An Introduction to Data Analysis & Presentation
Prof. Timothy Shortell, Department of Sociology, Brooklyn College

Organizing Data

Frequency Distributions
Imagine you've conducted a survey of the U.S. movie/tv elite. Your 96 respondents replied to the question: "For whom did you vote in the 1980 presidential election?" What trends do you see in this data? First, look at it like this. Now, how about this. Which makes more organizational sense?

A frequency distribution is simply a tabular presentation of data. It emphasizes the pattern of dispersion. Percentages help suggest tendencies.

Sometimes, a simple frequency table is not enough organization for a particular variable. Imagine that we have asked our movie/tv executives to tell us how old they are. We can use the simple frequency distribution. What can you tell about the pattern? How about in the grouped frequency distribution?

Proportions are ratios (one number divided by another) in which the frequency of an attribute is compared with the total frequency for that variable. For example, we might want to know the proportion of movie/tv executives who voted for Reagan.

Percents are proportions multiplied by 100. This is the standard, and most convenient, way to present comparison information in a frequency table. Percentages represent relative frequencies. They tell us how much of one attribute relative to the others. (In SPSS output, "valid percent" should always be used for this purpose.)

Rates are an especially useful kind of comparison. They specify the relative frequency of an attribute, standardized to a conventional unit. The denominator of the ratio represents the total possible frequency of the attribute. For example, if we are interested in the homicide rate in New York, we would compare the actual number of homicides to the total possible number of homicides. The latter would be the total number of people in New York.

Rates are ratios multiplied by a standard size to make them more comparable. Crime statistics, for example, are usually standardized to 100,000 population.

If we wanted to know the fertility rate in the U.S., what would be the denominator of the ratio? (Fertility and mortality demographics are standardized to 1,000, by the way.)

The Crosstabulation
Often, we want to know if one variable is related to another--that is, if attributes of one variables are associated with attributes of the other. So far, we have limited ourselves to one variable at a time. As it turns out, we have a frequency table that demonstrates contingent frequencies.

For example, we might want to know if there is a relationship between gender and vote in the 1980 presidential election, in a sample of U.S. elites. The crosstab illustrates this.

The crosstab is a simple but very useful tool for examining causal relations among categorical variables. Let's consider another example. Is there a relationship between ideology and frequency of attendance at religious services in our sample of U.S. elites?

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