This way to build the background

This way, to build the background index, which will be included in the control (X) used in Eq. (1), we calculate the mean for both disciplines for each student , where d=I represents mathematics and d=II represents Portuguese language. The control variables can be gathered in categories as follows: In the analysis of the effects of racial segregation, there is a problem of cities where only one school participated in Prova Brasil. In these cases, the GSK343 manufacturer index always equals zero, by construction. Thus, we ought to focus on the analysis of two sets of cities: those with at least two schools that participated in Prova Brasil and those with at least six participating schools. In this regard, the concern emerges that this sample resizing according to the number of schools participating in the test could generate a sample that is too different from the one that covers all the cities with at least two schools participating in Prova Brasil. Therefore, we performed tests of difference of means with a series of control variables used in the regression, as for the proficiency and the segregation index. We found no statistically significant difference in the share of blacks and whites in each sample, as was the case of the proficiencies. However, cities with more than six schools participating in the test present a higher proportion of black and mulatto students in these schools. Table 1 shows the sample overview of the main variables of the work. The first column contains the statistics or variables for 540 cities in the state of Sao Paulo that participated in Prova Brasil 2005 and which had at least one black student participating. The next column presents the resizing for the set of cities with at least six schools participating in the test. Table 2 brings the correlation between the segregation index and the other variables used in the model (explanatory and dependent) for the two samples of cities considered. The correlations between Group A variables and segregation index of cities are all positive and significant at 5%. For the other groups of regressors, the correlations are negative. Thus, in cities with more segregated schools, indicators for blacks are worse than for whites.
Results Before presenting the results of the model estimated in Eq. (7), Laurasia is necessary to analyze the estimations of the effect of racial composition of schools on the achievement of students in Eqs. (1) and (3). Eq. (1) analyzes to what measure the fraction of blacks and mulattos in the school is related to the students’ proficiency, without the correction for possible biases caused by the non-random student distribution in schools, neighborhoods and cities. In Eq. (3), we used city means of all variables, which allowed us to estimate the effects of racial composition eliminating the supposed biases that the non-randomness in the sorting inside the city could bring. Table 3 presents the estimations of Eq. (1) computed separately for white and black students for both disciplines. The rise in one percentage point in the fraction of blacks and mulattos in the schools is related to 0.64 point less for white students in mathematics and 0.42 point less for black students, on average. In Portuguese, the effects are similar. Thus, for both whites and blacks the proficiency is lower with the rise in the proportion of blacks and mulattos in schools. However, as we have already pointed out, these results may suffer from biases caused by the problem in estimation. The results given in Eq. (3) are presented in Table 4 for cities with six or more schools participating in Prova Brasil. In this table, the dependent variable is the city mean proficiency in the test. In general, the effects of racial composition are smaller than the ones obtained in Table 3. This fact shows that probably the estimations suffer from biases when we use the regression without using city means and that possibly this bias is toward a larger effect (or biased negatively, since the estimations are negative).