Qualitative Data
Qualitative data consists of categories or labels that describe characteristics rather than numerical measurements.
Definition
Qualitative data is information described with words or categories, not numbers, answering questions like "What kind?" or "Which group?" It classifies observations into groups with no inherent numerical value, and can be nominal (no order, like eye color) or ordinal (ordered categories, like class ranking). Formally, qualitative (categorical) variables take values from a finite set of categories: nominal variables are analyzed with chi-square tests and contingency tables, while ordinal variables can use non-parametric tests (Mann-Whitney, Kruskal-Wallis) or ordered logistic regression.
Example
Students' favorite school subjects (math, science, art, reading) or the color of cars in a parking lot are qualitative data. Blood type (A, B, AB, O) is nominal qualitative data, while survey responses on a scale of "strongly disagree" to "strongly agree" are ordinal qualitative data. A chi-square goodness-of-fit test compares observed category frequencies to expected frequencies under a null hypothesis: for a die rolled $60$ times, expected frequency per face is $10$, and the test statistic is $\chi^2 = \sum \frac{(O-E)^2}{E}$.
Key Insight
Qualitative data tells you the type or category, while quantitative data tells you the amount, and both are useful for different questions. Ordinal data has order but not equal spacing between levels, so treating it as if it were quantitative (e.g., averaging "strongly agree = 5") is statistically controversial. Encoding categorical variables as dummy (indicator) variables in regression allows integration of qualitative predictors into quantitative models, forming the basis of ANOVA and logistic regression.