APFIVE Sample Correlation Coefficient Formula
A researcher calculating the sample correlation coefficient for a dataset with n = 10 mistakenly divides the summation by 10 instead of 9. What mistake did the researcher commit?
EQUATION: $$r = \frac{1}{n-1}\sum \frac{(x-\bar{x})(y-\bar{y})}{s_x * s_y}$$
A
They omitted the use of Bessel’s correction; sample standard deviations (and related formulas) require division by n-1, not n, leading to a slight bias.
B
They should have squared the denominator after summation to correct for sample size.
C
The researcher misinterpreted the correlation coefficient as the coefficient of determination by failing to square r.
D
Dividing by 10 instead of 9 has no significant impact on the correlation coefficient for small samples.
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