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Formulas: Significance of the Difference between Two Slopes

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 for the difference between two slopes.

Beta function:
Beta function formula
Lower incomplete beta function:
Lower incomplete beta function formula
Regularized lower incomplete beta function:
Regularized lower incomplete beta function formula
where the numerator is the lower incomplete beta function, and the denominator is the beta function.
t-distribution cumulative distribution function (CDF):
t-distribution cumulative distribution function (CDF) formula
where v is the degrees of freedom, t is the upper limit of integration, and I is the regularized lower incomplete beta function.
t-value for the difference between two slopes:
t-value for the difference between two slopes formula
where b1 and b2 are the slopes of lines 1 and 2, sb1 and sb1 and sb2 are the standard errors for lines 1 and 2, and n1 and n2 are the sample sizes for lines 1 and 2.
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