Research that seeks to prove a causal relationship between one thing and another often expresses the results as "Relative Risk." Relative Risk is a ratio of the probability of the event in the exposed group versus a non-exposed group.
If, for example, you wanted to determine whether smoking causes a particular type of cancer, you would look at the cancer rates for non-smokers and compare that to the rate for smokers. The Relative Risk for the non-smokers = 1.0. If the RR for smokers were 1.5, this indicates that smoking increases the risk by 50%. If the RR were 2.0, then smoking would double the risk. If the RR for smokers were 0.8, this would indicate that smoking reduced the risk by 20%. Following?
A lot more goes into determining whether the results are statistically significant. How many cases are being considered? In general, the larger the sample size, the more accurate the measurement. Were other possible causal factors (e.g., exposure to asbestos) considered? Do the results differ by age or gender?
All that being said, in looking for evidence of the relationship between second-hand smoke and cancer, I came across this rather long document. http://cancercontrol.cancer.gov/tcrb/monographs/10/m10_7.pdf
When I found this table, I was very surprised at how small the Relative Risk numbers were. In some cases, there was even a negative effect (exposer to SHS appeared to be slightly protective against cancer.) In the one case where a large effect was seen (RR 7.01) there were only 4 cases.

If, for example, you wanted to determine whether smoking causes a particular type of cancer, you would look at the cancer rates for non-smokers and compare that to the rate for smokers. The Relative Risk for the non-smokers = 1.0. If the RR for smokers were 1.5, this indicates that smoking increases the risk by 50%. If the RR were 2.0, then smoking would double the risk. If the RR for smokers were 0.8, this would indicate that smoking reduced the risk by 20%. Following?
A lot more goes into determining whether the results are statistically significant. How many cases are being considered? In general, the larger the sample size, the more accurate the measurement. Were other possible causal factors (e.g., exposure to asbestos) considered? Do the results differ by age or gender?
RRThere are a number of problems in a simplistic application of RR...For these reasons most scientists (which includes scientifically inclined epidemiologists) take a fairly rigorous view of RR values. In observational studies, they will not normally accept an RR of less than 3 as significant and never an RR of less than 2. Likewise, for a putative beneficial effect, they never accept an RR of greater than 0.5. Sometimes epidemiologists choose to dismiss such caution as an invention of destructive sceptics, but this is not the case.
All that being said, in looking for evidence of the relationship between second-hand smoke and cancer, I came across this rather long document. http://cancercontrol.cancer.gov/tcrb/monographs/10/m10_7.pdf
When I found this table, I was very surprised at how small the Relative Risk numbers were. In some cases, there was even a negative effect (exposer to SHS appeared to be slightly protective against cancer.) In the one case where a large effect was seen (RR 7.01) there were only 4 cases.
