# Configural Frequency Analysis: Methods, Models, and Applications

## Synopsis

Configural Frequency Analysis (CFA) provides an up-to-the-minute comprehensive introduction to its techniques, models, and applications. Written in a formal yet accessible style, actual empirical data examples are used to illustrate key concepts. Step-by-step program sequences are used to show readers how to employ CFA methods using commercial software packages, such as SAS, SPSS, SYSTAT, S-Plus, or those written specifically to perform CFA.

CFA is an important method for analyzing results involved with categorical and longitudinal data. It allows one to answer the question of whether individual cells or groups of cells of cross-classifications differ significantly from expectations. The expectations are calculated using methods employed in log-linear modeling or a priori information. It is the only statistical method that allows one to make statements about empty areas in the data space.

Applied and or person-oriented researchers, statisticians, and advanced students interested in CFA and categorical and longitudinal data will find this book to be a valuable resource. Developed since 1969, this method is now used by a large number of researchers around the world in a variety of disciplines, including psychology, education, medicine, and sociology. Configural Frequency Analysis will serve as an excellent text for courses on configural frequency analysis, categorical variable analysis, or analysis of contingency tables. Prerequisites include an understanding of descriptive statistics, hypothesis testing, statistical model fitting, and some understanding of categorical data analysis and matrix algebra.

## Excerpt

Events that occur as expected are rarely deemed worth mentioning. In contrast, events that are surprising, unexpected, unusual, shocking, or colossal appear in the news. Examples of such events include terrorist attacks, when we are informed about the events in New York, Washington, and Pennsylvania on September 11,200 1; or on the more peaceful side, the weather, when we hear that there is a drought in the otherwise rainy Michigan; accident statistics, when we note that the number of deaths from traffic accidents that involved alcohol is smaller in the year 2001 than expected from earlier years; or health, when we learn that smoking and lack of exercise in the population does not prevent the life expectancy in France from being one of the highest among all industrial countries.

Configural Frequency Analysis (CFA) is a statistical method that allows one to determine whether events that are unexpected in the sense exemplified above are significantly discrepant from expectancy. The idea is that for each event, an expected frequency is determined. Then, one asks whether the observed frequency differs from the expected more than just randomly.

As was indicated in the examples, discrepancies come in two forms. First, events occur more often than expected. For example, there may be more sunny days in Michigan than expected from the weather patterns usually observed in the Great Lakes region. If such events occur significantly more ofren than expected, the pattern under study constitutes a CFA type. Other events occur less often than expected. For example, one can ask whether the number of alcohol-related deaths in traffic accidents is significantIy below expectation. If this is the case, the pattern under study constitutes a CFA antitype.

According to Lehmacher (2000), questions similar to the ones answered using CFA, were asked already in 1922 by Pfaundler and von Sehr. The authors asked whether symptoms of medical diseases can be shown to co-occur above expectancy. Lange and Vogel (1965) suggested that the term syndrom be used only if individual symptoms co-occurred above expectancy. Lienert, who is credited with the development of the concepts and principles of CFA, proposed in 1968 (see Lienert, 1969) to test for each cell in a cross-classification whether it constitutes a type or an antitype.

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