Odds ratios with 95% CI 

By taking the exponential of both sides of the regression equation as given above, the equation can be 

rewritten as: 

p

=

odds

e

=

b

0

e

1

b

1

X

e

b

2

X

2

e

b

3

X

3

...

e

b

k

X

k

1  p

It is clear that when a variable X

i 

 increases by 1 unit, with all other factors remaining unchanged, then the 

b

odds will increase by a factor 

i

e

.  This factor 

b

i

e

is the odds ratio (O.R.) for the independent variable X

i 

and it gives the relative amount by which the odds of the outcome increase (O.R. greater than 1) or 

decrease (O.R. less then 1) when the value of the independent variable is increased by 1 units.  

E.g. The variable SMOKING is coded as 0 (= no smoking) and 1 (= smoking), and the odds ratio for this 

variable is 3.2.  This means that in the model the odds for a positive outcome in cases that do smoke are 

3.2 times higher than in cases that do not smoke.  

Classification table 

The classification table can be used to evaluate the predictive accuracy of the logistic regression model.  In 

this table the observed values for the dependent outcome and the predicted values (at a cut off value of 

p=0.50) are cross classified.  In our example, the model correctly predicts 70% of the cases. 

Interpretation of the fitted equation 

The logistic regression equation is: 

logit(p)  =   4.48  +  0.11 x AGE  +  1.16 x SMOKING 

So for 40 years old cases who do smoke logit(p) equals 1.08.  Logit(p) can be back transformed to p by the 

following formula: 

1

p

logit(p)

1

e

Alternatively, you can use the table on p. 175.  For logit(p)=1.08 the probability p of having a positive 

outcome equals 0.75. 

Literature 

Pampel FC (2000) Logistic regression: A primer. Sage University Papers Series on Quantitative 

Applications in the Social Sciences, 07 132. Thousand Oaks, CA: Sage. 

One sample t test 

Use the one sample t test to test whether the average of observations differs significantly from a test value.  

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