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 COEFFICIENT It says … It allows us to … Compare the RANK ORDER of TWO Data Sets www.i-study.co.uk

4. The total of 6 x Spearman’s Rank Correlation Coefficient The DIFFERENCES between the RANKS assigned to each ‘price’ SQUARED The number of different factors in the study www.i-study.co.uk

5. The Maths For Argentina: d (rank difference) = 8.5 So d2 = 72.25 Repeat this calculation for each country Multiply the sum of all the d2 values by 6 to give the top line of the equation n = 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 6 R = 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 Disagreement Overall Neither Agree or Disagree Total Agreement rs close to -1 rs close to 1 rs close to 0 www.i-study.co.uk

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

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12. Tasks Repeat this exercise for the same countries, but this time replace the birth rate data with the data for life expectancy. www.i-study.co.uk