The researchers looked at how the chi-squared test statistic behaves in small samples compared to large samples when testing for independence in a two-way contingency table with fixed margins. They found that the test statistic follows a different distribution in small samples than in large samples. By directly calculating the exact small sample distribution for some cases and using a Monte Carlo algorithm for larger sample sizes, they compared the two distributions and found differences. This helps us understand how the chi-squared test behaves in different scenarios, which is important for accurate statistical analysis.