University of Arkansas System
Type of paper: Thesis/Dissertation Chapter
Spearman Coefficient Review
Correlation Coefficient remains one of the most important nonparametric measures of statistical dependence between two variables. The Spearman Correlation Coefficient facilitates the assessment of two variables using a monotonic function. This representation is only possible if the variables are perfect monotones of each other and if there are no repeated data values. This enables one to obtain a perfect Spearman correlation of either +1 or -1. The Spearman correlation coefficient nonparametric because, a perfect Spearman correlation results when X and Y are related by any monotonic function, can be contrasted with the Pearson correlation, giving a perfect value only when X and Y are related by a linear function. The other reason being, exact sampling distributions can be obtained without requiring knowledge of the joint probability distribution of X and Y (Sheskin, 2003).
The Spearman correlation coefficient is based on the assumption that both the predictor and response variables have numeric values, this assumption, however, the Spearman correlation coefficient can be used to analyze variables that are markedly skewed. The Spearman correlation coefficient operates on the null hypothesis that the ranks of one variable does not vary the same with the ranks of the other variable, meaning that, an increase in the ranks of one variable will most likely not produce an increase in the ranks of the other variable (Sheskin, 2003). The Spearman Correlation Coefficient formed the basis of analysis in finding out the Relationship between Patient Satisfaction and Inpatient Admissions across Teaching and Nonteaching Hospitals by Messina and Coyne. The research ‘The relationship between patient satisfaction and inpatient admission across teaching and nonteaching hospital’ was based on two main questions. The first was to determine, the nature of the relationship that existed between patient satisfaction and inpatient admissions in acute care hospitals. The Second one was to establish if the relationship between patient satisfaction and inpatient admissions differ between teaching hospitals and nonteaching hospitals. To answer these questions, the study focused on two variables, which were patient satisfaction and admissions.
The study was to provide Heath Executives with information to help them have a better understanding of the relationship between patient satisfaction and admission levels as there was an increase in patient expectations in the health sector. The Spearman coefficient correlation was used to analyze relationships between the independent variable, which was patient satisfaction, which was determined using patients’ satisfaction mean score, and the dependent variable which was admissions, admissions were measured using income (Lee & John 2013). The use of Spearman coefficient correlation enabled the researchers to answer the research questions as they were able to establish that, there exist a positive correlation between patient satisfaction and admission volumes in learning hospitals, whereas, there was a negative correlation between patient satisfaction and admission volumes in non-learning hospitals. The combined learning and non-learning study, a negative, statistically significant, correlation was observed between patient satisfaction and admission volumes. Admission volumes were found to partly affect the financial performance of both learning and non learning hospitals, while patient satisfaction determined the number of people both learning and non-learning hospitals received (Wager, Lee& Glaser. 2013). .
The researchers in this study effectively applied the Spearman correlation coefficient in this study as they were dealing with a case with few observations, and so the correlation coefficient was used to effectively quantify the data as this is one of the attributes of Spearman correlation coefficient. By using the Spearman coefficient correlation, the researchers were able to record values that can only be determined from descriptive attributes that have varying intensities. Using the Spearman coefficient correlation enabled the researchers to make generalizations while exploring the two variables, admissions and patient satisfaction. This generalization is necessary as there were other factors that determined customer satisfaction such as the quality of communication, perception of service provider competence, quality of facilities, the hospital staff conduct, and perception satisfaction and patient costs (Wager, Lee& Glaser. 2013).
The advantages of using Spearman correlation coefficient to study the relationship between patient satisfaction and admissions were; The fact that the correlation coefficient can be used to assess relationships for both continuous sets of data and discreet sets of data, the correlation was effective as the researchers were able to show correlations even when the actual values of the variables were unknown. This is because Spearman correlation coefficient uses ranks as a basis of establishing correlation between variables (Kelemen, Kelemen & Liang, 2008). First of all both variables are converted into ranks, once the two variables are converted to ranks, a correlation analysis is done on the ranks. The correlation coefficient is calculated for the two columns of ranks.
The P-value from the correlation of ranks is the P-value of the Spearman rank correlation. The ranks cannot be graphed against each other and, a line cannot be used for either predictive or illustrative purposes. The other advantage of the Spearman correlation coefficient is the fact that by arranging the ranks in either ascending or descending manner, a correct correlation will still be obtained from both arrangements. The Spearman correlation coefficient, however, can only be used to measure relationships of variables with linear relationships. Any change in the value in X causes a subsequent change in the value of Y. The Spear correlation coefficient is not effective in cases of categorical data such as gender (Kelemen, Kelemen & Liang, 2008).
David J.S. (2003). Handbook of Parametric and Nonparametric Statistical Procedures. Florida: CRC Press. Arpad K, Arpad K & Yulan L.(2008). Computational Intelligence in Medical Informatics. New York: Spinger. Karen W, Frances Lee & John G. (2013). Health Care Information Systems: A Practical Approach for Health Care Management. New Jersey: John Wiley & Sons.