30 Dec 2022


Spearman's Rank Correlation Coefficient (Spearman's Rho)

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Academic level: Master’s

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The Spearman’s rank coefficient, sometimes called Spearman’s rho is widely used in statistics. It is a nonparametric concept used to measure statistical dependence between two variables. It employs the use of a monotonic function to assess two variables. Spearman’s coefficient bears its name from Charles Spearman and usually denoted by the characters P, or r (Sedgwick, 2014). The correlation of variables under this concept is only feasible when both the variables are monotones of one another and in a situation where there is no repetition of data values. Monotony helps in obtaining a Spearman’s rho of either +1 or -1. While the based on the assumption that the variables, predictor and response, both have numerical values, the Spearman’s correlation coefficient can be used to measure the skewed variables (Sedgwick, 2014) as well. Another assumption employed is a null hypothesis that the change in ranks of one variable does not bring change to the levels of the other variable. This means that the levels of the two variables do not affect one another. 

The use of Spearman’s rho is highly plausible in the research report by Messina et al. (2009). The article goes by the title "The Relationship between Patient Satisfaction and Inpatient Admissions across Teaching and Nonteaching Hospitals." The research was carried out with two important research questions in mind. The first one is how patient satisfaction and admissions related to each other in acute care hospitals. Secondly, there is the question on how the relationship between patient satisfaction and admissions vary across teaching and non-teaching hospitals (Messina et al., 2009). From the two issues, it is clear that the two variables evident in the research are the level of patient satisfaction and number inpatient admissions. 

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The independent variable in the analysis is the degree of patient satisfaction, while the secondary one is the number of inpatient admission. The estimation scale that is utilized for the assessment of the quantitative qualities covered under the two factors is legitimately characterized and positioned to acquire substantial outcomes with expanded dependability. The factors are legitimately summarized as far as their distinct measures for encouraging proper comparison of the results in two health care settings. The research qualifies to use the Spearman’s rho because both the independent and dependent variables are continuous. The coefficient is used to examine the relationship between the independent and dependent variables and they are being represented by the numerical value measured from admissions and scores from patient satisfaction. 

The fact that Messina and the other researchers carried out the study on a small sample of seven teaching and seven non-teaching hospitals is a clear indication that it was appropriate in the analysis. The clear association between the two variables is obtained by the employment of Mann-Whitney test on the sub-samples of teaching and non-teaching hospitals. The results show that the mean of all admissions in teaching and non-teaching hospitals as 19,111 in the time range of 1999-2003. The highest is 4,513 and the highest 70,465. The average score for patient satisfaction is 82.57 within the same period, the maximum being 86.18 and minimum 79.0. To normalize the distribution, the researchers employed Kurtosis analysis (Messina et al., 2009). 

Messina, Scotti, Zipp, Ganey, and Driscoll (2009) used appropriate and suitable variables to determine the Spearman’s correlation coefficient. The Rho determines statistical independence between two variables and it is a fact that Messina and colleagues selected two variables, volume of inpatient admission and level of patient satisfaction in teaching and non-teaching hospitals. As seen earlier, Spearman’s coefficient is used where one variable is ordinal numeric and the other continuous or where both of the variables are continuous (Sedgwick, 2014). In the study, both of the independent and dependent variables are continuous. Hence the use of Spearman’s rho is qualified. The results obtained indicate that there is a negative correlation between patient satisfaction and number of admissions (r= -0.287, P= 0.018). Hence there is an answer to the research questions. 


Messina, J., Scotti, D. J., Driscoll, A. E., Ganey, R. & Zipp, G. P. (2009). The Relationship between Patient Satisfaction and Inpatient Admissions across Teaching and Nonteaching Hospitals. Journal of Healthcare Management. 54 :3. 177-189 

Sedgwick, P. (2014). Spearman's rank correlation coefficient.   BMJ: British Medical Journal (Online) ,   349

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