# Odd ratio interpretation- reference category

#### Marvin85

##### Member
Hello guys,

I am running an logistic regression. My DV is = do you have health insurance (yes/no). My main IV is ACA=Affortable Care Act. 1=live in state that are expanding ACA, 2= live in states that are NOT expanding ACA, and 3= live in states debating.

When my reference variable is ACA1 (live in states that are expaning) my results looks like this (controlling for some variables):

Insured Odd ratio
ACA2 .777 or -22.3%
ACA3 .138 or -86.2%

%

but when I used my ACA3 as the reference category

Insured Odd ratio
ACA1 7.23 or 623%
ACA2 5.61 or 461%

In the first regression ACA3 is 86% less likely to be insured than ACA1. but in my second regression ACA1 623% more likely to be insured. Shouldn't be the same in the second regression just the sign change (-)?

Marvin

#### Mean Joe

##### TS Contributor
Nope. Odds ratio (OR) is a ratio. So when you switch the reference category, your result gets inverted. eg 1 / 0.138 = 7.23

#### Marvin85

##### Member
Thank you Mean Joe. But can you explain the percentages? clients at ACA3 states are 83% less likely to be insured than ACA1 ones. But ACA1 are 623% more likely than ACA3 to be insured. ??

thank you,
Marvin

#### Mean Joe

##### TS Contributor
Alright. Let's just pretend the insured rate of ACA1 (adjusting for everything you did) is 10%.

Insured Odd ratio
ACA2 .777 or -22.3%
ACA3 .138 or -86.2%
The result is saying the insured rate of ACA3 (adjusting for everything you did) is 1.38%. As you say, this rate is -86.2% relative to ACA1, going from 10% to 1.38%.

but when I used my ACA3 as the reference category

Insured Odd ratio
ACA1 7.23 or 623%
ACA2 5.61 or 461%
Now we're going the other way, from 1.38% to 10%. This is an increase of +8.62% on a base of 1.38%. We calculate +8.62/1.38 = +623%.

That's why the odds ratio is 7.23 (because 10/1.38 = 7.23).

#### Marvin85

##### Member
Thank you for taking the time to explain this to me. It is a little bit more clear but I still need to do me studying in this.