Data/Science/Q/How are cross-tabs in polling different from a coefficient matrix?
How are cross-tabs in polling different from a coefficient matrix?
- Short answer: A cross-tab shows the joint distribution of survey responses across categories. A coefficient matrix contains numeric estimates of relationships among variables or model parameters. Cross-tabs keep the response categories visible; coefficients summarize them into estimates.
- Answer/Official from the U.S. Census Bureau’s American Community Survey glossary: a cross-tabulation repeats each category of one characteristic for the categories of another. In a poll, that commonly means a table of weighted percentages for an outcome question by a subgroup such as education, party identification, or age. Pew Research Center’s survey-data example shows approval responses by education and notes that a simple cross-tab alone does not establish whether observed differences are statistically meaningful.
- A coefficient matrix needs its type named. A correlation matrix places a correlation coefficient in each cell for a pair of numeric variables; R’s official documentation describes computing correlations between matrix columns. A regression coefficient table or matrix places estimated effects for predictors in cells; the estimates usually answer a conditional question after the model accounts for the other included predictors.
- Use a cross-tab to inspect who gave which categorical response and to find patterns worth explaining. Use a coefficient matrix when the estimand is an association or model effect, the variable encoding is appropriate, and the uncertainty and survey design have been handled. Neither output turns an observed association into a causal claim.