Relative Risks and Odds Ratios

Relative Risks and Odds Ratios

Relative risks and odds ratios are both used to measure the association between a continuous binary predictor variable and a binary outcome variable. Despite being unique in their way, they are often confused. Additionally, the terms are sometimes used interchangeably. This should not be the case because the two concepts are actually interpreted differently. The basic difference is that the odds ratio is a ratio of two odds. On the other hand, relative risk is a ratio of probabilities.

Relative risk can also be called the risk ratio. Let us use an example to explain this better:

Suppose you are the principal of a school that wants to test a new tutoring program. You decide to impose the new program (treatment) at the beginning of the school year to a group of students randomly selected from those failing at least one subject at the end of the semester. The other students receive the customary academic support (the control group). You measure the number of students in each group who have failed their classes at the end of the academic year.

  No event

(No student failed)


(There is a fail)



 j k

(No tutoring)

l m

Remember that failing a class is the outcome event we are interested in measuring. So we can construct a table using this data to describe the frequency of two possible outcomes for each of the two groups:

In the treatment group, the probability is j/(j+k) =R1. It refers to the number of tutored students who failed in class (event) out of the total number of tutored students. We can see it as the probability or risk of a student failing a class.Likewise, the control group event probability is l/ (l+m) = R2. It is the number of untutored students who failed a class out of the total number of untutored students.

To measure the effectiveness of the tutoring, we need to compare the risk of failure by the tutored students with the risk of failure by the untutored students. From this example, relative risk or risk ratio can be calculated using these two probabilities:

Relative Ratio = Risk of failing a class in the treatment group/ Risk of failing a class in the control group

The relative ratio should be less than one if the program is successful. If the ratio is one then it means the new tutoring program did not have any effect at all.  Any ratio above one means the program was a failure and the tutored group had a higher chance of failing than the controls.

Avail of our odds relative risk and odds ratio assignment help if you need assistance with assignments on these two concepts.

Odds Ratio

This is the ratio of the odds of an event in a treatment group to the odds of an event in a control group. The confusing term here is odds which is often used inappropriately. We can define the odds of an event as the number of events or non-events. This definition is equivalent to the probability of an event or non-events.

From our example above:

  • The odds of an event or non-event in the treatment group is the number of students who signed up for the program but still failed their classes, or the number of students who were tutored and passed all their classes.

The numerator is similar to what we used in RR. However, the denominator is different. It should not be the measure of events out of all possible events, but the ratio of events to non-events. Even if you switch back and forth between odds and probability, you will still get the same information but on different scales.

For example, if the odds of an event in the treatment group isAand the odds of events in the control group is B, then the odds ratio will be A/B. The odds ratio is just like the risk ratio. We can use it to measure the effect of the tutoring program on the odds of an event.

Odds Ratio = the odds of events in the treatment group/ odds of events in the control group = jm/kl

You can see that it is not the same as the Relative Risk which is the probability of the event occurring/ the probability of the event not occurring. Do you still need help with your odds ratio and relative risk assignment? Hire our top-rated online experts now.