crosstables

Crosstables are tabular representations used to organize and compare data. The term is used in sports to refer to a standings table that records the results of pairwise games in a tournament and, in statistics, to describe a cross-tabulation of categorical data. In tournament usage, a crosstable lists participants as both rows and columns. Each cell shows the result of the game between the corresponding pair (for example, 1 for a win, 0.5 for a draw, 0 for a loss, or a concrete score). The table is often accompanied by a row of total points and sometimes tiebreak information such as Buchholz, Sonneborn-Berger, or head-to-head results. Diagonals may be empty or marked with byes. Crosstables are common in round-robin events, Swiss systems, and national or world championships, and formats vary by discipline.

In statistics, a crosstab (cross-tabulation) summarizes the relationship between two or more categorical variables. The table's rows and columns represent categories, and each cell contains a frequency or percentage of observations falling into the corresponding combination. Marginal totals show overall counts, and the table is often subjected to tests of association such as the chi-squared test. Crosstabs can be produced by statistical software or spreadsheet programs and are widely used in market research, epidemiology, and social science.

Limitations include potential complexity in large tables and the inappropriate use with continuous variables without binning. When used appropriately, crosstables provide a compact, interpretable view of pairwise outcomes or joint distributions.