Re: comparing 2 slopes
Ellen Hertz wrote: Mike, Yes, you are correct. A purist might say that you didn't actually prove that the slopes are the same, only that you failed to demonstrate a significant difference between them (because non-significant parameters can become significant with more data). However, your interpretation is correct and, also, including an interaction term to examine its statistical significance is the best approach. Careful! I think you have to take the purist's view - with most data sets I could get a non-significant interaction even if the slopes are different, just by removing some of the data. If the data it plentiful, then the interpretation may be reasonable (even if still not strivtly correct). The interpretation you're advocating is logically dodgy - your conclusion could depend as much on the number of data points you have as on the difference between the slopes. If you want to argue that two slopes are the same, then it's better to look at the confidence limits, and see if they only cover a range that is practically insignificant, then you can say that any difference is too small to worry about. Bob -- Bob O'Hara Metapopulation Research Group Division of Population Biology Department of Ecology and Systematics PO Box 17 (Arkadiankatu 7) FIN-00014 University of Helsinki Finland tel: +358 9 191 28782 fax: +358 9 191 28701 email: [EMAIL PROTECTED] To induce catatonia, visit: http://www.helsinki.fi/science/metapop/ It is being said of a certain poet, that though he tortures the English language, he has still never yet succeeded in forcing it to reveal his meaning - Beachcomber = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: comparing 2 slopes
Mike, Yes, you are correct. A purist might say that you didn't actually prove that the slopes are the same, only that you failed to demonstrate a significant difference between them (because non-significant parameters can become significant with more data). However, your interpretation is correct and, also, including an interaction term to examine its statistical significance is the best approach. Ellen Hertz Mike Tonkovich [EMAIL PROTECTED] wrote in message news:3b20f210_1@newsfeeds... Was hoping someone might be able to confirm that my approach for comparing 2 slopes was correct. I ran an analysis of covariance using PROC GLM (in SAS) with an interaction statement. My understanding was that a nonsignificant interaction term meant that the slopes were the same, and vice versa for a significant interaction term. Is this correct and is this the best way to approach this problem with SAS? Any help would certainly be apprectiated. Mike Tonkovich -- Michael J. Tonkovich, Ph.D. Wildlife Research Biologist ODNR, Division of Wildlife [EMAIL PROTECTED] -= Posted via Newsfeeds.Com, Uncensored Usenet News =- http://www.newsfeeds.com - The #1 Newsgroup Service in the World! -== Over 80,000 Newsgroups - 16 Different Servers! =- = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: comparing 2 slopes
mccovey@psych [EMAIL PROTECTED] wrote in message news:[EMAIL PROTECTED]... in article [EMAIL PROTECTED], Tracey Continelli at [EMAIL PROTECTED] wrote on 6/13/01 4:14 PM: Mike Tonkovich [EMAIL PROTECTED] wrote in message news:3b20f210_1@newsfeeds... Was hoping someone might be able to confirm that my approach for comparing 2 slopes was correct. I ran an analysis of covariance using PROC GLM (in SAS) with an interaction statement. My understanding was that a nonsignificant interaction term meant that the slopes were the same, and vice versa for a significant interaction term. Is this correct and is this the best way to approach this problem with SAS? Any help would certainly be apprectiated. Mike Tonkovich -- Michael J. Tonkovich, Ph.D. Wildlife Research Biologist ODNR, Division of Wildlife [EMAIL PROTECTED] The slopes need not be the same if the interaction term is non-significant, BUT, the difference between them will not be statistically significant. If the differences between the slops *are* statistically significant, this will be reflected in a statistically significant product term. I have preferred using regression analyses with interaction terms, which can be easily incorporated by simply multiplying the variables together and then running the regression equation with each independent variable plus the product term [which is simply another name for the interaction term]. The results are much more straightforward in my mind. Tracey Continelli SUNY at Albany I agree completely but there can be problems interpreting the regression Output (e.g., mistakes like talking about main effects). For advice on avoiding the common interpretation pitfalls, see Aiken West (1991). Multiple regression: Testing and interpreting interactions. Sage. Irwin McClelland (2001). In Journal of Marketing Research. Gary McClelland Univ of Colorado Quite so. Once you add the product term, the interpretation changes, and the parameter estimates are now known as simple main effects. The interpretation is pretty straightforward however. The parameter estimate, or slope, for your focal independent variable in the interaction model simply represents the effect of your independent variable upon your dependent variable when your moderator variable is equal to zero, holding constant all other independent variables in your model. The same may be said for the slope of your moderator variable - it represents the effect of that variable upon your dependent variable when your focal independent variable is equal to zero. Because in my research [the social science variety] that information isn't terribly useful [because most of the time you won't