What is the difference between the following two T-Test formulas?
=(bi - b1) / Sb1
= r(n-2)^(1/2) / (1-r^2)^(1/2)
2nd one is correlation
1st is general
r(n-2)^(1/2) / (1-r^2)^(1/2) is used for testing significance of correlation coefficient between 2 variables, whereas (bi - b1) / Sb1 is used for general hypothesis testing if b1 takes on a certain value…
that’s my take on it.
The above two comment are correct, but to give a little more context, the correlation formula is derived from the general first formula with a little bit of algebra.
First note, t = (bi - b) / SE_b, where bi is the estimate, b is the hypothesized value, and SE_b is the standard error of the estimate.
For the specific case of correlation, bi = r, the correlation coefficient; b=0, because we are testing the null hypothesis that there is zero correlation; and SE_b = sqrt[(1-r^2) / (n-2)]. Combining this we get:
t = (r - 0) / sqrt[(1 - r^2) / (n - 2)]
= r * sqrt[(n - 2) / (1 - r^2)], which is the second formula.
yeah thats it