Return to Answer

Although this isn't a common analysis, it really is one of interest. I'm going to provide a reasonably well accepted technique that may or may not be equivalent (I'll leave it to better minds to comment on that).

This approach is to use the following Z test:

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

Where $SE\beta$ is the standard error of $\beta$.

This equation is provided by 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 is cited by Paternoster, R., Brame, R., Mazerolle, P., & Piquero, A. (1998). Using the correct statistical test for equality of regression coefficients. Criminology, 36(4), 859-866. equation 4, which is available free of a paywall. I've adapted Peternoster's formula to use $\beta$ rather than $b$ because it is possible that you might be interested in different DVs for some awful reason and my memory of Clogg et al. was that their formula used $\beta$. I also remember cross checking this formula against Cohen, Cohen, West, and Aiken, and the root of the same thinking can be found there in the confidence interval of differences between coefficients, equation 2.8.6, pg 46-47.

Although this isn't a common analysis, it really is one of interest. I'm going to provide a reasonably well accepted technique that may or may not be equivalent (I'll leave it to better minds to comment on that).

This approach is to use the following Z test:

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

Where $SE\beta$ is the standard error of $\beta$.

This equation is provided by 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 is cited by Paternoster, R., Brame, R., Mazerolle, P., & Piquero, A. (1998). Using the correct statistical test for equality of regression coefficients. Criminology, 36(4), 859-866. equation 4, which is available free of a paywall. I've adapted Peternoster's formula to use $\beta$ rather than $b$ because it is possible that you might be interested in different DVs for some awful reason and my memory of Clogg et al. was that their formula used $\beta$. I also remember cross checking this formula against Cohen, Cohen, West, and Aiken, and the root of the same thinking can be found there in the confidence interval of differences between coefficients, equation 2.8.6, pg 46-47.

Although this isn't a common analysis, it really is one of interest. The accepted answer fits the way you asked your question, but I'm going to provide another reasonably well accepted technique that may or may not be equivalent (I'll leave it to better minds to comment on that).

This approach is to use the following Z test:

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

Where $SE\beta$ is the standard error of $\beta$.

This equation is provided by 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 is cited by Paternoster, R., Brame, R., Mazerolle, P., & Piquero, A. (1998). Using the correct statistical test for equality of regression coefficients. Criminology, 36(4), 859-866. equation 4, which is available free of a paywall. I've adapted Peternoster's formula to use $\beta$ rather than $b$ because it is possible that you might be interested in different DVs for some awful reason and my memory of Clogg et al. was that their formula used $\beta$. I also remember cross checking this formula against Cohen, Cohen, West, and Aiken, and the root of the same thinking can be found there in the confidence interval of differences between coefficients, equation 2.8.6, pg 46-47.

Although this isn't a common analysis, it really is one of interest. I'm going to provide a reasonably well accepted technique that may or may not be equivalent (I'll leave it to better minds to comment on that).

This approach is to use the following Z test:

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

Where $SE\beta$ is the standard error of $\beta$.

This equation is provided by 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 is cited by Paternoster, R., Brame, R., Mazerolle, P., & Piquero, A. (1998). Using the correct statistical test for equality of regression coefficients. Criminology, 36(4), 859-866. equation 4, which is available free of a paywall. I've adapted Peternoster's formula to use $\beta$ rather than $b$ because it is possible that you might be interested in different DVs for some awful reason and my memory of Clogg et al. was that their formula used $\beta$. I also remember cross checking this formula against Cohen, Cohen, West, and Aiken, and the root of the same thinking can be found there in the confidence interval of differences between coefficients, equation 2.8.6, pg 46-47.

Although this isn't a common analysis, it really is one of interest. The accepted answer fits the way you asked your question, but I'm going to provide another reasonably well accepted technique that may or may not be equivalent (I'll leave it to better minds to comment on that).

This approach is to use the following Z test:

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

Where $SE\beta$ is the standard error of $\beta$.

This equation is provided by 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 is cited by Paternoster, R., Brame, R., Mazerolle, P., & Piquero, A. (1998). Using the correct statistical test for equality of regression coefficients. Criminology, 36(4), 859-866. equation 4, which is available free of a paywall. I've adapted Peternoster's formula to use $\beta$ rather than $b$ because it is possible that you might be interested in different DVs for some awful reason and my memory of Clogg et al. was that their formula used $\beta$. I also remember cross checking this formula against Cohen, Cohen, West, and Aiken, and the root of the same thinking can be found there in the confidence interval of differences between coefficients, equation 2.8.6, pg 46-47.

Although this isn't a common analysis, it really is one of interest. The accepted answer fits the way you asked your question, but I'm going to provide another reasonably well accepted technique that may or may not be equivalent (I'll leave it to better minds to comment on that).

This approach is to use the following Z test:

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

Where $SE\beta$ is the standard error of $\beta$.

This equation is provided by 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 is cited by Paternoster, R., Brame, R., Mazerolle, P., & Piquero, A. (1998). Using the correct statistical test for equality of regression coefficients. Criminology, 36(4), 859-866. equation 4, which is available free of a paywall. I've adapted Peternoster's formula to use $\beta$ rather than $b$ because it is possible that you might be interested in different DVs for some awful reason and my memory of Clogg et al. was that their formula used $\beta$. I also remember cross checking this formula against Cohen, Cohen, West, and Aiken, and the root of the same thinking can be found there in the confidence interval of differences between coefficients, equation 2.8.6, pg 46-47.