## Interpreting Data

**average**

An ambiguous term that generally suggests typical or normal. The mean, median, and mode are specific mathematical averages.

**bivariate analysis**

The analysis of two variables simultaneously for the purpose of determining the empirical relationship between them. The construction of a simple percentage table and the computation of a simple correlation coefficient are examples of bivariate analyses.

**contingency table**

A format for presenting the relationship among variables in the form of percentage distributions.

**descriptive statistics**

Statistical computations that describe either the characteristics of a sample or the relationship among variables in a sample. Descriptive statistics summarize a set of sample observations, whereas inferential statistics move beyond the description of specific observations to make inferences about the larger population from which the sample observations were drawn.

**dispersion**

The distribution of values around some central value, such as an average. The range is a simple measure of dispersion. Thus we may report that the mean age of a group is 37.9 and the range is from 12 to 89.

**frequency distribution**

A description of the number of times the various attributes of a variable are observed in a sample. The report that 53 percent of a sample were men and 47 percent were women is a simple example of a frequency distribution. Another example is the report that 15 of the cities studied had populations of less than 10,000, 23 had populations between 10,000 and 25,000, and so forth.

**inferential statistics**

The body of statistical computations relevant to making inferences from findings on the basis of sample observations to some larger population. See also

*descriptive statistics*.

**level of significance**

In the context of tests of statistical significance, the degree of likelihood that an observed, empirical relationship could be attributable to sampling error. A relationship is significant at the .05 level if the likelihood of its being only a function of sampling error is no greater than 5 out of 100.

**mean**

An average, computed by summing the values of several observations and dividing by the number of observations. If you now have a grade-point average of 4.0 based on 10 courses, and you get an F in this course, then your new grade-point (mean) average will be 3.6.

**median**

Another average, representing the value of the middle case in a rank-ordered set of observations. If the ages of five people are 16, 17, 20, 54, and 88, then the median is 20. (The mean is 39.)

**mode**

Still another average, representing the most frequently observed value or attribute. If a sample contains 1,000 residents of California, 275 from New Jersey, and 33 from Minnesota, then California is the modal category for residence.

**multivariate analysis**

The analysis of the simultaneous relationships among several variables. Examining simultaneously the effects of age, gender, and city of residence on robbery victimization is an example of multivariate analysis.

**nonsampling error**

Imperfections of data quality that are a result of factors other than sampling error. Examples are misunderstandings of questions by respondents, erroneous recordings by interviewers and coders, and data entry errors.

**null hypothesis**

In connection with hypothesis testing and tests of statistical significance, the hypothesis that suggests there is no relationship between the variables under study. You may conclude that the two variables are related after having statistically rejected the null hypothesis.

**range**

A measure of dispersion, the distance that separates the highest and lowest values of a variable in some set of observations. In your class, for example, the range of ages might be from 17 to 37.

**standard deviation**

A measure of dispersion about the mean. Conceptually, the standard deviation represents an average deviation of all values relative to the mean.

**statistical significance**

A general term for the unlikeliness that relationships observed in a sample could be attributed to sampling error alone. See also

*test of statistical significance*.

**test of statistical significance**

A class of statistical computations that indicate the likelihood that the relationship observed between variables in a sample can be attributed to sampling error only. See also

*inferential statistics*.

**univariate analysis**

The analysis of a single variable for purposes of description. Frequency distributions, averages, and measures of dispersion are examples of univariate analysis, as distinguished from bivariate and multivariate analyses