estimated using not the total chi-square value for model fit but rather the increase in the chi-square value (with one degree of freedom) due to deviation of the parameter from the best fit. In addition, numbers 7 and 8 are included to correct the language.

1. Page 42: Table 3 should be corrected as follows.

Table 3 The 3 × 3 frequencies observed and estimated for different values of Pearson’s correlation coefficient R between inter-individual components of liability of OMB and AST. The estimates of SD of inter-individual component used for calculation were 1.20 and 1.32, respectively.

	Trait expression (number of presences in the individual)											Rate of occurrence		Fit index
	OMB	0	0	0	1	1	1	2	2	2	Total	Rate of occurrence		χ²	df	P
	AST	0	1	2	0	1	2	0	1	2	Total	OMB	AST	χ²	df	P
Observed		932	157	73	205	82	32	82	37	29	1629	0.189	0.167
Best fit	R = 0.443	927.9	167.9	66.2	210.6	69.5	38.8	80.5	38.5	29.0	1629	0.189	0.167	5.11	3	0.164
Conventional	R = 0.330	910.7	176.6	73.9	219.0	65.8	35.8	88.5	35.2	23.5	1629	0.189	0.167	9.77	3	0.021
95% CI (lower)	R = 0.340	912.2	175.9	73.1	218.3	66.3	36.1	87.7	35.5	24.0	1629	0.189	0.167	3.841	1	0.050
(upper)	R = 0.543	940.7	162.0	58.5	205.1	74.3	41.2	72.4	41.3	33.5	1629	0.189	0.167	3.841	1	0.050

1 Increase from the value of ‘best fit.’

2. Page 42, left column, line 4: “df = 4, P = 0.045” should be read as “df = 3, P = 0.021.”

3. Page 42, left column, line 7: “0.277 or 0.597” should be read as “0.340 or 0.543.”

4. Page 42, left column, line 8: “0.277 and 0.597” should be read as “0.340 and 0.543.”

5. Page 42, right column, line 15: “df = 2” should be read as “df = 1.”

6. Page 43: Table 6 should be corrected as follows.

Table 6 Estimates of correlation coefficient between inter-individual components of liability compared among three methods. Chi-square statistics for goodness of fit and 95% CI were calculated using the 3 × 3 frequencies in Table 2b.

Pair of traits		n	Rate of occurrence		SD		Tetrachoric estimate						Direct method
Pair of traits			Rate of occurrence		SD		Conventional		Side-frequency method				Direct method
T₁	T₂		T₁	T₂	T₁	T₂	R	χ²₃	n1)	R	R_c2)	χ²₃	R	χ²₃	[95% CI]
OMB	AST	1629	0.189	0.167	1.20	1.32	0.33	9.77 *	1725.3	0.28	0.45	5.17	0.44	5.11	[ 0.34 0.54]
	PNB	1618	0.189	0.270	1.20	1.17	0.13	3.33	1725.9	0.12	0.21	1.54	0.21	1.54	[ 0.11 0.32]
	POS	1590	0.188	0.160	1.19	0.72	−0.04	1.43	1699.9	−0.06	−0.13	0.96	−0.10	0.83	[−0.25 0.05]
AST	PNB	1832	0.163	0.267	1.31	1.16	0.25	9.18 *	1899.1	0.23	0.38	2.83	0.38	2.83	[ 0.28 0.47]
	POS	1772	0.163	0.161	1.28	0.71	0.01	5.17	1850.2	0.01	0.02	5.09	0.04	5.01	[−0.10 0.18]
PNB	POS	1840	0.267	0.160	1.15	0.70	0.00	1.18	1920.0	−0.01	−0.02	1.28	0.00	1.18	[−0.13 0.14]
LPF	CIV	1212	0.076	0.074	0.76	1.48	0.33	12.76 **	1355.0	0.30	0.60	4.72	0.61	4.71	[ 0.41 0.79]
	CON	809	0.075	0.321	0.71	3.20	−0.18	2.06	941.4	−0.12	−0.22	1.49	−0.29	1.11	[−0.48 −0.07]
FRG	SOF	1564	0.234	0.613	2.21	1.58	0.38	11.03 *	1655.4	0.36	0.46	5.37	0.48	5.18	[ 0.40 0.55]

1) Harmonic mean of four combinations.

2) Obtained by dividing R by SD₁SD₂/√[(SD₁² + 1)(SD₂² + 1)].

* P < 0.05;

** P < 0.01.

7. Page 43, right column, line 13: “one freedom” should be read as “one degree of freedom.”

8. Page 43, right column, line 14: “remaining freedoms” should be read as “remaining degrees of freedom.”

9. Page 43, right column, line 16: “four freedoms” should be read as “three degrees of freedom.”

All other results and discussions remain unchanged. I apologize for any confusion caused by my mistakes.

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