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# Spearman's Rank correlation

## Data types that can be analysed with Spearman's Rank Correlation Coefficient

•  the relationship should be linear (draw scatter graph)
•  data points within samples should be independent from each other
•  ordinal scale data are most suitable for the Spearman's Rank
•  paired observations should be between 7 and 30
•  all individuals must be selected at random from the population
•  all individuals must have equal chance of being selected

## Limitations of the tests

•  a significant correlation does not necessarily mean cause and effect

## Introduction to Spearman's Rank

Correlation tests are used to assess whether there is a relationship between two or more variables. For instance, a tall Homo sapiens individual will have longer arms and legs when compared to a short Homo sapiens. The arms and legs will have some variation but generally longer arms will accompany longer legs, and vice versa. The evolutionary implications of the reverse (especially longer arms and shorter legs) are regressive. In a relationship where both variables (arm and leg length) increase the relationship is said to be positive. A negative relationship is where one of the variables decreases as the other increases. An example would be the growth of a plant species relative to altitude.

This latter example is a good one to discuss the lack of cause and effect. Just because the growth of a plant species declines with increasing altitude does not mean it is the fault of altitude. With altitude comes several other factors that could inhibit the growth of plants. Temperature, lack of oxygen, poor soil nutrients and a host of other potential variables, which could all be found to correlate negatively with plant growth.

## Data arrangement

Excel does not support Spearman's Rank but can be easily incorporated by using the function "CORREL" on the ranks of the data (see Shepherd, 1998), but the statistical packages nearly always use columns and these are required side by side.

## Results and interpretation

(Degrees of freedom = pairs of observations)

You can check that the program has used the right data by making sure that the degrees of freedom (8) are correct. The information you then need to use in order to reject or accept your HO, is the 1-tail Probability value (3.66E-06 [0.00000366]). When this value is below 0.05 there is a significant correlation between your data sets. The 1-Tail Probability is used because the slope of the line will be greater than 0 if it is significant, as any negative sign is ignored. The above negative correlation value indicates a negative relationship between the two variables.

If you have used the CORREL function or Correlation tool in Excel, you will need to look up the critical value and compare it with the calculated value (-0.9636 above). If the calculated value is greater than the critical value, the HO must be rejected. In the above case the correlation value is much higher than the critical value of 0.881 for 8 degrees of freedom at 0.01 confidence level. The correlation is therefore very highly significant.