There is also another issue: My 10 Independent variables are devided into 4 groups. I would like to know the effect of each one of the 10 variables, but I would also like to know the effect that the groups might have on my dependent variable.
What should I do?
Unless your dependent variable has an extremely non-normal distribution, your problem sounds quite amenable to multiple regression, using a distinct dummy variable (scored 1 for cases in a particular category, and 0 for cases not in that category) for each category of every nominal independent variable. (In practice, you would actually use dummy variables for only k-1 of the k categories in any given variable).
A t-test on the regression coefficient for each each dummy variable tells you whether that category differs significantly, on the DV, from the k-th category (the one for which no dummy variable is included in the regression). The magnitude of those coefficients tells you the effect size for being in that category. The choice of which category to omit from the regression is arbitrary; often, it makes sense to omit the largest category, so that all of the effects are relative to the modal category.
To determine whether each nominal variable is a significant predictor overall, across all its categories, you would enter all of the dummy variables for that nominal variable as a block, after all other variables are included in the regression, and use an F test on the change in R-square (with that block vs. without that block) to test the significance of the entire block. The magnitude of the R-square change could be taken as the overall effect size for that nominal variable, with all other variables controlled. Repeat for each of your 10 variables.
You could carry this logic one step further, and enter all of the dummy variables for a particular group of nominal variables as a block, after all other variables are included, and use the F test on the change in R-square (with that entire group vs. without that group) to test the significance of the whole group. Here again, the magnitude of the R-square change could be taken as a measure of the effect size for that group of nominal variables, with all other groups controlled. Repeat for each of your 4 groups.
If you want the effect size of a group of your nominal variables without controlling the other groups, you could use the R-square from that group of variables alone, with no other variables included in the regression. Repeat for each of your 4 groups.
Unless your dependent variable has an extremely non-normal distribution, your problem sounds quite amenable to multiple regression, using a distinct dummy variable (scored 1 for cases in a particular category, and 0 for cases not in that category) for each category of every nominal independent variable. (In practice, you would actually use dummy variables for only k-1 of the k categories in any given variable).
A t-test on the regression coefficient for each each dummy variable tells you whether that category differs significantly, on the DV, from the k-th category (the one for which no dummy variable is included in the regression). The magnitude of those coefficients tells you the effect size for being in that category. The choice of which category to omit from the regression is arbitrary; often, it makes sense to omit the largest category, so that all of the effects are relative to the modal category.
To determine whether each nominal variable is a significant predictor overall, across all its categories, you would enter all of the dummy variables for that nominal variable as a block, after all other variables are included in the regression, and use an F test on the change in R-square (with that block vs. without that block) to test the significance of the entire block. The magnitude of the R-square change could be taken as the overall effect size for that nominal variable, with all other variables controlled. Repeat for each of your 10 variables.
You could carry this logic one step further, and enter all of the dummy variables for a particular group of nominal variables as a block, after all other variables are included, and use the F test on the change in R-square (with that entire group vs. without that group) to test the significance of the whole group. Here again, the magnitude of the R-square change could be taken as a measure of the effect size for that group of nominal variables, with all other groups controlled. Repeat for each of your 4 groups.
If you want the effect size of a group of your nominal variables without controlling the other groups, you could use the R-square from that group of variables alone, with no other variables included in the regression. Repeat for each of your 4 groups.
Dear Pedro
Multiple regression analysis may solve your problem. Try it and then see the results.
https://www1.udel.edu/htr/Statistics/Notes816/class14.PDF
refer the art to get clarity on multiple regression.
In addition to a good explanation of Burke, it is sometimes interesting to include the interactions of your independent variables in the model by simply adding the products of dummies of different variables as new variables to measure the effect of interactions on the dependent variable.
I think that if you use the mean effect between each group with dependent variable,the make a vector as Xt and check the effect of Vs the dependent variable or you can use the f-test result of effect mean for each vs dependent variable.
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