The Spearman Coefficient Correlation Coefficient also called the Spearman’s rho (abbreviated-rs) is a statistical nonparametric measure of statistical dependence between two variables. In other words, it is a measure of the strength of association between two ranked variables. When a change in one variable leads to a change in the other variable, the two variables are said to be correlated (Hauke and Kossowski 88). The spearman product moment correlation coefficient can be calculated when the data is in ratio scale or intervals. The numerical value of the coefficient ranges from -1 to +1. In when rs > 0 indicates a positive agreement among ranks, rs < 0 implies a negative agreement while an rs=0 implies no agreement (Zar, 579). In this case, the Spearman Coefficient Correlation Coefficient showed proper statistical use of the measures and they suited the situation well since the variables were correlated.
In order to understand the use of the Spearman Coefficient Correlation Coefficient in this case it is good to establish the basics of the study. The study was conducted between 1999 to 2003 on seven teaching hospitals and 7 nonteaching hospitals in New Jersey (Messina et al). The study collected patient satisfaction data using discharge surveys in the selected hospitals. The patient satisfaction was measured using a five-point Likert scale as follows: 1= very poor, 2= poor, 3= fair, 4=good and 5= very good (Messina et al). The data was then converted to a larger scale (0-100) with 0 being the rank given to the lowest and 100 being very good.
The variables in order were patient satisfaction as the independent variable and admission rates or volume the dependent variable. The study showed a statistically significant and positive correlation between patient satisfaction and admission volume in teaching hospitals only. However, there was a non-significant correlation between patient satisfaction and admission in nonteaching hospitals (Messina et al). The combined teaching and nonteaching sample delivered a statistically significant negative correlation between patient satisfaction and admission volume.
The Spearman rank correlation coefficient requires that the data be ranked. Ranking entails numbering scores or entries according to their values. Where there are two or more equivalent values they are ranked according to the value of their mean. As such, Spearman rank correlation coefficient is a non-parametric measure, which the study satisfied.
The Spearman rank correlation coefficient also assumes a monotonic relationship between the variables. A monotonic variable is one in which the variables are proportionate to each other. For instance, when one variable increases, the other decreases and vice versa (Zar, 539).
The study used a Mann-Whitney U-test in collaboration with the Spearman Correlation testing. The tests determined the differences between the two independent groups (teaching and the nonteaching) based on the rank-ordered scores. As such, the study satisfies the requirements of the Spearman rank correlation coefficient. The mean rank for the teaching hospital patient satisfaction was 25.76 while that of the nonteaching hospital was 45.24.
The Spearman rank order correlation had a significant negative correlation (rs=-0.287, p=0.018) between patient satisfaction and admission for the combined sample (Messina et al). Higher patient satisfaction means scores are associated with lower inpatient volumes. The variables used responded to the reserch question on whether there was a relationship between patient Satisfaction and Inpatient Admissions across Teaching and Nonteaching Hospitals. The study shows that indeed patents were more satisfied in teaching hospitals. The study also satisfied the use of the Spearman correlation since high patient satisfaction goes with high admission volumes at teaching hospitals (positive response) while the vice versa is true for nonteaching hospitals.
Works Cited
Messina, et al. The Relationship between Patient Satisfaction and Inpatient Admissions across Teaching and Nonteaching Hospitals. Journal of Healthcare Management 54:3 May/June 2009 print.
Hauke Jan & Kossowski Tomasz. Comparison of Values of Pearson’s And Spearman’s Correlation Coefficients on the Same Sets of Data. Poland. Quaestiones Geographicae 30(2). 2011. Print
Zar, J. H. Significance Testing of the Spearman Rank Correlation Coefficient. Journal of the American Statistical Association, 67(339), 578-580. 1972. Print
