The Spearman's Rank Correlation Coefficient is a moderately complex tool
(Excel recommended) used to determine and measure the strength of the
correlation between two sets of data. Spearman's Rank Correlation Coefficient Formula where d is the difference between the ranks and N is the number of ranks.
Limitations:
IMPORTANT: you must rank BOTH sets of data from highest to lowest (ie: the highest value gets rank 1, the 2nd highest gets rank 2, etc). If 2 lines or more are tied with the same rank, you must give them the same rank number, equal to the middle between those 2 or more lines ( r = (t+2b+1)/2, where t = # of lines which are tied and b is the # of the last rank immediately before the lines that are tied)
The Spearman's Rank Correlation Coefficient is used to determine the strength or a correlation between two sets of data. A scatter graph can already suggest if there is a strong/weak negative/positive correlation (see below) but the Spearman's Rank Correlation Coefficient will allow us to quantify that correlation (in case there is one).
Note that the Pearson ProductMoment Correlation Coefficient is more sophisticated that the Spearman's Rank Test: it gives more accurate results because it uses the actual measured values of the data rather than their relative rankings. For the Pearson ProductMoment test to be used with validity however, the data MUST come from a normally distributed population. If unsure, use the Spearman's Rank Correlation test below.
Limitations:
 The data must be linear (draw a scatter graph with the line of best fit)
 The data must be independent from each other (ex: HDI and Fertility does NOT work because HDI is calculated using Fertility)
 There should be between 10 and 30 pairs of data
 Note that a strong correlation does not necessarily mean cause and effect. Ex: % of households owning a camera and % of person dying of lung cancer in the United States are both increasing between 1950 and 2000... But both elements are clearly NOT correlated!
IMPORTANT: you must rank BOTH sets of data from highest to lowest (ie: the highest value gets rank 1, the 2nd highest gets rank 2, etc). If 2 lines or more are tied with the same rank, you must give them the same rank number, equal to the middle between those 2 or more lines ( r = (t+2b+1)/2, where t = # of lines which are tied and b is the # of the last rank immediately before the lines that are tied)
The Spearman's Rank Correlation Coefficient is used to determine the strength or a correlation between two sets of data. A scatter graph can already suggest if there is a strong/weak negative/positive correlation (see below) but the Spearman's Rank Correlation Coefficient will allow us to quantify that correlation (in case there is one).
Note that the Pearson ProductMoment Correlation Coefficient is more sophisticated that the Spearman's Rank Test: it gives more accurate results because it uses the actual measured values of the data rather than their relative rankings. For the Pearson ProductMoment test to be used with validity however, the data MUST come from a normally distributed population. If unsure, use the Spearman's Rank Correlation test below.
1. Verify that you can run this test:

2. Calculate the Spearman's Rank Correlation Coefficient (Rs):
Use Excel to rank each sets of data and calculate Rs using the formula found at the top of this page (see podcast below). IMPORTANT 1: you must rank BOTH sets of data from highest to lowest (ie: the highest value gets rank 1, the 2nd highest gets rank 2, etc) IMPORTANT 2: if 2 lines or more are tied with the same rank, you must give them the same rank number which must be the average between the tied ranks. Example: if two lines are tied for rank #5 and rank #6, give them both the rank (5+6)/2 = rank #5.5. The ranking will then resume with the following line at rank #7, since technically speaking ranks #5 and #6 have been "used". 
3. Interpret the result:
4. Verify if the result is meaningful
There is a possibility that the correlation you have observed is not meaningful, but just happened by chance. In other words, if you had taken a different sample, you might have found completely different results. If the correlation is truly meaningful (i.e.: it doesn't happen by chance), you will find similar results no matter which sample you take. By default, the minimum "level of certainty" or "confidence level" required is 95% (i.e.: there should be at least a 95% chance that the correlation is NOT a coincidence). It's the same a saying, in reverse, that the "significance level" must be no more than 100%  95% = 5% (i.e.: there should be no more than 5% chance that the correlation was a coincidence).
To determine if the correlation is meaningful, use the diagram below using Rs and the degrees of freedom of your sample (df = # of pairs of data  2):
5. Conclude while pointing out the limitations of the test:
Click here to see two examples
 Note: Rs is always between 1 and +1
 If Rs is close to 0, the correlation is weak.
 If Rs is close to ± 1, there is a strong correlation, as follows:
 If Rs is close to 1, there is a strong negative correlation (one factor increases when the other one decreases)
 If Rs is close to +1, there is a strong positive correlation (both factors increase or decrease at the same time).
4. Verify if the result is meaningful
There is a possibility that the correlation you have observed is not meaningful, but just happened by chance. In other words, if you had taken a different sample, you might have found completely different results. If the correlation is truly meaningful (i.e.: it doesn't happen by chance), you will find similar results no matter which sample you take. By default, the minimum "level of certainty" or "confidence level" required is 95% (i.e.: there should be at least a 95% chance that the correlation is NOT a coincidence). It's the same a saying, in reverse, that the "significance level" must be no more than 100%  95% = 5% (i.e.: there should be no more than 5% chance that the correlation was a coincidence).
To determine if the correlation is meaningful, use the diagram below using Rs and the degrees of freedom of your sample (df = # of pairs of data  2):
 If the result you find is BELOW the line "5%", the confidence level is too low: this means that you cannot reliably say that the correlation you have observed is really meaningful and probably just happened by luck. If you took a different sample of data, you might obtain different results.
 If the result you find is ABOVE the line "5%" (the closer to the upper right hand corner of the diagram, the better!), it means that the correlation is significant with less than a 5% margin of error (i.e.: a level of certainty of 95% or more)
5. Conclude while pointing out the limitations of the test:
 If your sample does not meet the required confidence level (95% or more), you cannot conclude: either there is no correlation at all, or the correlation you have measured is just the result of luck, not of an actual underlying trend
 If Rs is close to +/ 1 AND your sample meets the required confidence level (95% or more), you can conclude that there is a strong and reliable correlation. HOWEVER, a strong correlation does NOT necessarily mean cause and effect! You would need more research more information (which this test does NOT provide)
Click here to see two examples