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Spearman Rank Correlation Co-Efficient used with ordinal data... Note that a ‘statistical relationship’ can occur where no ‘meaningful relationship’ is.

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Presentation on theme: "Spearman Rank Correlation Co-Efficient used with ordinal data... Note that a ‘statistical relationship’ can occur where no ‘meaningful relationship’ is."— Presentation transcript:

1 Spearman Rank Correlation Co-Efficient used with ordinal data... Note that a ‘statistical relationship’ can occur where no ‘meaningful relationship’ is possible. Such a relationship is spurious. So any positive statistical result must always be backed up by sound reasoning. NominalOrdinalInterval IndependentChi-Square (association) Mann-Whitney U test (difference) RepeatedSign test (difference) Wilcoxon Matched Pairs Signed Ranks test (difference) Spearman Rank Correlation test (correlation) Matched pairs

2 Scatter graphs It is usually wise to draw a scatter graph, if undertaking any correlation. It is an easy way to highlight any relationship that may exist and its type, whether direct or inverse.

3 GNP and adult literacy Null hypothesis (H o ) – that there is no relationship between GNP per capita and % adult literacy. GNP per capita% adult literacy Nepal21039.7 Sudan29055.5 Gambia34034.5 Peru246089 Turkey316081.4 Brazil457084 Argentina897097 Israel1594096 U.A.E.1822074.3 Netherlands24760100

4 GNP and adult literacy GNP per capita% adult literacy Nepal21039.7 Sudan29055.5 Gambia34034.5 Peru246089 Turkey316081.4 Brazil457084 Argentina897097 Israel1594096 U.A.E.1822074.3 Netherlands24760100 Spearman’s Rank correlation coefficient (Rs) is the best method to use, as the GNP data is skewed. Spearman’s Rank can only be used with ordinal data so rank- order the data first.

5 Setting out Spearman’s Rank...

6 Summing ‘d 2 ’... Now sum ‘d 2 ’...... which gives the answer 44.

7 Calculating Spearman’s Rank... Insert the figures into the equation... Rs = 1 - ( 6 x 44 ) (1000 – 10) Rs = 1 – 0.277 Rs = 0.733

8 Probability level Degrees of Freedom.05.01 7.714.893 8.643.833 9.600.783 10.564.746 12.506.712 14.456.645 16.425.601 18.399.564 20.377.534 Critical values for Spearman’s Rank

9 Null hypothesis (H o ) was that there was no relationship between GNP per capita and % adult literacy. The degrees of freedom are (n – 1). So ‘df’ = 9. Spearman’s Rank correlation coefficient (Rs) result of 0.733 exceeds the 95% probability value of 0.60 at 9 degrees of freedom. Therefore the H o must be rejected and replaced by the alternative hypothesis (H 1 ) – that there is a relationship between GNP per capita and % adult literacy. Your (Rs) findings...

10 Try again... HeightIQ 1.5797 1.68112 1.81106 1.9495 1.6381 1.82134 1.51145 1.86134 1.92120 1.7289 1.8399 1.88107 1.7295 1.56107 1.6093

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