I have a dataset that I analyzed using the ANOVA; is it possible to analyze the same dataset using dummy regression and what is a good justification for that?
Thanks in advance,
Hello Mohammad,
ANOVA is a special case of the general linear model (multiple linear regression) in which the independent variables (factors) are categorical rather than continuous. So, yes, you may certainly use OLS (ordinary least squares) regression as the analytic framework for an "ANOVA problem."
Note that different coding schemes for the factors exist, and each has implications for how you would interpret the resultant values of the unstandardized regression coefficients. Otherwise, the comparable significance tests (e.g., does this factor or this interaction help account for differences in the dependent variable scores?) can be obtained.
About the only common instance in which the two methods can yield different results is for multi-factor designs in which cell sizes are unequal ("unabalanced design"). A regression solution may or may not match the ANOVA solution, depending on the method used to compute sums of squares (SS) for the effects in the model. In SPSS, the default method is Type III ("simultaneous" or regression-type estimate), though other methods are available by choice for ANOVA type models. I believe that the base statistics package in R for ANOVA uses a Type I SS estimation.
Good luck with your work.
Hello Mohammad,
ANOVA is a special case of the general linear model (multiple linear regression) in which the independent variables (factors) are categorical rather than continuous. So, yes, you may certainly use OLS (ordinary least squares) regression as the analytic framework for an "ANOVA problem."
Note that different coding schemes for the factors exist, and each has implications for how you would interpret the resultant values of the unstandardized regression coefficients. Otherwise, the comparable significance tests (e.g., does this factor or this interaction help account for differences in the dependent variable scores?) can be obtained.
About the only common instance in which the two methods can yield different results is for multi-factor designs in which cell sizes are unequal ("unabalanced design"). A regression solution may or may not match the ANOVA solution, depending on the method used to compute sums of squares (SS) for the effects in the model. In SPSS, the default method is Type III ("simultaneous" or regression-type estimate), though other methods are available by choice for ANOVA type models. I believe that the base statistics package in R for ANOVA uses a Type I SS estimation.
Good luck with your work.
There are no differences, if both have been applied correctly. The results are the same. For sure, regression is always correct. in case a programmer has used a special case formula for ANOVA, an error can occur as Prof. Morse indicates. You should always be able to trust regression, we hope.
Best, David Booth
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