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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

What This Tool Helps With

This generator is intended for researchers, students, and practitioners who need a quick way to counterbalance condition order in controlled experiments.

Counterbalance Experimental Conditions

Use balanced Latin squares to assign multiple interface, prototype, or task conditions in a way that reduces order effects such as learning, fatigue, and carryover.

Support Within-Subject Studies

The tool is especially useful for within-subject and repeated-measures designs in HCI, UX, psychology, and other empirical research contexts.

Prepare Study Material Quickly

Edit condition names directly in the table and export the resulting sequence as CSV to use it in recruiting sheets, lab notes, or experiment scripts.

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.

FAQ

What is a balanced Latin square?

A balanced Latin square is an ordering scheme in which each condition appears in each position equally often and precedes every other condition equally often.

When should I use this generator?

Use it when all participants experience multiple conditions and you need a principled ordering for prototypes, tasks, stimuli, or interfaces in a repeated-measures study.

Why are odd numbers of conditions different?

For odd square sizes, a balanced Latin square needs twice as many rows so that immediate sequential effects remain balanced across the full set of assignments.

Source Code

Project repository and the original tool that inspired this version.