I conducted a 2 by 2 between-subjects experiments. Using OLS regression to analyze the data, I obtain the same SEs for all coefficients when using effect coding (1, -1). When I use dummy coding, however, the SEs are different. Why is that?
Best,
Andreas
Hello Andreas,
Several differences are at work when you compare dummy (1, 0) and effects (1, -1) coding for a 2x2 design. First, I presume that you did include an interaction term for the analysis (e.g., row effect = IV1, column effect = IV2, interaction = IV3). As well, for simplicity, I assume a balanced design (each of the four cells having equal number of cases).
In dummy coding, the row and column effects will correlate with the interaction term, whereas all three terms will be uncorrelated in effects coding. So, there is some collinearity among the IVs in dummy coding, but not in effects coding. That will generally cause the interaction term to have a different standard error than the row and column effect terms in dummy coding.
The effects coded regression solution should yield exactly the same statistical test results as would a 2 x 2 anova (though perhaps as t-tests rather than F-tests; remember here, t-squared for an effect = F)
Second, remember that the interpretation of the coefficients will differ between the two coding methods. In dummy coding, the standard errors tend to be larger, since there is one numeric unit separating the two levels (0 vs. 1), whereas in effects coding, there are two numeric units separating the two levels (-1 vs. 1). Recall that the usual interpretation of a regression coefficient is that it represents the estimated difference in the dependent variable (Y) per unit change in the independent variable, holding all other IVs constant.
Good luck with your work.
Hello Andreas,
Several differences are at work when you compare dummy (1, 0) and effects (1, -1) coding for a 2x2 design. First, I presume that you did include an interaction term for the analysis (e.g., row effect = IV1, column effect = IV2, interaction = IV3). As well, for simplicity, I assume a balanced design (each of the four cells having equal number of cases).
In dummy coding, the row and column effects will correlate with the interaction term, whereas all three terms will be uncorrelated in effects coding. So, there is some collinearity among the IVs in dummy coding, but not in effects coding. That will generally cause the interaction term to have a different standard error than the row and column effect terms in dummy coding.
The effects coded regression solution should yield exactly the same statistical test results as would a 2 x 2 anova (though perhaps as t-tests rather than F-tests; remember here, t-squared for an effect = F)
Second, remember that the interpretation of the coefficients will differ between the two coding methods. In dummy coding, the standard errors tend to be larger, since there is one numeric unit separating the two levels (0 vs. 1), whereas in effects coding, there are two numeric units separating the two levels (-1 vs. 1). Recall that the usual interpretation of a regression coefficient is that it represents the estimated difference in the dependent variable (Y) per unit change in the independent variable, holding all other IVs constant.
Good luck with your work.
- Badges
- Science topic
- Similar topics
- Computer Science and Engineering
- Coding