Inequality, segregation, and diversity are complex phenomena that occur across multiple levelsof social and spatial organization. In the United States, the racial and ethnic diversity of thenational population has grown in recent decades, but there is considerable variation in the level ofdiversity and pace of change across communities and regions (Frey 2015; Hall, Tach, and Lee 2016;Lichter, Parisi, and Taquino 2015). Over the same period, income inequality has increased, andthere are wide and persistent income gaps between ethnoracial groups (Bloome 2014; Burkhauserand Larrimore 2014).Growing ethnoracial diversity provides new opportunities for intergroup contact, but recentdeclines in racial residential segregation at the neighborhood-level have been offset by increases insegregation between municipalities (Lichter et al. 2015). Income inequality is implicated as botha cause and consequence of segregation, but the extent to which socioeconomic advancement isassociated with spatial integration varies by race group (Iceland and Wilkes 2006; Lichter, Parisi,and Taquino 2012).Decomposable measures of inequality, segregation, and diversity are critical tools for understandingthe social and spatial dynamics of these complex phenomenon. For example, they allow usto examine how much of the total income inequality in the U.S. occurs among individuals withinparticular groups (e.g. ethnoracial or educational) and how much occurs between the groups. Suchan analysis allows to assess the extent to which group membership is a determinant of inequality(Breen and Chung 2015). Entropy-based measures have long been a staple of decomposition studies.Theil (1967, 1972; 1971) introduced the concept of entropy to the social sciences as a measure ofpopulation diversity (see also: Reardon and Firebaugh 2002; White 1986) and income inequality.Despite having decomposable measures of both inequality and diversity, we lack a decomposablemeasure of segregation. The Dissimilarity Index (Duncan and Duncan 1955; Jahn, Schmid, andSchrag 1947; Taeuber and Taeuber 1965) is the most widely used measure of residential segregation,but it can not be decomposed into the segregation occurring within and between groups or places(Reardon and Firebaugh 2002; Reardon and O’Sullivan 2004; Theil 1972). The Information TheoryIndex (Reardon and Firebaugh 2002; Reardon and O’Sullivan 2004; Theil and Finizza 1971; White1986) has become the gold standard for decomposition studies of segregation (Bischoff 2008; Farrell2008; Fischer 2008; Fischer et al. 2004; Parisi, Lichter, and Taquino 2011). However, I argue that itis misleading to interpret the Information Theory Index as a measure of segregation – it measuresthe diversity of local areas relative to the region’s overall diversity, rather than measuring thedifference between the local and overall proportions of each group.