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 are useful to reduce order-effects when designing empirical experiments with multiple conditions. For example, in an experimental design comparing a prototype A vs B vs C, if all participants test A first, then B, then C, we might observe poor results for C because of participants' fatigue and not because C is worse than A or B. Instead, we can order conditions based on a Latin square like this:

Note: You can quickly insert your conditions using copy-paste (separated by lines) | Download .csv

A condition will precede another exactly once (or twice, if the number of conditions is odd). This page uses the method that James V. Bradley proposed and mathematically proved [1].

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.

Prof. Dr. Valentin Schwind. University of Applied Sciences Frankfurt. No liability for external links, correctness, completeness and up-todateness of any content. Site visits might result in storing of anonymized data (date, time, page viewed). Utilization at the own risk of the user. Data can be stored on the computers to facilitate the user's website access. Contribute here.

Find/cite the publication of the toolkit here:
Valentin Schwind, Stefan Resch, and Jessica Sehrt. 2023. The HCI User Studies Toolkit: Supporting Study Designing and Planning for Undergraduates and Novice Researchers in Human-Computer Interaction. In Extended Abstracts of the 2023 CHI Conference on Human Factors in Computing Systems (CHI EA '23), April 23-28, 2023, Hamburg, Germany. ACM, New York, NY, USA, 7 pages. https://doi.org/10.1145/3544549.3585890