Frequency table

A table of category counts, often accompanied by sample proportions or percentages. Its denominator must be stated, especially when observations contain missing data.

The expected value of the number of observations in a category under a specified statistical model. For $n$ observations with common category probability $p_j$, linearity of expectation gives $E_j=n{p}_j$; the calculation does not itself require independence. In a contingency table, fitting independence gives $E_{ij}=n_{i+}{n}_{+j}/n$. These are model-based counts, which may be fractional, rather than an additional set of observed responses. Pearson's chi-squared test compares observed counts with their corresponding expected frequencies.

The sum of category percentages up to a specified position in an ordering. It has a substantive interpretation for an ordinal categorical variable; the cumulative percentage of an arbitrarily ordered nominal categorical variable changes when the labels are reordered.

A percentage whose denominator excludes observations missing the variable being summarized. It can differ from a percentage calculated over the complete dataset's sample size. Valid percentages for two different variables need not use the same observations.