Odds ratio


In a retrospective study the subjects with positive and negative outcome are known and are subsequently grouped according to a specific characteristic. Use the Odds ratio calculator to calculate the ratio of the odds of the outcome in two groups.

Required input

  • The number of subjects in the 1st and 2nd group that have a positive or negative outcome.


The program calculates:

  • the odds ratio, this is the ratio of the odds of the outcome in the two groups
  • 95% confidence interval for the odds ratio
  • z-statistic and associated P-value

If P is less than 0.05 it can be concluded that the odds ratio is significantly different from 1 and that there is an increased relative risk in one group compared to the other.

Computational notes

The odds ratio (OR), its standard error and 95% confidence interval are calculated according to Altman, 1991.

The odds ratio is given by

Odds ratio

with the standard error of the log odds ratio being

Odds ratio standard error

and 95% confidence interval

Odds ratio confidence interval

Where zeros cause problems with computation of the odds ratio or its standard error, 0.5 is added to all cells (a, b, c, d) (Pagano & Gauvreau, 2000; Deeks & Higgins, 2010).

Test of significance: the P-value is calculated according to Sheskin, 2004 (p. 542). A standard normal deviate (z-value) is calculated as ln(OR)/SE{ln(OR)}, and the P-value is the area of the normal distribution that falls outside ±z (see Values of the Normal distribution table).


  • Altman DG (1991) Practical statistics for medical research. London: Chapman and Hall.
  • Altman DG, Deeks JJ, Sackett DL. Odds ratios should be avoided when events are common [letter]. BMJ 1998;317:1318.
  • Deeks JJ, Higgins JPT (2010) Statistical algorithms in Review Manager 5. Retrieved from
  • Pagano M, Gauvreau K (2000) Principles of biostatistics. 2nd ed. Belmont, CA: Brooks/Cole.
  • Parshall MB (2013) Unpacking the 2 x 2 table. Heart & Lung 42:221-226. PubMed
  • Sheskin DJ (2004) Handbook of parametric and nonparametric statistical procedures. 3rd ed. Boca Raton: Chapman & Hall /CRC.


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