# F-test equality coefficients same model

#### damirv

##### New Member
Hi,

I have binary logistic model with only binary independent variables (which were originally 3 multi-valued nominal variables).

For example, 4 of the binary independent variables are price_1000, price_2000, price_4000, and price_5000 (price_3000 being the base).. How do I test whether the effect of price_1000 and price_2000 are significantly different from each other? I have found this but there it is assumed that all other variables are zero. Any ideas?

#### noetsi

##### No cake for spunky
When you have more than two iv variables in your model you can not directly compare a dummy variable value to the reference level, because the reference level will reflect the value when all the dummy variables are zero not the impact of one. You can make the reference level price 1000 but you are still left with this problem

#### Dason

I think they're only have one "IV" but it has 5 different levels. They're interested in comparing between two levels where one of them isn't the reference group. Is this correct damirv?

#### noetsi

##### No cake for spunky
I thought they had four dummy variables representing a 5 level categorical variable. But in general can't you just recode the data to make the variable you want to compare the reference level?

In ANOVA I would think you could do a posthoc test like Tukey's HSD to compare these levels (or perhaps a planned contrast).

#### Dason

I thought they had four dummy variables representing a 5 level categorical variable. But in general can't you just recode the data to make the variable you want to compare the reference level?
That was my understanding as well. But I guess I don't quite understand what you were saying then.

But you can definitely compare to levels by coding up the appropriate contrast.

#### noetsi

##### No cake for spunky
I was not clear. I meant, assuming you had four dummy variables for a five level category variable, if you wanted to directly compare two of the levels you would recode the data to make one of the levels you wanted to compare the reference level and be sure the other level you wanted to compare it to be one of the dummies.

My memory is bad here, but I also think the Tukey HSD test will compare the means on the DV of all levels of an IV (I dont think the test requires dummy variables be created - it works directly from the categorical variable).

The fact that ANOVA does not use dummies for categorical variables unlike regression has always fasinated me. Since it is a different form of regression.

#### Dason

The fact that ANOVA does not use dummies for categorical variables unlike regression has always fasinated me. Since it is a different form of regression.
It can. That's how SAS and R do ANOVA if I recall correctly...

(note that I use proc glm or proc mixed for anova purposes in SAS)

#### damirv

##### New Member
Hi,

Thank you all for your comments and suggestions, I really appreciate it.

To clarify a few things:

I have 3 categorical variables in the model (price, nr of participants, and price distribution type). Each of them is coded in binary variables. Now here's the problem I have:

For nr of participants, I can't just re-code the model. It's fairly complicated but let me explain. Between the variable "nr of participants" and "price distribution type" there exists a restriction. When "nr of participants"=1, the price distribution type can only be "Constant_for_top_1", i.e., there is only 1 value from "price distribution type" that occurs with "nr of participants"=1. So in order to avoid perfect correlation in my iv variables, i took "nr of participants"=1 as base, and left out the "price distribution type" value "Constant_for_top_1" out.

Anyway's, what it boils down to is that I cannot change the base of the "price distribution type" because I introduce perfect correlation amongst my iv variables. So I was wondering is there some adapted t-test or something where I could plugin the standard deviation and coefficient values and compute if they're statistically different from each other.