Spearman Correlation Analysis Introduction A Spearman correlation analysis was conducted between Temp and Severity_of_Illness. 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 Spearman correlation requires that the relationship between each pair of variables does not change direction (Conover & Iman, 1981). 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 Temp and Severity_of_Illness Results The result of the correlation was examined based on an alpha value of .05. There were no significant correlations between any pairs of variables. Table 1 and Table 2 presents the results of the correlation. Table 1 Spearman Correlation Matrix Between Temp and Severity_of_Illness Variable 1 2 1. Temp - 2. Severity_of_Illness .15 - Note. '*' indicates p < .05. Table 2 Spearman Correlation Results Between Temp and Severity_of_Illness Combination r 95.00% CI n p Temp-Severity_of_Illness .15 [-.12, .40] 55 .281 References Cohen, J. (1988). Statistical power analysis for the behavior sciences (2nd ed.). West Publishing Company. Conover, W. J., & Iman, R. L. (1981). Rank transformations as a bridge between parametric and nonparametric statistics. The American Statistician, 35(3), 124-129. https://doi.org/10.1080/00031305.1981.10479327 Intellectus Statistics [Online computer software]. (2025). Intellectus Statistics. https://statistics.intellectus360.com Glossaries Spearman Correlation Spearman rank correlation is a non-parametric test used to measure the degree of association between two variables. It was developed by Spearman; thus it is called the Spearman rank correlation. Spearman rank correlation test does not make any assumptions about the distribution of the data and is the appropriate correlation analysis when the variables are measured on a scale that is at least ordinal level. Fun Fact! Correlation is a widely used term in statistics. In fact, it entered the English language in 1561, 200 years before most of the modern statistic tests were discovered. It is derived from the [same] Latin word correlation, which means relation. Correlation Coefficient (r): Ranges from -1 to 1; describes to the strength of the relationship between the variables. Critical Value: The minimum value at which an observed correlation coefficient is statistically significant. Effect Size: The strength of the relationship. Ordinal Data: Ordinal scales rank order the items that are being measured to indicate if they possess more, less, or the same amount of the variable being measured. An ordinal scale allows us to determine if X > Y, Y > X, or if X = Y. p-value: The probability of obtaining the observed results if the null hypothesis is true. A result is usually considered statistically significant if the p-value is .05. Raw Output Spearman Correlation Test Included Variables: Temp and Severity_of_Illness Sample Size (Complete Cases): N = 55 Correlation Matrix: Variable 1 2 1. Temp - 2. Severity_of_Illness 0.148 - Note. '*' indicates p < 0.0500. Correlation Results: Combination r 95.000% CI n p Temp-Severity_of_Illness 0.148 [-0.122, 0.398] 55 0.281