realistically see the moderator variable at zero, i.e., a zero crime rate or a zero poverty rate], what I will do is a mean centering trick. I'll subtract the mean from the moderator variable, rerun the equation with the new mean centered variable and product term, and NOW the parameter estimates of the simple main effects are meaningful for me. Now, when I look at the parameter estimates of the focal independent variable, it is telling me the effect of that independent variable upon the dependent variable when my moderator variable is at its mean. The actual product term remains identical to the original equation [of course], but now the simple main effects are realistically meaningful. I'll also apply the same technique for when the moderator variable is 2 standard deviations below the mean, 1 below the mean, all the way up to 2 standard deviations above the mean. This gives one a nice graphic sense of the way in which the slope between your focal independent variable and your dependent variable changes with successive changes in your moderator variable. Tracey Continelli Doctoral candidate SUNY at Albany = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: comparing 2 slopes
in article [EMAIL PROTECTED], Tracey Continelli at [EMAIL PROTECTED] wrote on 6/20/01 7:06 AM: mccovey@psych [EMAIL PROTECTED] wrote in message news:[EMAIL PROTECTED]... in article [EMAIL PROTECTED], Tracey Continelli at [EMAIL PROTECTED] wrote on 6/13/01 4:14 PM: Mike Tonkovich [EMAIL PROTECTED] wrote in message news:3b20f210_1@newsfeeds... Was hoping someone might be able to confirm that my approach for comparing 2 slopes was correct. I ran an analysis of covariance using PROC GLM (in SAS) with an interaction statement. My understanding was that a nonsignificant interaction term meant that the slopes were the same, and vice versa for a significant interaction term. Is this correct and is this the best way to approach this problem with SAS? Any help would certainly be apprectiated. Mike Tonkovich -- Michael J. Tonkovich, Ph.D. Wildlife Research Biologist ODNR, Division of Wildlife [EMAIL PROTECTED] The slopes need not be the same if the interaction term is non-significant, BUT, the difference between them will not be statistically significant. If the differences between the slops *are* statistically significant, this will be reflected in a statistically significant product term. I have preferred using regression analyses with interaction terms, which can be easily incorporated by simply multiplying the variables together and then running the regression equation with each independent variable plus the product term [which is simply another name for the interaction term]. The results are much more straightforward in my mind. Tracey Continelli SUNY at Albany I agree completely but there can be problems interpreting the regression Output (e.g., mistakes like talking about main effects). For advice on avoiding the common interpretation pitfalls, see Aiken West (1991). Multiple regression: Testing and interpreting interactions. Sage. Irwin McClelland (2001). In Journal of Marketing Research. Gary McClelland Univ of Colorado Quite so. Once you add the product term, the interpretation changes, and the parameter estimates are now known as simple main effects. The interpretation is pretty straightforward however. The parameter estimate, or slope, for your focal independent variable in the interaction model simply represents the effect of your independent variable upon your dependent variable when your moderator variable is equal to zero, holding constant all other independent variables in your model. The same may be said for the slope of your moderator variable - it represents the effect of that variable upon your dependent variable when your focal independent variable is equal to zero. Because in my research [the social science variety] that information isn't terribly useful [because most of the time you won't realistically see the moderator variable at zero, i.e., a zero crime rate or a zero poverty rate], what I will do is a mean centering trick. I'll subtract the mean from the moderator variable, rerun the equation with the new mean centered variable and product term, and NOW the parameter estimates of the simple main effects are meaningful for me. Now, when I look at the parameter estimates of the focal independent variable, it is telling me the effect of that independent variable upon the dependent variable when my moderator variable is at its mean. The actual product term remains identical to the original equation [of course], but now the simple main effects are realistically meaningful. I'll also apply the same technique for when the moderator variable is 2 standard deviations below the mean, 1 below the mean, all the way up to 2 standard deviations above the mean. This gives one a nice graphic sense of the way in which the slope between your focal independent variable and your dependent variable changes with successive changes in your moderator variable. Tracey Continelli Doctoral candidate SUNY at Albany I hope everyone in the social sciences using product terms or moderator regression reads Tracey's thoughtful comments above. Failing to realize the coefficient for one of the components of a product is the effect of that variable when the other variable of the product is zero is one of my candidates for most common statistical error in the social sciences. Mean centering is indeed quite useful, even if one does not have products in the model. Also note that mean centering will always reduce the correlation between the product and its components and if the component distributions are symmetric it will reduce it to zero. There always exists a change of origin for the components that will make the correlation zero; hence, the colinearity warnings when testing products are not meaningful. Gary McClelland Univ of Colorado = Instructions for joining and leaving this list and remarks about the problem
