Final answer:
The correct formula for the correlation coefficient between two data arrays in original units is the Pearson correlation coefficient, represented by A) Correlation = Covariance / (Standard Deviation_x × Standard Deviation_y), where a high absolute value indicates a significant relationship that can be confirmed by a t-test.
Step-by-step explanation:
The appropriate formula for calculating the correlation coefficient between two arrays of data in their original units is given by the Pearson correlation coefficient formula, which is choice A. This formula can be mathematically expressed as:
Correlation = Covariance / (Standard Deviation_x × Standard Deviation_y)
The correlation coefficient, which usually is represented by the letter r, tells us how strongly two variables are linearly related and the direction of their relationship. It is a measure that can range from -1 to +1 where a coefficient close to +1 indicates a strong positive association, a coefficient close to -1 indicates a strong negative association, and a coefficient around 0 suggests no association between the variables.
A high absolute value of the correlation coefficient, whether positive or negative, indicates that the relationship between the variables is significant. However, the statistical significance of a correlation can also be determined by conducting a t-test to calculate the probability that the observed correlation occurred by chance, given a specific alpha level (typically 0.05).