<p>In the correspondence analysis literature, advocates over the past 45 years (or so) have discussed the advantages of studying the square root of the cell counts of a contingency table, rather than the cell counts themselves. Doing so means that the Freeman-Tukey statistic is used as an alternative measure of association to Pearson’s chi-squared statistic. While there are advantages to using the classic Freeman-Tukey statistic, it is not always beneficial since it does not always behave like a chi-squared random variable. To address this issue, various improvements to the classic Freeman-Tukey statistic have been proposed, including a class of Freeman-Tukey statistics introduced in the early 1990s. This paper shows how correspondence analysis can be performed using two special cases of this class. By using these two special cases, we discuss the construction and properties of a low-dimensional space that visually represents the structure of a statistically significant association. We also quantify and interpret the distance between two row (or column) points in this low-dimensional space in terms of the link between their Hellinger and chi-squared differences.</p>