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Measuring xenophobiaOf particular interest to this chapter is that the 86,272 respondents (indexed 862 72) spread across 60 countries, were asked if they would like, as their neighbours, persons from three specific categories: (1) immigrants or foreign workers, (2) persons from a different race, and (3) persons from a different religion. A respondent’s xenophobia score (X,) was defined by the number of categories from which respondent /(/=!,..., 86272) did not want such neighbours. Thus, X_{t} = 3 if respondent i did not want a neighbour from any of the three categories; X, = 2 for respondents who did not want a neighbour from two of the three categories; X, = 1 for respondents who did not want a neighbour from one of the three categories; X, = 0 for respondents who did not object to having a neighbour from any of the three categories. More formally, suppose that there are К different types of “strangers” (race, religion, country), indexed k = 1,..., K, who might be “undesirable” from the perspective of the “native” population of a country and that N natives (indexed i = 1, N) are asked, individually, whether they would like persons from each of the К types as a neighbour. For i = 1,. . ., N, k = 1, . . ., K, the variable Sf = 1 if respondent i declares that he or she would not like a person of type k as a neighbour, that is, is prejudiced against persons of type k; S^{1}* = 0 otherwise. к For every respondent, define X, = У. Then 0 < X_{(} < К: X, =k (k = 0,..., k= K) means that respondent i is prejudiced against persons from k of the К types. The value of X, represents a person’s xenophobia score: a person is “xenophobiafree” if X, = 0 and “xenophobic” if X, > 0, the strength of xenophobia being greater for higher values of X_{r} This implies that z = 1 is the “xenophobia line”, with xenophobic persons having scores at or above this line.^{12} In other words, persons who expressed antipathy to at least one of the three types (race, religion, and country) were regarded as “xenophobic” while those who did not express antipathy to any of the three groups were not xenophobic. Therefore, one way of measuring xenophobia was to express M, the number of persons that objected to having as their neighbour persons from at least one of the К types (K = 3 in this chapter), as a proportion of N, the total number of persons in the sample. This proportion is the headcount measure of xenophobia and is referred to in this chapter as the xenophobia count ratio: XCR = M/N. The headcount measure, however, does not take account of the degree of xenophobia  those who object to persons of just one type are regarded as equally xenophobic as those expressing antipathy towards persons of all three types. A corollary to this is that xenophobia, as measured by XCR, would not reflect a situation in which society became more xenophobic through a rise in the number of types of persons regarded by nativists as undesirable. In order for a xenophobia measure to reflect the degree of xenophobia, one can first define the xenophobia gap of those who are xenophobic as the difference between their xenophobia score (X,) and the xenophobia line (z) and, following from this, compute the mean xenophobia gap, defined over м / the M xenophobic persons as^fX, z) M. The Mean Gap Ratio (MGR) is then defined as the ratio of the mean xenophobia gap to the xenophobia line, z:
.VI / wherep* = ^_{J}X_{i} Mis the mean xenophobia score of those who are xenophobic. The MGR shows the mean score surplus of those who are xenophobic as a proportion of the xenophobia line. The MGR, however, focuses only on those who are xenophobic and does not take account of those who might not be xenophobic. Thus, two regions, A and B, may have the same number of xenophobic persons (say, M) yielding the same MGR, but region A's population, N_{a}, may be larger than that of region B, N_{B}. Then, since region A has a larger number of nonxenophobic persons than region В (N_{A}  M vs. N_{a}  M), intuitively, the xenophobia measure should be lower for A than for B. This is accommodated through the Xenophobia Gap Ratio (XGR) which computes the mean xenophobia gap over all the N persons in a region  not just over the M persons who are xenophobic  and expresses this as a proportion of the xenophobia line:^{13} The XGR shows the mean score surplus of all those in the sample, whether xenophobic or not, as a proportion of the xenophobia line. As equation (6.2) shows, the XGR is the product of the MGR and the XCR. A drawback of all the three measures discussed earlier is that they are not decomposable in the sense that they do not establish sensible relationships between xenophobia in the regions and overall xenophobia. This, in turn, means that one cannot determine how much xenophobia in a region contributed to global xenophobia. A xenophobia index, modelled on the poverty index proposed by Foster et al. (1984; hereafter, FGT index) allows one to do so. This index  defined on a vector of xenophobia scores X ={X,}; a xenophobia line, z; and a parameter a  is represented as when a = 0, FGT(X, z, 0) = M/N = XCR and when a = 1, FGT(X, z, 0) = M/N = MGR x XCR = XGR. If the sample of respondents is portioned into /(/=!,...,/) regions, with N, respondents in each region, ^ = N, then / the FGT index is additively decomposable because the overall index can be represented as the weighted average of the individual regional indices with the regional population shares, v_{f} = N JN, as weights: where is the FGT index for region j (j = 1, . . . , J) such that M. is the number of xenophobic persons in region j and X_{tj} is the xenophobia score for person i in that region. The decomposition of the FGT index, encapsulated in equations (6.4) and (6.5), allows one to identify regions which were particularly prone to xenophobia and to determine how much the region contributed to overall xenophobia. For region /', this contribution was
Attempts to assess regional contributions using the nondecomposable measures  XCR, MGR, and XGR, described earlier  could lead to two sets of problems. First, the regional contributions might not sum to unity. Second, a rise in the xenophobia index in a region may ceteris paribus lead to a fall in the value of the overall index. Both these problems are avoided by the FGT index  the first because the weighted sum of the regional indices will sum to unity and the second because a rise in xenophobia in a region will automatically lead to a rise in overall xenophobia. The FGT index also allows one to calculate the risk of xenophobia. This is defined as a region’s share in overall xenophobia to its share in the overall population and is represented as
If p > 1, region j contributes more to xenophobia than its population share warrants; if p. < 1, region / contributes less to xenophobia than its population share warrants; and, last, if p_{i} = 1, region j's contributions to xenophobia and the population are the same. 
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