Analyze data using Spearman’s rank correlation coefficient (rho)
- It measures the relationship between two logically related variables. Like the conventional correlation coefficient (r), Spearman rho can have any value between -1 to +1. A Spearman correlation of 1 results when the two variables being compared are monotonically related, even if their relationship is not linear. In a monotonic relationship, the variables tend to move in the same relative direction, but not necessarily at a constant rate. Monotonic relationship can be nonlinear. In a linear relationship, the variables move in the same direction at a constant rate.
CLICK HERE to refer to the diagrams of Linear, Nonlinear and monotonic relationships.
In Statistics, Correlation is largely a measure of an association between variables. In logically correlated data, the change in the magnitude of 1 variable is related to a corresponding change in the magnitude of another variable, either in the same (positive correlation: High-High, Low-Low) or in the opposite (negative correlation: Low-High or High-Low) direction. Very often, the term correlation is used in the context of a linear relationship between 2 continuous variables and expressed as Pearson product-moment correlation. For monotonically (nonlinear) distributed continuous ordinal data(indicate the order or rank of things) or for data with relevant outliers, Spearman rank correlation can be used as a measure. Spearman rho refers to the ranked values rather than the original measurements.
Determine how these two variables are correlated using Spearman’s rank correlation coefficient?
|Variable A |
(arranged in an ascending order-smallest to largest)
(assigned after arranging in order)
|Variable B||Rank (R2)||Difference in rank|
|Total d² = 320|
where n = number of paired observations
There are (n) degrees freedom (10)
Significance LevelCompare your result to the critical values for Spearman's Rank correlation (ignoring + / -). If rho is greater than or equal to the critical value, then there is a significant correlation and the null hypothesis can be rejected.
|Number of pairs of measurement|
|p = 0.05|
(+ or -)
|p = 0.01
(+ or -)
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