# VI. **Testing for Significance of Changes in Distribution of Welfare**

Here we construct a nonparametric test to assess the significance of overtime change in the distribution of welfare and wealth, drawing from the Spearman coefficient of rank correlation defined in (5). The dimension of analysis includes economic regions and socioeconomic groups. The test on the latter being further extended to urban and rural areas to account for urban-rural differences. The two related samples are the distribution of income across SEG in 1994 (sample 1) and 1998 (sample 2). And we are testing for significance in changes in distribution of wealth between these two periods on the welfare rank ordering scale. The other two related samples attempt to test for significance of overtime changes in the poverty map.

The null hypothesis specified in Section 3 asserts that the distributions of income _f(x,_ *) and _f(x,,_ 1X) at time periods t, and **t 2** are independent, implying that there is no association between the rank ordering of SEG and economic regions on the wealth sphere between the two periods. The conditioning factors for these distributions include spatial considerations and SEG. The alternative is a two-sided test asserting existence of association. However, accounting for the sign and magnitude of the test statistics ( _p >_ 0), the inference is restricted to a one-sided direct association. The test of overtime changes in the poverty maps is based on the distributions _P(x, I*_ ) and _P(x,_ I*), where the conditioning factors include the poverty lines, the income distribution and the a - _level._ Here, we focus on the incidence of poverty (a = 0), because overtime changes in the rank ordering of SEG and poverty maps are not significant for larger a.

On the distribution of income, the highest ranking score is attributed to regions and SEG with the largest income share (i.e. the highest concentration of wealth, (Annex VIII and IX). Whereas on the welfare rank ordering scale which provides the distribution of total poor across geographical regions and SEG, the highest ranking score is affected to the region or SEG which has the largest concentration of poor (Annex VIII and IX). At the national level, the regions "Autres Villes" had the highest score on the rank ordering scale in 1994, and "Ouaga-Bobo" had the highest score in 1998. During these two periods, the "Sud" region continues to account for the lowest income share and thus had the lowest rank. The distribution of poor provides the region's or SEG's share of poor expressed as a percentage of all poor. When the dimension of analysis is restricted to economic regions, the "Centre-Nord" exhibits the large concentration of poor in 1994, and "Autres Villes" accounts for the largest share in 1998. The sum of square deviation on the rank ordering scale is relatively large _(Di =_ 74) when the dimension of analysis is geographical regions, suggesting significant overtime changes in the poverty maps. This statistic is much smaller when the overtime comparison is based on the distribution of welfare across SEG, suggesting less variation in the rank ordering of SEG overtime; invariably, subsistence farmers have the highest rank.

Table 7 below provides the summary inferential statistics, the sum of squared deviation, the Spearman rank correlation, with their associated p _- values._ These statistics are derived for comparisons of overtime changes in the distribution of income and welfare across SEG in urban and rural areas, and at the national level, where the number of groups is restricted to _(n_ = 7). The statistics derived for these two distributions across geographical regions are based on a much larger number of groups _(n_ = 8). These statistics are proportional to the number of groups, and the sum of squares deviations _(Di2)_ tends to increase with large _n ._ 19