Logistic Odds Ratio

[Emily Ross]

I've read multiple things on how to interpret odds ratio. For an odds ratio of 1.55 on a dummy variable, where 1 codes for female and 1 codes for male. Is it females are 55% more likley or 1.55 times the odds likely to do the response variable (also coded as a dummy variable, 1 means they do the activity 0 means they dont).

thanks

[Marcos Almeida]

You're on the right track. Odds ratio are part and parcel of the interpration of logistic regression. I gather this is core-knowledge, I mean, it is not polemic at all, hence we're not supposed to read "multiple things" about it. You can find the interpretation in any decent book|chapter|article. Please take the time to learn thoroughly about this issue.

[Carlo Lazzaro]

Emiliy:
In addition to Marco's helpful advice, you may find the following toy example helpful:.

use http://www.stata-press.com/data/r15/lbw
logistic low  i.race
Logistic regression                             Number of obs     =        189
                                                LR chi2(2)        =       5.01
                                                Prob > chi2       =     0.0817
Log likelihood = -114.83082                     Pseudo R2         =     0.0214

------------------------------------------------------------------------------
         low | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        race |
      black  |   2.327536   1.078613     1.82   0.068     .9385072    5.772385
      other  |   1.889234   .6571342     1.83   0.067     .9554577    3.735597
             |
       _cons |   .3150685   .0753382    -4.83   0.000     .1971825     .503433
------------------------------------------------------------------------------
Note: _cons estimates baseline odds.

. bysort race: tab low

------------------------------------------------------------------------------------------------------------------------
-> race = white

birthweight |
     <2500g |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |         73       76.04       76.04
          1 |         23       23.96      100.00
------------+-----------------------------------
      Total |         96      100.00

------------------------------------------------------------------------------------------------------------------------
-> race = black

birthweight |
     <2500g |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |         15       57.69       57.69
          1 |         11       42.31      100.00
------------+-----------------------------------
      Total |         26      100.00

------------------------------------------------------------------------------------------------------------------------
-> race = other

birthweight |
     <2500g |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |         42       62.69       62.69
          1 |         25       37.31      100.00
------------+-----------------------------------
      Total |         67      100.00

*Odds white_race (_cons or baseline odds of logistic regression)*
di .2396/(1-.2396)
.31509732
*Odds black_race*
di .4231/(1-.4231)
.73340267
*Odds other_race*
di .3731/(1-.3731)
.59515074
*Odds ratio black_race vs white_race. Black_race has 2.3275433 times low-birth babies that white_race*
di .73340267/.31509732
2.3275433
*Odds ratio other_race vs white_race. Other_race has 1.8887839 times low-birth babies that white_race*
di .59515074/.31509732
1.8887839

NB: the small difference between odds ratios from -logistic- and those calculated by hand are due to rounding.