If I understand it correctly, you have a continuous response variable Y and a continuous predictor X and a dichotomous variable M. You want to find out whether M affects the regression of Y on X. Is that right? If not, please ignore.

Given that this is so, you first create a binary variable I which is =0 for the one category of M and =1 for the other category of M. You then also create an interaction term IX (I times X). You then fit a (multiple) regression of Y on I, X and IX, say Y=a+bI+cX+d(IX). This means that Y=a+cX for the I=0 category and Y=(a+b)+(c+d)X for the I=1 category. If b and d are both not significant, then one model will suffice for both categories, i.e. M does not affect the relationship between X and Y; if b is significant then you have different intercepts; if d is significant then you have different slopes.

I hope this pages can be helpful.

http://www.jeremydawson.co.uk/slopes.htm

http://pages.uoregon.edu/stevensj/MRA/interaction.pdf

Good luck with your paper!

May be this article helps

Fairchild, A. J., & MacKinnon, D. P. (2009). A general model for testing mediation and moderation effects. Prevention Science, 10(2), 87-99.

If I understand it correctly, you have a continuous response variable Y and a continuous predictor X and a dichotomous variable M. You want to find out whether M affects the regression of Y on X. Is that right? If not, please ignore.

Given that this is so, you first create a binary variable I which is =0 for the one category of M and =1 for the other category of M. You then also create an interaction term IX (I times X). You then fit a (multiple) regression of Y on I, X and IX, say Y=a+bI+cX+d(IX). This means that Y=a+cX for the I=0 category and Y=(a+b)+(c+d)X for the I=1 category. If b and d are both not significant, then one model will suffice for both categories, i.e. M does not affect the relationship between X and Y; if b is significant then you have different intercepts; if d is significant then you have different slopes.

Another interesting paper: http://mlrv.ua.edu/2013/vol39_1/Robinson%20et%20al..pdf

It is easier than it first appeared. You have to run two independent regressions (one per category in the moderator) and then compute a t-test with the difference between slopes in the numerator and the pooled standard deviation from both groups in the denominator. I have learnt a very interesting point for my own research. Thanks!

Dear Javier,

Note 1

In the paper that You recommeded: equation 8 calculated pooled SE.

It seems there is something wrong with this equation...

1 pooled SE for two samples and pooled SE for two slopes from regressions are not the same things.

The slope is a result of calculation, not observation (sampling).

(approach for calculation pooled SE based on error propagation wlii be more appropriate?)

2 The equation of pooled SE for two samples usually in the nominator contains (n1-1) instead of n1, (n2-1) instead of n2.

The authors do not justify the use of equaton 8.

Note 2

To break set of data into two subset in the one research - it decreases the reliability of statistical results as a rule.

Maybe I'm missing something here, but the suggestion Francois Steffens gave you seems to me complete and absolutely correct. What the need for simple slope test when you have one categorical variable (binary, to be worst)?? The interaction term significance is the test you need (I suppose you have test the significance of the interaction term estimate). You can interpret it as a change in slope of the predictor form group 0 to 1. As simple as that.

Regards,

Marko

Yes, but do you think that it will be enough for reviewer? He may be waiting for statiatical analyses to test for different slopes

If you want to give them some formal test (F, df, eta and so on) you could perform a simple hierarchical regression (model comparison or whatever name do you want to gave it). First model, main effect model (so, y=b0 +b1*X + b2*M+error). Second model add the interaction ( y=b0 +b1*X + b2*M+b3*M*X+ error) end test for R^2 increase (performed automatically in canned software like SPSS and similar). You will have an F with 1 degree of freedom and an effect site (difference in R^2 of the two models). I think it is as good as it gets (all other analyses are completely redundant and not that precise).

Regrads,

Marko

Dear Marko,

I presented both delta R^2, that is significant, and the interaction term significance (significant), but referee explicitly requested simple slope tests, that I did not know.

I will follow the suggestion of Olga, because I think that is easier one sample - one model. I will perform this analysis and I will update you about the referee response.

Dear Antonino,

thanks. Francois said the same more clearly.

It was intresting for me too - what is "simple slope test". Usually for publication is enough to show the model with interaction.

But I found this "simple slope test".

Appoach is very "applied". For Your case:

We take three point for continuos variable ( in Your case M),

mean(M)- 1 SD

mean (M)

mean (M) +1 SD

For each point we calculate prediction value of Y (response) and its SE for binary predictor 1 and 0.

Then we perform t (z) test 3 times (is difference between 0 and 1 at each point statistically significant?).

I used information from http://pages.uoregon.edu/stevensj/MRA/interaction.pdf and

http://www.jeremydawson.co.uk/slopes.htm

========

My advise: to show model and interaction plot with (!) confidence band. May be it will be persuasively.

Antonio,

Please check DeShon & Alexander (1996). This is my guess but I believe that the reviewers asked for the simple slope tests because of the heterogeneous errors in the two groups on moderator. This is one situation where the simple slope test has more power than moderated multiple regression (MMR). But, if MMR showed a significant interaction effect, you would get the same results. Maybe you can conduct the analysis to make sure you get the same results and explain why you would get the same results anyway based on this article: With a less powerful test, you get a significant interaction effect.

Good luck!