This document explains how to use Spearman's rank correlation coefficient to determine the strength and significance of the relationship between two variables. It provides steps to calculate the coefficient using birth rate and economic development data from 12 Central and South American countries. These steps are then applied to determine if there is a correlation between life expectancy and economic development in the same countries.

1. Spearman’s Rank Statistical Analysis to show Relationship Strength.www.i-study.co.uk

2. Is birth rate connected to economic development in Central and South American countries?Data taken from Philip’s International School Atlas (2nd Edition) published 2006 www.i-study.co.uk

3. SPEARMAN’S RANK CORRELATION COEFFICIENTIt says …It allows us to …Compare the RANK ORDER of TWO Data Setswww.i-study.co.uk

4. The total of6 xSpearman’s Rank Correlation CoefficientThe DIFFERENCES between the RANKS assigned to each ‘price’ SQUAREDThe number of different factors in the studywww.i-study.co.uk

5. The MathsFor Argentina:d (rank difference) = 8.5So d2 = 72.25Repeat this calculation for each countryMultiply the sum of all the d2 values by 6 to give the top line of the equationn = the number of countries in the sample =12. n³ - n : 1728 – 12 = 1716 (now we have the bottom line of the equation)Plug in the appropriate numbers to the full equation: your answer for step 4 your answer for step 6R = 1-www.i-study.co.uk

6. What does this R value mean?The closer Ris to +1 or -1, the stronger the likely correlation. Perfect positive correlation is +1 Perfect negative correlation is -1. Therefore, what sort of relationship do your calculations suggest?www.i-study.co.uk

7. What is it showing?Total DisagreementOverall Neither Agree or DisagreeTotal Agreementrs close to -1rs close to 1rs close to 0www.i-study.co.uk

8. The significance of the relationship!The R value must be looked up on the Spearman Rank significance table.

9. 'degrees of freedom' : This is the number of pairs in your sample minus 2 (In this case, 12 – 2 = 10)

10. Using the R value (y axis) the degrees of freedom value (x axis) plot the position of the graph (next page).www.i-study.co.uk