In the following section, I use data from the IHDS-II to provide information on the average annual household income among different caste groups in 2011–12 (Tables A4.1 and A4.2). Comparing the mean annual income of the different caste groups, the tables show a significant difference between the average annual household incomes across different caste groups. In both rural and urban India, Brahmins and Forward Castes have the highest average annual income and SCs and STs the lowest. However, the high value of standard deviation, represented in the last column of both the tables indicates that annual household incomes are significantly higher than the mean values, suggesting a large variation of household income within the caste groups. Such a high level of standard deviation suggests a low level of confidence in any statistical conclusion (in this case, the relationship between caste membership and household income).

The following two histograms (Figures A4.1 and A4.2) show the distribution of annual household income in rural and urban India, respectively. It is evident that the distributions are highly skewed and heavy-tailed, suggesting that there are few data points (annual household income) with extremely large values on the right side of the distribution. In simple terms, this means that the annual household incomes are very likely to be highly heterogeneous. This type of distribution is referred to as the Pareto distribution. Such a highly skewed distribution of income will create issues when we compare the statistics of the income distributions between different castes. The average and other statistical features of fat-tailed distributions are not well defined and this is easily observed in Tables A4.1 and A4.2 – the standard deviations calculated for the income within each caste is far greater than the mean value, leading to a large error in the calculated mean.

To resolve this issue, we must transform the income variable logarithmically and work with the logarithm of annual household income from this point on. The logarithmic transformation will turn the skewed distributions with extremely large values to a localised value close to the normal distribution. There are many natural variables that grow exponentially, such as expenditure and income, and to be able to apply standard statistical tests on them we need to consider them in the logarithmic space.