Different formulas of T statistic ?

[hassan.mahfooz]

What is the difference between the following two formulas:

1.

t = r * (n-2)^0.5 / (1-r^2)^0.5

2.

t = slope coefficient / standard error

When should we use formula 1 and when should we use formula 2 ?

 

[S2000magician]

The first is the t-statistic for whether the correlation coefficient equals zero or not in a simple regression model.
The second is the t-statistic for whether a slope coefficient equals zero or not in a simple regression model or a multiple regression model.

 

[Harrogath]

Many weeks ago someone asked the same.
“Tickersu” (forum member) gave a good answer why apparently are different calculations of a T-test, but indeed they are the same. The only different thing is the calculation of the standard error.
As S2000magician says, the first t-statistic is for the correlation coefficient:
t = r * (n-2)^0.5 / (1-r^2)^0.5
This formula comes from t = ( r - 0 ) / standard error. However, the standard error here does not come from a T-table, but from a standard error calculation as follow:
standard error = [(1-r^2) / (n-2)]^0.5 … (if you see well, it is reversed)
When you replace this standard error, as it divides the ( r - 0 ) you finally get T = r * (n-2)^0.5 / (1-r^2)^0.5 Just basic math.
So the 1st and 2nd T-tests are the same calculation method (you are standardizing the coefficient) with the form T = [ Coefficient - 0 ] / standard error
Hope this helps!
Regards

 

[tickersu]

I would do some searching to find the thread that Harrogath is referring to here. There was a little more discussion behind it (slightly). More or less, he’s summarized it, though.

 

[tickersu]

Harrogath wrote:
This formula comes from t = ( r - 0 ) / standard error. However, the standard error here does not come from a T-table, but from a standard error calculation as follow: If I’m not mistaken, standard errors never come from t-tables (they’re calculated).

 

[Harrogath]

tickersu wrote:

Harrogath wrote:
This formula comes from t = ( r - 0 ) / standard error. However, the standard error here does not come from a T-table, but from a standard error calculation as follow: If I’m not mistaken, standard errors never come from t-tables (they’re calculated).

Oops! you right, my bad. Standard errors are, indeed, calculated.