Reporting results when using dummy variables The model I am working on includes a control variable with 6 categories. These categories have been added to the structural equation model (SEM) as dummy variables.
I understand how to interpret the output, but I am unsure as to how to report the results.
The dummys each have an estimate and p value, should I report each of these in the results section? Or is there a way to calculate an estimate and p value for the variable as a whole?
 A: Old question but I feel the answers are missing an important concept which is ANOVA (Analysis of variance).
When we fit a model with categorical variables, logistic or linear regression we will get coefficients for each of the dummy variables, and we get a p_value for each of these variables. It is straightforward to interpret the coefficients but the p_values don't say much. In such a situation I resolve to hypothesis testing. This is straight forward if you are working with R, you can call the Anova function from package 'car'. In Python, this is a type 2 test if you are working with the stats models package. 
This groups all your dummy variables under one name and gives the significance of that category as a whole. If you manually want to perform this test, let's assume we are performing a logistic regression. We fit one model (say fit1) with the categorical feature. The second model (fit2) without the categorical variable (we omit the dummy variables). We now want to test the significance of that categorical feature.
To do this we need to calculate the deviance
$$\text{Deviance}=\text{Diviance}_\text{fit1}-\text{Deviance}_\text{fit2}$$
Finally the significance of the catagorical feature as a whole is calculated using the Chi-sq test,
$$\text{p_value} = 1-\text{sci.chi2.cdf(deviance,df)}$$
(In python and using scipy)
Where df = # Dummy variables for that feature. This procedure also works with continuous features with df=1.
A: Generally, if the dummy variables themselves are not of interest, but are just needed as controls to better estimate other coefficients, then you can simply make note of the fact that they where included in the model(s) and do not need to report their estimates and standard errors.  However, if you are trying to publish, the guidelines for reporting results may vary between journals and organizations, so perhaps it would best to check with them.
A: This is how I report output of dummy variables. 
Say you have following estimate and p value for a particular dummy variable. (location = California)


*

*Estimate = -0.643

*p value = 8.9E-09

*odds ratio = 0.53

*Comment - if the record/observation has location as California, then odds of "whatever you have modeled" decrease to 0.53%. 


When I have to report output of more than one dummy variables,  I create a table where first column is the "sensible" name of dummy variable (like location_California for this example), 2nd column is the estimate, 3rd column is the std. error, 4th column is the p value and 5th column is the comment. Hope this helps.
Explanation for comment - So if you are modelling attrition, and average odds of attrition are 0.8, then if location is California for a particular record, then for that particular record, odds of attrition will become 0.8 * 0.53 = 0.424. (I do not write the "explanation part" while reporting.)