Re: comparing 2 slopes
in article [EMAIL PROTECTED], Tracey Continelli at [EMAIL PROTECTED] wrote on 6/13/01 4:14 PM: Mike Tonkovich [EMAIL PROTECTED] wrote in message news:3b20f210_1@newsfeeds... Was hoping someone might be able to confirm that my approach for comparing 2 slopes was correct. I ran an analysis of covariance using PROC GLM (in SAS) with an interaction statement. My understanding was that a nonsignificant interaction term meant that the slopes were the same, and vice versa for a significant interaction term. Is this correct and is this the best way to approach this problem with SAS? Any help would certainly be apprectiated. Mike Tonkovich -- Michael J. Tonkovich, Ph.D. Wildlife Research Biologist ODNR, Division of Wildlife [EMAIL PROTECTED] The slopes need not be the same if the interaction term is non-significant, BUT, the difference between them will not be statistically significant. If the differences between the slops *are* statistically significant, this will be reflected in a statistically significant product term. I have preferred using regression analyses with interaction terms, which can be easily incorporated by simply multiplying the variables together and then running the regression equation with each independent variable plus the product term [which is simply another name for the interaction term]. The results are much more straightforward in my mind. Tracey Continelli SUNY at Albany I agree completely but there can be problems interpreting the regression Output (e.g., mistakes like talking about main effects). For advice on avoiding the common interpretation pitfalls, see Aiken West (1991). Multiple regression: Testing and interpreting interactions. Sage. Irwin McClelland (2001). In Journal of Marketing Research. Gary McClelland Univ of Colorado = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: comparing 2 slopes
Mike Tonkovich [EMAIL PROTECTED] wrote in message news:3b20f210_1@newsfeeds... Was hoping someone might be able to confirm that my approach for comparing 2 slopes was correct. I ran an analysis of covariance using PROC GLM (in SAS) with an interaction statement. My understanding was that a nonsignificant interaction term meant that the slopes were the same, and vice versa for a significant interaction term. Is this correct and is this the best way to approach this problem with SAS? Any help would certainly be apprectiated. Mike Tonkovich -- Michael J. Tonkovich, Ph.D. Wildlife Research Biologist ODNR, Division of Wildlife [EMAIL PROTECTED] The slopes need not be the same if the interaction term is non-significant, BUT, the difference between them will not be statistically significant. If the differences between the slops *are* statistically significant, this will be reflected in a statistically significant product term. I have preferred using regression analyses with interaction terms, which can be easily incorporated by simply multiplying the variables together and then running the regression equation with each independent variable plus the product term [which is simply another name for the interaction term]. The results are much more straightforward in my mind. Tracey Continelli SUNY at Albany -= Posted via Newsfeeds.Com, Uncensored Usenet News =- http://www.newsfeeds.com - The #1 Newsgroup Service in the World! -== Over 80,000 Newsgroups - 16 Different Servers! =- = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
comparing 2 slopes
Was hoping someone might be able to confirm that my approach for comparing 2 slopes was correct. I ran an analysis of covariance using PROC GLM (in SAS) with an interaction statement. My understanding was that a nonsignificant interaction term meant that the slopes were the same, and vice versa for a significant interaction term. Is this correct and is this the best way to approach this problem with SAS? Any help would certainly be apprectiated. Mike Tonkovich -- Michael J. Tonkovich, Ph.D. Wildlife Research Biologist ODNR, Division of Wildlife [EMAIL PROTECTED] -= Posted via Newsfeeds.Com, Uncensored Usenet News =- http://www.newsfeeds.com - The #1 Newsgroup Service in the World! -== Over 80,000 Newsgroups - 16 Different Servers! =- = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: COMPARING 2 SLOPES
In sci.stat.edu Mike Tonkovich [EMAIL PROTECTED] wrote: : Was hoping someone might be able to confirm that my approach for comparing 2 : slopes was correct. : I ran an analysis of covariance using PROC GLM (in SAS) with an interaction : statement. My understanding was that a nonsignificant interaction term : meant that the slopes were the same, and vice versa for a significant : interaction term. Is this correct and is this the best way to approach this : problem with SAS? Any help would certainly be apprectiated. Like any hypothesis testing situation, a non-significant interaction term means that you failed to reject the null hypothesis, in this case, that that the slopes are parallel. It's important to understand why this isn't the same as saying the slopes are the same. You have to be very careful about how to interpret this test. Depending on a number of things, including the joint distributions of the main effects involved, the significance test for the interaction term can be associated with relatively low power. Mike Babyak = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
