# How to Calculate Spearman Rank Correlation in R

In statistics, correlation 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: a perfect negative relationship between two variables
• 0: no relationship between two variables
• 1: a perfect positive relationship between two variables

One special type of correlation is called Spearman Rank Correlation, which is used to measure the correlation between two ranked variables. (e.g. rank of a student’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 <- cor.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 <- c(70, 78, 90, 87, 84, 86, 91, 74, 83, 85)
y <- c(90, 94, 79, 86, 84, 83, 88, 92, 76, 75)

#calculate Spearman rank correlation between x and y
cor.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 is 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 <- data.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 is 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.