I am following the methods described in:

Clogg, C. C., Petkova, E., & Haritou, A. (1995). Statistical methods for comparing regression coefficients between models. American Journal of Sociology, 100(5), 1261-1293. and Paternoster, R., Brame, R., Mazerolle, P., & Piquero, A. (1998). Using the correct statistical test for equality of regression coefficients. Criminology, 36(4), 859-866.

which uses the following approach for a Z test:

$$Z = \frac{\beta_1-\beta_2}{\sqrt{(SE\beta_1)^2+(SE\beta_2)^2}}$$

I found two discussions here (1, 2), but I am still not drawing the connection of what is deemed significant from the Z-value.

This might be a stupid question (Im sorry), but can anyone explain or provide the reference to how to interpret the Z value?



1 Answer 1


If your null hypothesis is that the two slopes are equal, then you expect z to be zero on average, with random sampling giving it a value away from zero. If the null is false, you expect z to be far from zero. So you need to compute the appropriate p-value from the z ratio. That can be done with lots of programs.

Here is one: https://www.graphpad.com/quickcalcs/statratio1/

And here is the Excel formula for a two-sided p-value:


The p-value answers the question: If the null hypothesis were true (and all other assumptions of the analysis are true), what is the chance of getting a z ratio as far from zero (or further) than observed?


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