Lieberson's Isolation IndexAuthor(s): Barrie MorganSource: Area, Vol. 13, No. 2 (1981), pp. 174-175Published by: The Royal Geographical Society (with the Institute of British Geographers)Stable URL: http://www.jstor.org/stable/20001711 .

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174 Corment

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2. Lieberson's isolation index

Barrie Morgan (King's College London) writes:

Vaughan Robinson' has recently published in Area a paper entitled ' Lieberson's isolation index: a case study evaluation', which demonstrates that this index (P*) captures a dimension of the segregation of Asian immigrants in Blackburn which is lost when only the index of dissimilarity (D) is used.2 Geographical bandwaggons being what they are, this is probably the first of a number of analyses reporting P* indices for a range of ethnic groups in a range of towns and cities. The object of this comment is to put the record straight at the outset concerning the origin of this index since Robinson mis-attributes it in the title of his paper.

Robinson writes: 'He (Lieberson3) considers that a modified version of Bell's isolation index may be a useful and complementary statistic to aid a deeper understanding of trends in segregation ... He terms this modified index P*, defining it as the " average probability of interacting with some specified population based on the distribution of persons by subareas and the assumption that interaction is with someone in the same subarea "'.4

The description of P* as a modified version of Bell's isolation index is highly misleading. P* comprises the numerator of Shevky and Williams'5 ' index of isolation ' and is a distinct component of the numerator of Bell's6 'revised index of isolation' (Robinson is muddled about which author contributed which index). These two indices differ in the way P* is standardised to take account of the probability of contact if there were no segregation. More over, Bell realised the potential of P* as an index in its own right. After spelling out the

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Comment 175

derivation and interpretation of P* in some detail he goes on: ' P* (may) be used. . . as the measure of neighbourhood concentration. P* is directly interpretable as the pobability of intra-group contact. It is the average probable interaction among members of the same group. The direct comparison of this measure for different groups in the same cities, the same groups in different cities, or different groups in different cities is possible and sociologically meaningful. In every case P* is the probability of a randomly selected member of any given group next meeting a member of the same group '7 P* clearly should be attributed to Bell, not Lieberson.

None of this is to minimise Lieberson's contribution.8 This is two-fold in the writer's opinion. Firstly, he has rightly focused attention on the additional insights gained by using P*, which is a behaviourally more significant measure, in addition to D in studies of residential segregation (in this particular instance on black-white segregation in Northern cities in the United States between 1890 and 1930). He is not the first to do this. however. Brigitte Mach Erbe9 has used P* (she terms it the index of asymmetric intergroup contact'?) to examine the residential contiguity of socio-economic status groups in the white and black populations of the Chicago SMSA in 1970. Secondly, and more importantly, Lieberson has forced us to ask (if not yet answer) some fundamental questions about the relationship between the degree of unevenness of two population distributions and the degree of inter group contact. For instance, whereas it is traditionally suggested that the influx of blacks into the Northern cities in the United States this century has led to an increase of prejudice and hence more uneven population distributions, Lieberson suggests these distributional changes may not be the result of changes in white attitudes but the result of whites attempting to maintain the same level of isolation from blacks at the time when compositional shifts were working in the opposite direction. This relationship between population distributions and intra- and inter-group contact is far too complex for much light to be shed on it by studies comparing trends in D and P* in individual towns, whatever their other merits.

Notes 1. Robinson, V. (1980) ' Lieberson's isolation index: a case study evaluation ', Area 12, 307-12

2. Duncan, 0. D. and Duncan, B. (1955) 'A methodological analysis of segregation indices ', Am. Soc.

Rev. 20, 210-17

3. Lieberson defines P*, and discusses its merits in: Lieberson, S. (1 980a) A piece of the pie: black and

white immigrants since 1880 (Berkeley), and, Lieberson, S. (1980b) ' An asymmetrical approach to

segregation ', unpubl. pap. presented to Anglo-American Symposium on ' Ethnic Segregation in

Cities ', Oxford 4. Robinson, V. op cit. 308

5. Shevky, E. and Williams, M. (1949) The social areas of Los Angeles, analysis and typology (Berkeley)

6. Bell, W. (1954) 'A probability model for the measurement of ecological segregation ', Soc. Forces 32,

357-4 7. Ibid., 358 8. Lieberson, S. op cit. 9. Mach Erbe, B. (1975) ' Race and socioeconomic segregation ', Am. Soc. Rev. 40, 801-12

10. P* may be calculated for inter-group interaction as well as intra-group interaction

University of East Anglia, School of Development Studies New and forthcoming publications in geography: Discussion papers DP68 'Efficiency 'as a concept in irrigation design, by L. Vincent. ?130 DP69 Irrigated farming: debt or profit? Underutilisation of water in the Medjarda

scheme, Tunisia, by L. Vincent. ?1.85

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