T-Test Statistic Equation

[oryan5000]

In the reading on Correlation and Regression, we’re presented with two different t-test statistic equations. Cn anyone explain to me why and when you use one of these versus the other?

t = (r * square root(n-2))/square root(1-r²)

and

t = (estimate b₁ - actual b₁)/ standard deviation of estimated b₁

[S2000magician]

The first is for testing whether a correlation coefficient is zero or not.

The second is for testing whether a slope coefficient is a particular value or not.

[oryan5000]

Thanks you, much appreciated as always

[tickersu]

@oryan5000

In the reading on Correlation and Regression, we’re presented with two different t-test statistic equations. Cn anyone explain to me why and when you use one of these versus the other?

t = (r * square root(n-2))/square root(1-r²)

and

t = (estimate b₁ - actual hypothesized** /theoretical** b₁)/ standard deviation of estimated b₁

Keep in mind, with a bit of algebra, the first t-statistic formula fits the classic: (estimate-hypothesized value)/ standard error.

t = (r * square root(n-2))/square root(1-r²) => (r-rho)/[(square root(1-r²))/(square root(n-2))]= (estimate-hypothesized value)/ standard error

… which fits the latter formula you gave