Final answer:
In factor analysis, items are evaluated for their association with particular factors through the coefficient of correlation, a measure of how two variables are linearly related.
Step-by-step explanation:
A critical component in factor analysis is how items correlate with a particular factor or coefficient of correlation.
Professionals across various fields, including social psychology and geography, use the coefficient of correlation, developed by Karl Pearson, to measure the strength and direction of the linear association between the independent variable (x) and the dependent variable (y). It quantifies how changes in one variable are associated with changes in another.
The formula for Pearson's Correlation Coefficient is:
nΣ xy -[Σ xΣ y]
√√(nΣ x² − (tΣ x] )(nΣ y² − (tΣ y])
A correlation coefficient close to 1 or -1 indicates a strong relationship, whereas a correlation closer to 0 indicates a weaker relationship. A positive value suggests a direct relationship, while a negative value indicates an inverse relationship. If variables are completely unrelated, the correlation coefficient will be 0.