Descriptive statistics are used to summarize data under study. A frequency distribution shows the number of cases that have each of the attributes of a given variable. Measures of central tendency reduce data to an easily manageable form, but they do not convey the detail of the original data. Measures of dispersion give a summary indication of the distribution of cases around an average value. Rates are descriptive statistics that standardize some measure for comparative purposes.
Bivariate analysis and subgroup comparisons examine some type of relationship between two variables. The rules of thumb in interpreting bivariate percentage tables to make the subgroup comparisons are (1) if percentaged down, then read across or (2) if percentaged across, then read down. Multivariate analysis is a method of analyzing the simultaneous relationships among several variables and may be used to more fully understand the relationship between two variables.
Inferential statistics are used to estimate the generalizability of findings arrived at in the analysis of a sample to the larger population from which the sample has been selected. Inferences about a characteristic of a population—such as the percentage that favors gun control laws—must contain an indication of a confidence interval (the range within which the value is expected to be—for example, between 45 and 55 percent favor gun control) and an indication of the confidence level (the likelihood that the value does fall within that range—for example, 95 percent confidence). Tests of statistical significance estimate the likelihood that an association as large as the observed one could result from normal sampling error if no such association exists between the variables in the larger population. Statistical significance must not be confused with substantive significance, which means that an observed association is strong, important, or meaningful. Tests of statistical significance, strictly speaking, make assumptions about data and methods that are almost never satisfied completely by real social research.
ACTIVITIES AND ASSIGNMENTS:
1. Start with several data sets to illustrate for the class the measures of central tendency and measures of dispersion.
a. Have one data set be very compact with little variation in range.
b. Select another data set that illustrates dispersion with a great deal of variation.
c. As a class for each data set compute the:
5. Standard Deviation
d. End with a discussion about the inferences that can be made about a set of data by looking at the measures of central tendency and dispersion.
2. Using information from the class: gender, age, race and any other variables that seem appropriate, make tables to illustrate the concepts from this chapter.
3. Distribute the following table and ask students to interpret it. The table is from Bullock, Henry Allen. 1961. “Significance of the Racial Factor in Length of Prison Sentence”. Journal of Criminal Law, Criminology and Police Science, 52: 411-417. For a comment on the article’s error, see Hagan, John. 1974. “Criminal Sentencing: An Assessment of a Sociological Viewpoint”. Law and Society Review, 8: 357-383.
The students should notice that the table has been percentaged in the wrong direction. This is, instead of percentaging within categories of independent variable, race; the table was percentaged within the categories of the dependent variable, offense. Use this to illustrate that errors do appear in journals. Students must read both the text and the tables to evaluate the study.
Percent Distribution of 3,644 Prisoners According
To Type of Offense, Length of Sentence, and Race SHORT SENTENCE
OFFENSE PERCENT PERCENT TOTAL BLACK WHITE
Burglary 35.9 64.1 1141
Rape 36.3 63.7 135
Murder 62.1 37.9 702
Total 45.2 54.8 1978
LONG SENTENCE OFFENSE PERCENT PERCENT TOTAL BLACK WHITE
Burglary 47.5 52.5 341
Rape 29.3 70.7 239
Murder 55.3 44.7 1086
Total 50.0 50.0 1666
INTERNET RESOURCES: Florida Department of Law Enforcement. Florida Statistical Analysis Center. http://www.fdle.state.fl.us/FSAC/
Tennessee Bureau of Investigation. Statistical Analysis Center. http://www.tbi.state.tn.us/divisions/isd_csu_sac.htm
United States Department of Justice. Office of Justice Programs. Bureau of Justice Statistics. Technical Report. Displaying Violent Crime Trends Using Estimates From the National Crime Victimization Survey.