The researchers developed new methods to compare multiple sets of data in a statistical analysis called MANOVA. They wanted to see if their techniques could find differences between groups when working with small sample sizes. By running computer simulations, they discovered the new methods could detect these differences better than older ones, especially when comparing all possible pairs of sets. Overall, the technique based on the Lawley-Hotelling trace showed the most power in many situations, meaning it could accurately identify differences between groups more effectively. This study aimed to improve ways of analyzing data to make better comparisons between different groups, even when working with limited data.