Setting Up an Online Survey Instrument for Effective Quantitative Cross-Tabulation Analysis

Introduction

A basic cross tabulation analysis (aka “contingency table”) is comprised of a data table or matrix in which variables are placed in the column headers and the row headers, and the corresponding intersecting values for those variables are in the respective column and row cells. These tables represent a joint frequency distribution, and these “multi-dimensional table(s) (are) used to compare the correlation between two variables (Cross-Tabulation Analysis, 2011, as cited in Lee, Aug. 15, 2015, p. 28) at a time, in a dyadic way. Even two variables being compared may be fairly complex, with scale values in some cases, and other related observations. Multiple variables may be explored at a time in a cross tabulation analysis. At the most basic, a cross tabulation analysis table contains at least two variables, in a 2x2 table. This may be seen in the bolded section at the top left of Table 1.

In qualitative cross tabulation analyses, the intersecting cells may be comprised of frequency counts, common shared terms (words from the respective text sets), or other measures. Some qualitative cross tabulation analyses enable clustering of textual responses to survey (interview, focus group, and others) data by demographic features, responses to particular questions (all those who expressed something), and others.

In a quantitative cross tabulation analysis, the respective intersecting or crossover cells (where the row and column intersect) usually contain a percentage calculation from the observed values / expected values. The “observed values” are the data collected from the research. The “expected values” are calculated based on the potential ranges of values given the numbers of cells (based on the available numbers of variables). The “degrees of freedom” (df) in the construct is calculated based on the number of variables minus one (n – 1). The chi-squared calculation is based off of an expected chi-squared distribution that would exist if the null hypothesis is true (only random chance is acting on the observed data and not some other influence). This chi-squared calculation is applied to each cell.

The p-value (probability value) is a threshold value at which the null hypothesis may be rejected, usually at < .05 or < .01; the lower the p-value, the rarer the observed data has to be before the null hypothesis may be rejected. A p-value (or “alpha value”) of < .05 means that the observed results may fall on either end of the tails of the bell curve distribution at .025 at either end (extreme standard deviations from the center), and a p-value of < .01 means that the observed results may fall on either end of the tails at .005. (The assumption of a normal bell curve distribution applies to some data but not necessarily to categorical data analyzed using a cross tabulation analysis, with the chi-squared statistic.) The calculations in each cell point to possible (non)associations between each pairing (of the variables in the particular row/stub and the column/banner header). In some research, the rows and the columns may contain a mix of variables; in others, one contains the independent variable(s) and the other the dependent variable(s). [The independent variables (IVs) are theorized or hypothesized to have effects on the dependent variables (DVs). The dependent variables are the ones being tested or explored in research.]