Answer to Question 1
(a) LinearityIf the relationship between two variables is nonlinear, the Pearson Product-Moment Correlation will not give you the best information about the strength of the association.
(b) Restriction in rangeIf you measured variables over a limited range of their values, the correlation coefficient will be lower than it would be if you used the entire range.
(c) Homogeneity of subgroupsIf there are subgroups in the total sample you use and if those subgroups are different from one another, you might wind up with correlations that don't represent the true relationship between variables.
Answer to Question 2
If you variables are nonlinearly related, you should be cautious about using the standard Pearson correlation. You might need to test for nonlinearity and use a different correlational approach to identify whether the relation between variables is reliable.
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