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

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Presentation transcript:

Spearman’s Rank Statistical Analysis to show Relationship Strength.

Is birth rate connected to economic development in Central and South American countries? Birth rateRankGNP per capita ($US) Rankdd2d2 Argentina Belize Bolivia Brazil Chile Colombia Costa Rica El Salvador Nicaragua Panama Peru Uruguay Data taken from Philip’s International School Atlas (2nd Edition) published

SPEARMAN’S RANK CORRELATION COEFFICIENT It says … It allows us to … Compare the RANK ORDER of TWO Data Sets Compare the RANK ORDER of TWO Data Sets

Spearman’s Rank Correlation Coefficient The total of 6 x The DIFFERENCES between the RANKS assigned to each ‘price’ SQUARED The number of different factors in the study

The Maths For Argentina: 1.d (rank difference) = So d 2 = Repeat this calculation for each country 4.Multiply the sum of all the d 2 values by 6 to give the top line of the equation 5.n = the number of countries in the sample = n³ - n : 1728 – 12 = 1716 (now we have the bottom line of the equation) 7.Plug in the appropriate numbers to the full equation: your answer for step 4 your answer for step 6 R = 1-

What does this R value mean? The closer R is 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?

What is it showing? Total Disagreement Total Agreement Overall Neither Agree or Disagree r s close to 1r s close to 0 r s close to -1

The significance of the relationship! The R value must be looked up on the Spearman Rank significance table. 'degrees of freedom' : This is the number of pairs in your sample minus 2 (In this case, 12 – 2 = 10) Using the R value (y axis) the degrees of freedom value (x axis) plot the position of the graph (next page).

Tasks Repeat this exercise for the same countries, but this time replace the birth rate data with the data for life expectancy.