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In statistics,Â **correlationÂ **refers to the strength and direction of a relationship between two variables. The value of a correlation coefficient can range from -1 to 1, with the following interpretations:

**-1:Â**a perfect negative relationship between two variables**0:Â**no relationship between two variables**1:Â**aÂ perfect positive relationship between two variables

One special type of correlation is calledÂ **Spearman Rank Correlation**, which is used to measure the correlation between two ranked variables. (e.g. rank of a studentâ€™s math exam score vs. rank of their science exam score in a class).

To calculate the Spearman rank correlation between two variables in R, we can use the following basic syntax:

corr test(x, y, method = 'spearman')

The following examples show how to use this function in practice.

**Example 1: Spearman Rank Correlation Between Vectors**

The following code shows how to calculate the Spearman rank correlation between two vectors in R:

#define data x #calculate Spearman rank correlation between x and ycor.test(x, y, method = 'spearman') Spearman's rank correlation rho data: x and y S = 234, p-value = 0.2324 alternative hypothesis: true rho is not equal to 0 sample estimates: rho -0.4181818

From the output we can see that the Spearman rank correlation is **-0.41818** and the corresponding p-value isÂ **0.2324**.

This indicates that there is a negative correlation between the two vectors.

However, since the p-value of the correlation is not less than 0.05, the correlation is not statistically significant.

**Example 2: Spearman Rank Correlation Between Columns in Data Frame**

The following code shows how to calculate the Spearman rank correlation between two column in a data frame:

#define data frame df frame(team=c('A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J'), points=c(67, 70, 75, 78, 73, 89, 84, 99, 90, 91), assists=c(22, 27, 30, 23, 25, 31, 38, 35, 34, 32)) #calculate Spearman rank correlation between x and y cor.test(df$points, df$assists, method = 'spearman') Spearman's rank correlation rho data: df$points and df$assists S = 36, p-value = 0.01165 alternative hypothesis: true rho is not equal to 0 sample estimates: rho 0.7818182

From the output we can see that the Spearman rank correlation is **0.7818** and the corresponding p-value isÂ **0.01165**.

This indicates that there is a strong positive correlation between the two vectors.

Since the p-value of the correlation is less than 0.05, the correlation is statistically significant.

**Additional Resources**

How to Calculate Partial Correlation in R

How to Calculate Autocorrelation in R

How to Calculate Rolling Correlation in R

How to Report Spearmanâ€™s Correlation in APA Format