The coefficient or the p value of the interaction term is not affected by how the moderator variable is coded. If there is a statistically significant moderation/interaction, you will detect it in either way since the interaction term would have the same significance status. The value and the interpretation of the regression coefficient for the independent variable would be different, though.

In dummy coding (using 0 and 1), the IV's coefficient should be interpreted as the conditional effects of your IV on the dependent variable for the equity norm group (assuming they are coded as 0). If you want to know the effect of the IV on DV for the favoritism group, just reverse the coding and rerun the analysis.

If you code your moderator as 1, and -1, and have a balanced design (approximately equal sample sizes for the two groups), the regression coefficient for the IV would indicate the average effect of your IV on the DV across the two groups.

Dear Dr. Dolma,

Firstly, thank you for your answer.

Yes, coefficient or p value of interaction is not affected by coding system but as you say, p value and regression coefficient for prediction is different.

Two groups are approximately same size but I can not be sure which coding system appropriate is.

According to Aiken & West (1991, p.129) "when the interactions involve a categorical variable and a continuous variable, dummy variable coding produces immediately interpretable contrast wit the comparison group, whereas simple effect coding does not. (...) When the interactions of interest involve two or more categorical variables, effect coding is preffered because it produces results that are immediately comparable with standard ANOVA procedures. For example, when there are equal ns in each cell, effect coding produces main effects and interactions that are orthogonal just as in ANOVA. However, dummy coding produces correlations between the contrast vectors for the main effects and those for the interactions. Thus, some (minor) adjustments are needed in the result of the dummy code d analyses (...).

Also, according to Kerlinger & Pedhazur (1973, p.151), "when, for example, one wishes to compare several treatment groups with a control group, dummy coding is the appropriate method. (...) Effect coding also simplifies calculations. Its main virtue, however, is that the resulting regression equation reflects the linear model.

I am interested that whether prediction of a predictor differentiate according to moderator variable which include two groups and, I want to compare these two groups in different predictor's level (high, mean, low) in terms of dependent variable (basicly Hayes' Process Macro Model 3).

I think, according to my purposes, effect coding is more appropriate but still I can not be sure.

Ref.

Aiken, L. S. & West, S. G. (1991). Multiple regression: Testing and interpretting interactions. Sage Publ.

Kerlinger, F. N. & Pedhazur, E. J. (1973). Multiple regression in behavioral research. Holt, Rinehart & Winston.

Unless you specifically want to have your results to be more compatible with those of ANOVA, I would suggest dummy coding in general, since it is simpler to interpret.

There is another issue in your case. You mention that you "want to compare these two groups in different predictor's level (high, mean, low) in terms of dependent variable". This way of expressing your research goal renders the role of the variables in your model somewhat ambiguous. That is, from this sentence, reader might also think that the group norm is not your moderator but is instead your independent variable. It is totally ok (i) if you are not sure whether you are interested in the effect of X on Y depending on M or the effect of M on Y depending on X, or (ii) if you are interested in both of these effects. But, if one of these is the case, although the statistical procedures would be the same, the effect you are testing should better be referred to as interaction effect instead of moderator effect, since which variable is the IV and which variable is the moderator is not fully distinguished in your model.

Dear Dolma,

Thank you for reply.

I read the statement again after I saw your answer and I agree with you, I will revise the sentence you mentioned.

By the way, on the contrary of it, we will use the ANOVA results with same variables to support our regression results. To examine similarity of results, we crate two groups (categorical var.) on continious indp. variable by using median. Also we noticed that effect coding in process model 3 gives more similar results (ANOVA, chi-square[1], Z-ratio[2]) than dummy coding.

Thanks again.

Ref.

Post-hoc for chi square;

1. Sharpe, D. (2015). Your chi-square test is statistically significant: Now what?. Practical Assessment, Research & Evaluation, 20(8)-1-10.

About Z-ratio test

2. Fleiss, J. L., Levin, B., & Paik, M. C. (2004). Statistical Methods for Rates and Proportions. New Jersey: John Wiley & Sons.

Sami,

I stumbled upon your post while I was searching for answers to other questions I have. You mentioned about dichotomizing a continuous variables. Are you aware of dangers with such a practice? It seems you already know the regression analysis well. I am not sure why you try a procedure seriously questionable. Please refer MacCallum et al.'s (2000) article. The bottom line is, 'Never dichotomize a continuous variable.'

Hope the article will clarify.

Dear Moon,

Firstly, I apologize for my late answer.

I have already chosen regression models as you recommend because I have read some researchers. They especially suggested that dichotomizing a continuous variable leads loss of information because of narrowing the variance in order to create new dichotom variables.

I searched MacCallum's some chapters and articles but I think I could not find exact study. Would you please share the name of article?

Rogers et al. (2012) cited to Royston, Altman & Sauerbrei's study (2006) titled Dichotomizing continuous predictors in multiple regression: A bad idea for dichotomizing a continuous variable. I think they are similar but I want to read MacCallum's article.

Thank you very much for your recommendation.