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 can be significant even if R is only slightly larger than zero. With practice, one can tentatively identify whether two variables are significantly correlated by examining a crossplot, and Figure 16 is provided to aid that experience gathering. With very large N, however, the human eye is less able to identify correlations, and the significance test of Table 7 is much more reliable.

There is an adage: “One doesn’t need statistics to determine whether or not two variables are correlated.” This statement not only ignores scientists’ preference for quantitative rather than qualitative conclusions; it is simply wrong when N is very small or very large. When N is very small (e.g., N<6), the eye sees correlations that are not real (significant). When N is very large (e.g., N>200), the eye fails to discern subtle correlations.

Nonlinear Relationships
The biggest pitfall of linear regression and correlation coefficients is that so many relationships between variables are nonlinear. As an extreme example, imagine applying these techniques to the annual temperature variation of Anchorage (Figure 10b). For a sinusoidal distribution such as this, the correlation coefficient would be virtually zero and regression would yield the absurd conclusion