Statistics for Environmental Engineers

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The Spearman Rank Correlation Coefficient Critical Values for 95% Confidence


n


One-Tailed Test


Two-Tailed Test


n


One-Tailed Test


Two-Tailed Test


5


0.900


1.000


13


0.483


0.560


6


0.829


0.886


14


0.464


0.538


7


0.714


0.786


15


0.446


0.521


8


0.643


0.738


16


0.429


0.503


9


0.600


0.700


17


0.414


0.488


10


0.564


0.649


18


0.401


0.472


11


0.536


0.618


19


0.391


0.460


12


0.504


0.587


20


0.380


0.447

Familiarity sometimes leads to misuse so we remind ourselves that:


1.    The correlation coefficient is a valid indicator of association between variables only when that association is linear. If two variables are functionally related according to у = a + bx + cx , the computed value of the correlation coefficient is not likely to approach ±1 even if the experimental errors are vanishingly small. A scatterplot of the data will reveal whether a low value of r results from large random scatter in the data, or from a nonlinear relationship between the variables.


2.    Correlation, no matter how strong, does not prove causation. Evidence of causation comes from knowledge of the underlying mechanistic behavior of the system. These mechanisms are best discovered by doing experiments that have a sound statistical design, and not from doing correlation (or regression) on data from unplanned experiments.

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