Which one of the following formulas is used to calculate probable error of correlation coefficient between two variables of $$’n’$$ pairs of observations?

$$” option2=”$$0.5758\left[ {\frac{{1 – {r^2}}}{{\sqrt n }}} \right]$$” option3=”$$0.675\left[ {\frac{{1 – {r^2}}}{n}} \right]$$” option4=”$$0.5758\left[ {\frac{{1 – {r^2}}}{n}} \right]$$” correct=”option1″]

The correct answer is: A. $0.6745\left[ {\frac{{1 – {r^2}}}{{\sqrt n }}} \right]$

The probable error of correlation coefficient is a measure of how much the correlation coefficient is likely to vary from sample to sample. It is calculated using the following formula:

$$\text{Probable error of correlation coefficient} = 0.6745\left[ {\frac{{1 – {r^2}}}{{\sqrt n }}} \right]$$

where $r$ is the correlation coefficient and $n$ is the number of pairs of observations.

Option A is the only option that includes the correct formula for the probable error of correlation coefficient. Option B is incorrect because it uses the wrong value for the constant $0.6745$. Option C is incorrect because it divides by $n$ instead of $\sqrt{n}$. Option D is incorrect because it uses the wrong value for the constant $0.5758$.