Significance test of the adjusted Rand index. Application to the free sorting task

• The association between two partitions of stimuli is investigated.
• For this purpose, the adjusted Rand index is used.
• A permutation test to assess its significance is discussed.
• A computationally less involving test is also proposed.
• The interest of the whole strategy of analysis in free sorting task is highlighted.

The adjusted Rand index is widely used in connection with the free sorting task to assess the degree of association between two partitions of a set of stimuli. A hypothesis testing framework regarding the significance of this index is set up. It consists in a permutation test which involves the simulation of a large number of partitions from the original two partitions being compared. However, since this strategy of analysis may be time consuming, an alternative method is also proposed. It is based on statistical properties regarding the distribution of the values generated by the procedure of permutation. The two strategies of analysis are illustrated and compared on the basis of free sorting data and a simulation study.