Transcription of SPEARMAN RANK CORRELATION COEFFICIENT
1 SPEARMAN RANK CORRELATION COEFFICIENT Measures the strength and direction of the relationship between two variables The data can be plotted as a scatter graph There must be more than 5 pairs of measurements (10+ gives better results) It makes no assumption about data distribution The value for rs ( SPEARMAN rank) will be between +1 and -1, where +1 indicates a perfect positive CORRELATION and -1 a perfect negative CORRELATION .
2 0 indicates no CORRELATION at all. Equation: Where: rs = 1 - 6 d2 rs = SPEARMAN Rank CORRELATION COEFFICIENT n (n2 - 1) d2 = Sum of the squared differences between ranks n = number of pairs of observations in the sample Method: 1. State the Null Hypothesis H0 (this is always the negative form. there is no significant CORRELATION between the variables) and the alternative hypothesis (H1). 2.
3 Copy your data into the table below as variable x and variable y and label the data sets. Rank R1 Rank R2 d (R1 - R2) d2 (variable x) (variable y) 3. Rank the individual data sets in order in increasing order as separate sets of data ( give the lowest data value the lowest rank) 4.
4 Calculate the difference (d) between each pair of ranks (If completed correctly, the sum of the differences should equal zero) R1 R2 (include negatives) 5. Square the differences (d2) for each pair of ranks 6. Sum d2 7. Calculate rs. The result must be between +1 and -1 rs = 1 - 6 d2 = n (n2 - 1) 8. Compare your result to the critical values for SPEARMAN Rank CORRELATION at the appropriate number of pairs of measurements (ignoring the sign + or -). If rs is greater than or equal to the critical value, then there is a significant CORRELATION and the null hypothesis can be rejected.
5 Table 1 - Critical values for the SPEARMAN s Rank CORRELATION COEFFICIENT Significance level Number of pairs of measurements (n) p = (95%) (+ or -) p = (99%) (+ or -) 5 6 7 8 9 10 11 12 13
6 14 15 16 17 18 19 20 25 30 35 40
