Arsenic Contamination in West Bengal and Bangladesh: Statistical Errors.

In their paper "Groundwater Contamination in Bangladesh and West Bengal, India," Chowdhury et al. (1) address arsenic contamination in groundwater from two countries in Asia. Although arsenic contamination is a serious concern for the entire world, Chowdhury et al. bring out the proportion of people at risk in these areas by measuring arsenic levels using various biochemical parameters, but there are errors and missing information in their statistical presentation. As much as possible, I would like to clarify the statistical presentation of their data.

Chowdhury et al. (1) did not classify all the cases for the Bangladesh data in Figure 2 of their paper. The total of the percentages shown for Bangladesh is 98.9; thus 1.1% is missing. This 1.1% represents 121 cases that were not classified. Fortunately, the percentage of tube wells affected by arsenic (100-1,000 [micro]g/L) was provided in the text. These 121 cases may have been omitted from the first two class intervals. Therefore, these cases were distributed in the first two class intervals for further analysis, namely 61 cases to the first interval (10-50 [micro]g/L) and 60 cases to the second class interval (51-99 [micro]g/L).

The mean arsenic level ([+ or -] SD) was 186.16 [+ or -] 225.23 [micro]g/L for tube well water in Bangladesh and 67.00 [+ or -] 107.84 [micro]g/L in West Bengal. The difference between these mean levels of arsenic are statistically significant (p [is less than] 0.001). This significant difference reveals that, on average, the groundwater arsenic contamination in Bangladesh is 2.8 times higher than that in West Bengal. Similarly, the proportion of tube wells containing water contaminated with arsenic at concentrations [is greater than] 50 [micro]g/L is also statistically significant (p [is less than] 0.001) between these countries.

The second error is in Table 2 of Chowdhury et al.'s paper (1), under the skin scale of West Bengal. The given SD of 4,750 is not possible, and it is not consistent with other results shown in the table. The skin scale arsenic level ranged from 1,280 to 1,550 ([micro]g/L), and a range of 270. Thus, the given SD of 4,750 is not possible.

Table 2. Correlation analysis for arsenic data from Bangladesh.

                     Urine arsenic   Hair arsenic    Nail arsenic
                     ([micro]g/kg)   ([micro]g/kg)   ([micro]g/kg)

Urine arsenic              1
 ([micro]g/kg)
Hair arsenic               1               1
 ([micro]g/kg)
Nail arsenic             0.999             1               1
 ([micro]g/kg)
Skin scale arsenic       0.999           0.999             1(*)
 ([micro]g/kg)

All of the correlation coefficients are statistically
significant (p <0.001; n = 7).
(*) Used for regression analysis.

From Chowdhury et al.'s (1) Table 2, I calculated the mode value and obtained approximate values of the first and third quartiles (2). Chowdhury et al. used seven values in the analysis of their data, but because the mode was not well-defined for urine data from West Bengal and hair and urine data from Bangladesh, only six values could be used to calculate the mode.

I used these values for further analysis. I calculated the correlation matrix (3) for West Bengal (Table 1) and Bangladesh (Table 2) to determine the linear relationship of arsenic concentrations among the biochemical parameters. For the Bangladesh data (Table 2), the nail arsenic level and the skin scale arsenic level have perfect correlation. Moreover, the nail arsenic level includes the normal range shown by Chowdhury et al. in their Table 2. Although Chowdhury et al. (1) declared that there is no normal arsenic level for skin scale, it is possible to use these data to determine the corresponding skin scale arsenic level (micrograms per kilogram) by simple regression analysis (4); that is, for a given nail arsenic level, it is possible to determine the skin scale arsenic level using the following linear regression equation:

Table 1. Correlation analysis for arsenic data from
West Bengal.

                                  Urine           Hair
                                 arsenic         arsenic
                              ([micro]g/kg)   ([micro]g/kg)

Urine arsenic ([micro]g/kg)         1
Hair arsenic ([micro]g/kg)        0.999             1
Nail arsenic ([micro]g/kg)        0.998           0.999

All of the correlation coefficients are statistically significant
(p < 0.001). Skin scale data was not used due to the
inconsistency of the data (n = 6 because the mode was
not well-defined).

Skin scale arsenic ([micro]g/kg) = 180.75 + 0.663 nail arsenic ([micro]g/kg).

The regression coefficient is statististically significant (p [is less than] 0.001). Because the correlation is 1, the [R.sup.2] = 1; that is, the explained variance of the dependent variable (skin scale arsenic) is 100% through the independent (skin scale arsenic) variables. The analysis of variance for the fitted model is also significant (p [is less than] 0.001).

If nail arsenic is 430 [micro]g/kg, skin scale arsenic will be 466 [micro]g/kg; if nail arsenic is 1,080 [micro]g/kg, skin scale arsenic will be 897 [micro]g/kg. Therefore, when the nail arsenic level is in the normal range, the skin scale arsenic will be 466-896 [micro]g/kg on average.

REFERENCES AND NOTES

(1.) Chowdhury UK, Biswas BK, Chowdhury TR, Samanta G, Mandal BK, Basu GC, Chanda CR, Lodh D, Saha KC, Mukherjee SK, et al. Groundwater contamination in Bangladesh and West Bengal, India. Environ Health Perspect 108:393-397 (2000).

(2.) Gupta SC, Kapoor VK. Fundamentals of Mathematical Statistics. New Delhi:Sultan Cahand and Sons, 1982.

(3.) Gilchrist W. Statistical Modelling. New York:Wiley, 1984.

(4.) Montgomery DC, Peck EA. Introduction to Linear Regression Analysis. New York:Wiley, 1982.

P. Marimuthu Department of Statistics and Demography National Institute of Health and Family Welfare New Delhi, India Fax: [phone]