Significance of the Difference between Two Slopes Formulas

Significance of the Difference between Two Slopes Formulas

Below you will find descriptions and details for the 5 formulas that are used to compute probability values (p-values) for the difference between two slopes.

Beta function:

Cumulative distribution function (CDF) for the t-distribution:

Variable definitions:
v = degrees of freedom
t = upper limit of integration
I = regularized lower incomplete beta function

Lower incomplete beta function:

Regularized lower incomplete beta function:

Variable definitions:
the numerator = lower incomplete beta function
the denominator = beta function

t-value for the difference between two slopes:

Variable definitions:
b₁ and b₂ = the slopes of lines 1 and 2
s_b1 and s_b2 = the standard errors for lines 1 and 2
n₁ and n₂ = the sample sizes for lines 1 and 2