Often in literature summary statistics are used to support the author’s claims, with numbers to quantify the arguments made, the reader feels more confident in accepting the conclusion the author is attempting to draw. However, due to the author’s misinterpretation of statistical data the reader can be lead into believing facts that are grossly incorrect.
Here is an example: In a research study performed, it estimated the probability a subject would be referred for cardiac catheterization was 0.906 for whites and 0.847 for blacks. An Associated Press story describing the study stated, “Doctors were only 60% as likely to order cardiac catheterization for blacks as for whites.”
At first glance the reader might seem to believe that this procedure was overwhelming recommended for White patients. Applying some statistical interpretation to this it is apparent the paper has described the odds ratio rather than the relative risk.The odds ratio is the ratio of the odds of an event occurring in one group to the odds of it occurring in another group. The relative risk (RR) is defined as the ratio of the probability of the event occurring in the exposed group versus a non-exposed group.
Calculating the Odds Ratio
odds1 = π2/(1-π2) = 5.53
odds2 = π1/(1-π1) = 9.63
θ = odds1/odds2 = 0.5742, which was rounded up and multiplied by 100 to get to 60% incorrectly. This should be interpreted as the odds of success in row 1 are 0.5742 times the odds of success in row2, or equivalently 1/0.5742 = 1.74 times as high in row 2 as row 1.
Lets calculate the relative risk instead:
Let p1=π1=0.906, and p1=π2=0.847
RR = p1/p2 = 0.906/0.847, leading us to the conclusion that Doctors are 6.9% more likely to order cardiac catheterization for White patients than Black patients, this is substantially
smaller than the 60% previously stated. In general when stating results to the general public it is better to use the relatively risk than the odds ratio.
Ref: An Introduction to Categorical Data Analysis, Second Edition, Alan Agresti