Question on rank correlation

Almost an extract from Statistical Questions in Evidence-based Medicine by Martin Bland and Janet Peacock.

This question is a bonus, as it was not actually included in Statistical Questions in Evidence-based Medicine, due to lack of space. We hope that the topic will be useful in own right, as well as giving a flavour of the book.

Question

In a study of coronary artery disease and education in rural India, subjects were classified into five age groups and four education groups as follows:

Years of education for different age groups, rural India
Age
(years) Years of education

nil 1-5 6-10 >10 Total
20-29 106 75 238 152 571
30-39 126 118 181 70 459
40-49 131 106 101 28 366
50-59 170 35 45 18 268
60+ 232 16 26 8 282
Total 765 350 591 276 1982

Years of education for different age groups, rural India
Age (years)	Years of education
nil	1-5	6-10	>10	Total
20-29	106	75	238	152	571
30-39	126	118	181	70	459
40-49	131	106	101	28	366
50-59	170	35	45	18	268
60+	232	16	26	8	282
Total	765	350	591	276	1982

The relationship between age and years of education was analysed using Spearman's rank correlation coefficient, rho = -0.45, P<0.0001. It is the category variables which are being correlated not individual exact ages or years of education. These may be very difficult to ascertain in this population (Gupta et al. 1994).

+ 1. Why would a rank correlation be preferred to the product moment correlation coefficient?
Check answer 1

+ 2. Do you think Spearman's is the best choice here?
Check answer 2

The patients were given a clinical examination and systolic and diastolic blood pressure and lipoprotein lipid concentrations were obtained. The relationships of these to educational level were tested using Kendall's tau. The following rank correlations, Spearman's and Kendall's, between blood pressure and educational level were quoted, all significant (P<0.001):

Rank correlations between blood pressure and educational level

Men Women

rho tau rho tau
Systolic -0.08 -0.059 -0.12 -0.062
Diastolic -0.08 -0.101 -0.14 -0.121

Rank correlations between blood pressure and educational level
	Men	Women
	rho	tau	rho	tau
Systolic	-0.08	-0.059	-0.12	-0.062
Diastolic	-0.08	-0.101	-0.14	-0.121

+ 3. Does it make any difference which rank correlation is used? Is there any advantage in quoting both?
Check answer 3

+ ! 4. Does the fact that the Kendall's tau is less than Spearman's in three of the four cases tell us anything?
Check answer 4

Reference: Gupta, R, Gupta, VP, Ahluwalia, NS. (1994) Educational status, coronary heart disease, and coronary risk factor prevalence in a rural population of India. British Medical Journal 309 1332-1336.
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