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Balanced Latin Square Generator

A Latin square is "an n × n array filled with n different symbols, each occurring exactly once in each row and exactly once in each column". Latin squares help reduce order effects in empirical studies with multiple conditions by creating a balanced ordering so each condition appears in every position as evenly as possible.

Configuration

Choose the number of conditions for your study. For odd sizes, the balanced design needs twice as many rows.

Odd sizes require twice as many rows to be balanced.

Balanced Square

Edit the first row directly or paste a line-separated list of condition names into any input field.

CSV Export

Download the current balanced square as a CSV file for further use in your study materials.

Download .csv

Method

A condition will precede another exactly once, or twice for odd numbers of conditions, based on Bradley's balanced Latin square construction.

Reference

Bradley, J. V. (1958). Complete counterbalancing of immediate sequential effects in a Latin square design. Journal of the American Statistical Association, 53(282), 525-528.

Source Code

Project repository and the original tool that inspired this version.