Essay on Spearmans Rho Measures

Correlation refers to the extent to which two variables possess a linear relationship with each other (MacDonald, 2007). Correlation is used to predict relationships in real life e.g. the relationship between drug abuse and crime. Statistical approaches to correlation differ depending on the normality of data being analyzed. If the data being analyzed is normally distributed, Pearson correlation procedures are used to examine the relationship between two variables. If the data is not normally distributed (negatively or positively skewed), Spearmans Rho statistical analysis is used.

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Spearmans Rho correlation is a statistical measure used to determine the strength of a monotonic relationship between paired data (Jain, 2006). It is a non-parametric test used to measure the strength and direction of the relationship between two variables that are on an ordinal scale. Non-parametric tests do not require the populations distribution to have certain parameters e.g. normality. The Spearman correlation coefficient is denoted by rs. Like the Pearson correlation coefficient values, the value of rs (Spearmans correlation coefficient) ranges from -1 to +1. A positive correlation coefficient shows that as one variable increases in value, the second variable also increases in value while a negative correlation indicates a negative relationship i.e. as one variable value increases, the other variable value decreases. A correlation coefficient of 0 shows that there is no relationship between the two variables. Moreover, if the correlation coefficient is +1, it means there exist a perfect positive correlation between the two variables, whereas a value of -1 indicates a perfect negative correlation. The measure can also be used to analyze continuous data that have failed to meet the assumptions needed to conduct the Pearson's product-moment correlation.

For Spearmans Rho analysis to be conducted, the two variables of interest must meet certain assumptions. First, both variables should be measured on either ordinal, interval or ratio scale. The second assumption is that there should be a monotonic relationship between the variables (Assoc, 2015). A monotonic relationship exists when two variables increase in value concurrently, but not necessarily at the same rate. The relationship also exists if one variable value increases as the other variable value decreases. One of the ways of checking if a monotonic relationship exists between two variables is by creating a scatterplot and then visually checking scatterplot for monotonicity.

What Spearmans Rho measures, when it is used, and why the measure is important

Spearmans Rho is used investigate if a relationship exists between two ordinal variables. More specifically, it is used to find out if a rank order association exist between two quantitative variables. For instance, a researcher might use Spearmans Rho correlation to find out whether the order in which students complete a test is related to the number of weeks they have revised the content. This statistical measure is used when the variables whose relationship is being examined are both ordinal. It is also used when the data is not normally distributed and when the sample size is small. Moreover, it is the best approach to correlation if the data has outliers because it is not sensitive to outliers like Pearson correlation (Assoc, 2015). It plays almost the same role as a Pearson's correlation. The only difference is that Pearson correlation is used when the sample is normally distributed, the level of measurement is interval, and when the sample size is large.

References

Assoc, M. T. (2015). CMT Level II 2016: Theory and Analysis. John Wiley & Sons.

Jain. (2006). Business Statistics For B.Com (Hons). Tata McGraw-Hill Education.

MacDonald, T. H. (2007). Basic Concepts in Statistics and Epidemiology. Radcliffe Publishing.