Ch 9: Quantitative Data Analysis

Base Number (N)

The total number of cases in a distribution.

Bimodal

A distribution that has two nonadjacent categories with about the same number of cases, and these categories have more cases than any others.

Central Tendency

The most common value (for variables measured at the nominal level) or the value around which cases tend to center (for a quantitative variable).

Chi-Square

An inferential statistic used to test hypotheses about relationships between two or more variables in a cross-tabulation.

Combined Frequency Display

A table that presents together the distributions for a set of conceptually similar variables having the same response categories; common headings are used for the responses.

Compressed Frequency Display

A table that presents cross-classification data efficiently by eliminating unnecessary percentages, such as the percentage corresponding to the second value of a dichotomous variable.

Contingency Table

In the simplest case, a bivariate (two variable) distribution, showing the distribution of one variable for each category of another variable; can be elaborated using three or more variables.

Correlational Analysis

A statistical technique that summarizes the strength of a relationship between two quantitative variables in terms of its adherence to a linear pattern.

Correlation Coefficient

A summary statistic that varies from 0 to 1 or −1, with 0 indicating the absence of a linear relationship between two quantitative variables and 1 or −1 indicating that the relationship is completely described by the line representing the regression of the dependent variable on the independent variable.

Cross-Tabulation (Crosstab)

In the simplest case, a bivariate (two variable) distribution, showing the distribution of one variable for each category of another variable; can be elaborated using three or more variables.

Curvilinear

Any pattern of association between two quantitative variables that does not involve a regular increase or decrease.

Data Cleaning

The process of checking data for errors after the data have been entered in a computer file.

Data Entry

The process of typing (word processing) or otherwise transferring data on questionnaires or other instruments into a computer file.

Descriptive Statistics

Statistics used to describe the distribution of and relationship between variables.

Elaboration Analysis

The process of introducing a third variable into an analysis to better understand—to elaborate—the bivariate (two-variable) relationship under consideration. Additional control variables also can be introduced.

Frequency Distribution

A numerical display showing the number of cases, and usually the percentage of cases (the relative frequencies), corresponding to each value or group of values of a variable

Frequency Polygon

A graphic for quantitative variables in which a continuous line connects data points representing the variable's distribution.

Gamma

A measure of association that is sometimes used in crosstabular analysis.

Interquartile Range

The range in a distribution between the end of the first quartile and the beginning of the third quartile.

Marginal Distribution

The summary distributions in the margins of a cross-tabulation that correspond to the frequency distribution of the row variable and of the column variable.

Mean

The arithmetic, or weighted, average, computed by adding the value of all the cases and dividing by the total number of cases. 

Measure of Association

A type of descriptive statistic that summarizes the strength of an association.

Median

The position average, or the point that divides a distribution in half (the 50th percentile).

Mode

The most frequent value in a distribution; also termed the probability average.

Monotonic

A pattern of association in which the value of cases on one variable increases or decreases fairly regularly across the categories of another variable.

Normal Distribution

A symmetric, bell-shaped distribution that results from chance variation around a central value.

Outlier

An exceptionally high or low value in a distribution.

Percentages

Relative frequencies, computed by dividing the frequency of cases in a particular category by the total number of cases and then multiplying by 100.

Probability Average

The most frequent value in a distribution; also termed the mode.

Quartiles

The points in a distribution corresponding to the first 25% of the cases, the first 50% of the cases, and the first 75% of the cases.

Range

The true upper limit in a distribution minus the true lower limit (or the highest rounded value minus the lowest rounded value, plus one).

Regression Analysis

A statistical technique for characterizing the pattern of a relationship between two quantitative variables in terms of a linear equation and for summarizing the strength of this relationship in terms of its deviation from that linear pattern.

Skewness

The extent to which cases are clustered more at one or the other end of the distribution of a quantitative variable rather than in a symmetric pattern around its center. Skew can be positive (a right skew), with the number of cases tapering off in the positive direction, or negative (a left skew), with the number of cases tapering off in the negative direction.

Specification

A type of relationship involving three or more variables in which the association between the independent and dependent variables varies across the categories of one or more other control variables.

Standard Deviation

The square root of the average squared deviation of each case from the mean.

Statistical Significance

The mathematical likelihood that an association is due to chance, judged by a criterion set by the analyst (often that the probability is less than 5 out of 100 or p < .05).

Subtables

Tables describing the relationship between two variables within the discrete categories of one or more other control variables.

Unimodal

A distribution of a variable in which there is only one value that is the most frequent.

Variability

The extent to which cases are spread out through the distribution or clustered in just one location.

Variance

A statistic that measures the variability of a distribution as the average squared deviation of each case from the mean.