Method calculating the coefficient: – Create a table from your data. Rank the two data sets. Ranking is achieved by giving the ranking '1' to the biggest value in a column, '2' to the second biggest value and so on. The smallest value in the column will get the lowest ranking. This should be done for both sets of measurements. Tied scores are given the mean (average) rank. Find the difference in the ranks (d): This is the difference between the ranks of the two values on each row of the table. The rank of the second value is subtracted from the rank of the first (distance). Square the differences (d²) to remove negative values and then sum them (d²). x-axis Distance (m) Rank Length of Rank Difference (d) Difference squared (d2) (cm) 0 12 13 12 0 0 5 11 14 11 0 0 10 10 22 9 1 –1 15 9 26 8 1 –1 20 8 19 10 2 4 25 7 27 7 0 0 30 6 42 5 1 –1 35 5 34 6 1 1 40 4 60 4 0 0 45 3 73 2 1 –1 50 2 71 3 1 1 55 1 78 1 0 0 d2 = 10 ∑ Calculate the coefficient (R) using the formula below. The answer will always be between 1.0 (a perfect positive correlation) and (a perfect negative –1.0 correlation). When written in mathematical notation, the Spearman Rank formula looks like this: Now put all these values into the formula.
Method – calculating the coefficient: Create a table from your data. Rank the two data sets. Ranking is achieved by giving the ranking '1' to the biggest value in a column, '2' to the second biggest value and so on. The smallest value in the column will get the lowest ranking. This should be done for both sets of measurements. Tied scores are given the mean (average) rank. Find the difference in the ranks (d): This is the difference between the ranks of the two values on each row of the table. The rank of the second value is subtracted from the rank of the first (distance). Square the differences (d²) to remove negative values and then sum them (d²). Distance (m) Rank Length of x-axis (cm) Rank Difference (d) Difference squared (d2) 0 12 13 12 0 0 5 11 14 11 0 0 10 10 22 9 –1 1 15 9 26 8 –1 1 20 8 19 10 2 4 25 7 27 7 0 0 30 6 42 5 –1 1 35 5 34 6 1 1 40 4 60 4 0 0 45 3 73 2 –1 1 50 2 71 3 1 1 55 1 78 1 0 0 ∑ d2 = 10 Calculate the coefficient (R) using the formula below. The answer will always be between 1.0 (a perfect positive correlation) and –1.0 (a perfect negative correlation). When written in mathematical notation, the Spearman Rank formula looks like this: Now put all these values into the formula.
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