Spearman Rank Correlation
Spearman’s rank correlation is a measure of the association between two variables. It has a value between -1 and 1. This calculation does not require your data to be normally distributed.
- You want to know whether two numerical variables are monotonically correlated.
- Your data is ordinal or continuous (see Types of Data for more information).
- Your data has outliers (see Outliers in your Data for more information).
- Your data is linked (paired) – each value of your independent variable has a matching value for the dependent variable (like X-Y coordinates).
Spearman’s rank correlation can evaluate a monotonic relationship between two variables (which are continuous or ordinal). It is based on the ranked values for each variable rather than the raw data.
Monotonic means that as one variable increases the other also does OR as one variable increases the other decreases. There does not have to be a linear relationship (as with the Pearson Correlation Coefficient).
The pictures below show the difference between a positive monotonic relationship (as x-values increase, y-values also increase), a negative monotonic relationship (as x-values increase, y-values decrease) and a non-monotonic relationship (as x-values increase, y-values perhaps decrease and then increase, or increase and then decrease). We can only use the Spearman Rank Correlation in the first two instances.
Spearman’s rank correlation is a measure of the association between two variables. It has a value between -1 and 1 where:
- -1 indicates a perfectly negative correlation between the two variables.
- 0 indicates no correlation between the two variables.
- 1 indicates a perfectly positive correlation between the two variables.
Remember that correlation does not imply causation. Just because two variables are strongly correlated this does not mean that one variable causes the other.
An online calculator can be found HERE.
Checking for statistical significance
Once you have determined the Spearman Rank correlation coefficient you can check whether the correlation you have found is statistically significant.
The online calculator suggested above will give you the following message if your correlation is significant:
By normal standards, the association between the two variables would be considered statistically significant.
You are investigating the effect of the flow rate of a river on the density of invertebrates. You count the number of blackflies in quadrats at 10 different locations along a stream and measure the flow rate. Your data is as shown to the right. You now want to determine whether these two variables (flow rate and fly density) are correlated. Since the data is not assumed to be normally distributed Spearman Rank correlation is appropriate. You use the online calcuator HERE. |  |
Match the X and Y values below.
Fly count Flow rate
X values =
Y values =
The X values should be the flow rate as it is believed this influences the fly density (Y values).
If you put the data the other way around, you are implying that the fly count influences the river's flow rate, which makes no sense!
Once you have done the calculations you can conclude...
negative positive not statistically significant statistically significant increases decreases increases decreasesThe correlation between flow rate and fly count is and this result can be considered . This means that it is reasonable to assume that as the flow rate the fly count .
The calculated correlation of -0.86239 is negative. This means that as the flow rate increases, the fly count decreases.
Is the correlation of -0.86239 statistically significant?
By normal standards, the association between the two variables would be considered statistically significant.