Tables

This presentation is a part of a series of lessons on the Analysis of Categorical Data. This lecture covers the following: sparse tables, sampling zeros, structural zeros, and log-linear model (and limitations).

The same set of statistics can produce opposite conclusions at different levels of aggregation. is a quote useful in teaching about Simpson's Paradox from American Economist Thomas Sowell (1930 - ). The quote may be found on page 102 of his 1996 book "The vision of the Anointed: Self-Congratulation As a Basis for Social Policy". The quote may also be found at the science history website www.todayinsci.com.

As discussed, the murder rates for Blacks in the United States are substantially higher than those for Whites, with Latino murder rates falling in the middle. These differences have existed throughout the 20th and into the 21st century and, with few exceptions, are found in different sections of the United States. Although biological and genetic explanations for racial differences in crime rates, including murder, have been discredited and are no longer accepted by most criminologists, both cultural and structural theories are widespread in the literature on crime and violence. It is also important to remember that Latino is an ethnic rather than a racial classification. The point of this exercise is to examine differences in selected structural positions of Blacks, Whites and Latinos in the United States that may help explain long-standing differences in their murder rates.

This paper presents rules for determining whether an index variable in such a table is part or whole depending on whether the associated margin value is an average, a sum or a 100% sum. Tables with missing margin values -- date-indexed tables, half tables and control tables -- are analyzed. Recommendations are made to improve reader understanding of any table involving rates or percentages.