Kendall Correlation Analysis Introduction A Kendall correlation analysis was conducted between Pos_Relations_Pre and Env_Mastery_Pre. Cohen's standard was used to evaluate the strength of the relationship, where coefficients between .10 and .29 represent a small effect size, coefficients between .30 and .49 represent a moderate effect size, and coefficients above .50 indicate a large effect size (Cohen, 1988). Assumptions Monotonic Relationship. A Kendall correlation requires that the relationship between each pair of variables does not change direction (Millard & Neerchal, 2000). This assumption is violated if the points on the scatterplot between any pair of variables appear to shift from a positive to negative or negative to positive relationship. Figure 1 presents the scatterplot of the correlation. A regression line has been added to assist the interpretation. Figure 1 Scatterplots with the regression line added for Pos_Relations_Pre and Env_Mastery_Pre Results The result of the correlation was examined based on an alpha value of .05. A significant positive correlation was observed between Pos_Relations_Pre and Env_Mastery_Pre, with a correlation of .60, indicating a large effect size (p < .001, 95.00% CI = [.39, .76]). This suggests that as Pos_Relations_Pre increases, Env_Mastery_Pre tends to increase. Table 1 and Table 2 presents the results of the correlation. Table 1 Kendall Correlation Matrix Between Pos_Relations_Pre and Env_Mastery_Pre Variable 1 2 1. Pos_Relations_Pre - 2. Env_Mastery_Pre .60* - Note. '*' indicates p < .05. Table 2 Kendall Correlation Results Between Pos_Relations_Pre and Env_Mastery_Pre Combination r 95.00% CI n p Pos_Relations_Pre-Env_Mastery_Pre .60 [.39, .76] 50 < .001 References Cohen, J. (1988). Statistical power analysis for the behavior sciences (2nd ed.). West Publishing Company. Intellectus Statistics [Online computer software]. (2025). Intellectus Statistics. https://statistics.intellectus360.com Millard, S. P., & Neerchal, N. K. (2000). Environmental statistics with S-Plus. CRC Press. https://doi.org/10.1201/9781420037173 Glossaries Kendall Correlation Kendall rank correlation is a non-parametric test that measures the strength of dependence between two variables. It is used to test the similarities in the ordering of data when it is ranked by quantities. Unlike other types of correlation coefficients, which use the observations themselves as the basis for measuring association, the Kendall correlation coefficient uses pairs of observations, and determines the strength of association based on the pattern of concordance or discordance among observation pairs. Fun Fact! The Kendall rank correlation was developed by Maurice Kendall, whose statistics were widely used and eventually used to create the roulette wheel. Concordant: A pair of observations (x1, y1) and (x2, y2) is considered concordant if (x2 - x1) and (y2 - y1) have the same sign. Critical Value: The minimum value at which an observed correlation coefficient is statistically significant. Discordant: A pair of observations (x1, y1) and (x2, y2) is considered discordant if (x2 - x1) and (y2 - y1) have opposite signs. Raw Output Kendall Correlation Test Included Variables: Pos_Relations_Pre and Env_Mastery_Pre Sample Size (Complete Cases): N = 50 Correlation Matrix: Variable 1 2 1. Pos_Relations_Pre - 2. Env_Mastery_Pre 0.604* - Note. '*' indicates p < 0.0500. Correlation Results: Combination r 95.000% CI n p Pos_Relations_Pre-Env_Mastery_Pre 0.604 [0.392, 0.755] 50 2.889 10-09