• Skip to primary navigation
  • Skip to main content
  • Skip to primary sidebar
The Analysis Factor

The Analysis Factor

Statistical Consulting, Resources, and Statistics Workshops for Researchers

  • Home
  • About
    • Our Programs
    • Our Team
    • Our Core Values
    • Our Privacy Policy
    • Employment
    • Guest Instructors
  • Membership
    • Statistically Speaking Membership Program
    • Login
  • Workshops
    • Online Workshops
    • Login
  • Consulting
    • Statistical Consulting Services
    • Login
  • Free Webinars
  • Contact
  • Login

The Difference Between Relative Risk and Odds Ratios

by Audrey Schnell 24 Comments

by Audrey Schnell

Odds Ratios and Relative Risks are often confused despite being unique concepts.  Why?

Well, both measure association between a binary outcome variable and a continuous or binary predictor variable.

And unfortunately, the names are sometimes used interchangeably.  They shouldn’t be because they’re actually interpreted differently.  So it’s important to keep them separate and to be precise in the language you use.

The basic difference is that the odds ratio is a ratio of two odds (yep, it’s that obvious) whereas the relative risk is a ratio of two probabilities.  (The relative risk is also called the risk ratio).  Let’s look at an example.

Relative Risk/Risk Ratio

Suppose you have a school that wants to test out a new tutoring program.  At the start of the school year they impose the new tutoring program (treatment) for a group of students randomly selected from those who are failing at least 1 subject at the end of the 1st quarter.  The remaining students receive the customary academic support (control group).

At the end of the school year the number of students in each group who fail any of their classes is measured. Failing a class is considered the outcome event we’re interested in measuring. From these data we can construct a table that describes the frequency of two possible outcomes for each of the two groups.

img1

The probability of an event in the Treatment group is a/(a+b)= R1 .  It’s the number of tutored students who experienced an event (failing a class) out of the total number of tutored students.  You can think of it this way, if a student is tutored, what is the probability (or risk) of failing a class?

Likewise, the probability of an event in the Control group is c/(c+d) = R2.  Again, it’s just the number of untutored students experienced an event out of the total number of untutored students.

Although each of these probabilities (i.e., risks) is itself a ratio, this isn’t the risk ratio.  The risk of failing in the tutored students needs be compared to the risk in the untutored students to measure the effect of the tutoring.

The ratio of these two probabilities R1/R2 is the relative risk or risk ratio. Pretty intuitive.

img2

If the program worked, the relative risk should be smaller than one, since the risk of failing should be smaller in the tutored group.

If the relative risk is 1, the tutoring made no difference at all.  If it’s above 1, then the tutored group actually had a higher risk of failing than the controls.

Odds Ratio

The odds ratio is the ratio of the odds of an event in the Treatment group to the odds of an event in the control group. The term ‘Odds’ is commonplace, but not always clear, and often used inappropriately.

The odds of an event is the number of events / the number of non-events.

This turns out to be equivalent to the probability of an event/the probability of a non-event.

You’ll often see odds written as P/(1-P).

So for example, in the Treatment group, the odds of an event is the number of tutored students who failed a class/the number of students in the tutored group who passed all their classes.

The numerator is the same as that of a probability, but the denominator here is different.  It’s not a measure of events out of all possible events.  It’s a ratio of events to non-events.  You can switch back and forth between probability and odds—both give you the same information, just on different scales.

If O1 is the odds of event in the Treatment group and O2 is the odds of event in the control group then the odds ratio is O1/O2.  Just like the risk ratio, it’s a way of measuring the effect of the tutoring program on the odds of an event.

img3

Compare this to RR which is the probability of an event occurring (a/a+b)/the probability of the event not occurring (c/c+d).

 


References and Further Reading:

  • Case-Control Studies: Design, Conduct, Analysis (Monographs in Epidemiology and Biostatistics) 1st Edition James J. Schlesselman
  • Foundations of Epidemiology 2nd Edition Lilienfeld and Lilienfeld.
  • Essentials of Biostatistics.  Robert C. Elston and William D. Johnson  1994
  • Why use Odds Ratios in Logistic Regression
  • Understanding Probability, Odds, and Odds Ratios in Logistic Regression

 

Understanding Probability, Odds, and Odds Ratios in Logistic Regression
Despite the way the terms are used in common English, odds and probability are not interchangeable. Join us to see how they differ, what each one means, and how to tame that tricky beast: Odds Ratios.

Tagged With: interpreting odds ratios, odds, odds ratio, relative risk, risk ratio

Related Posts

  • Logistic Regression Analysis: Understanding Odds and Probability
  • Confusing Statistical Term #8: Odds
  • How to Understand a Risk Ratio of Less than 1
  • The Difference Between Logistic and Probit Regression

Reader Interactions

Comments

  1. Hayder u. says

    March 9, 2020 at 11:17 am

    Thanks, really helpful.

    Reply
  2. Dikshant says

    October 17, 2019 at 12:55 am

    A very easy and helpful explanation indeed. What i fail to understand though is how an OR is better than the RR. If the difference between the size of Treatment and Control is significatly large would it not make the OR misleading?

    Reply
  3. ARM says

    September 19, 2019 at 8:05 am

    For cohort studies (i.e. retrospective, ambispective, prospective), I usually use RRs as long as I have a clear idea of the temporality of my X’s and Y’s. If I cannot establish which variable comes first or comes last (i.e. heart failure vs kidney failure), I usually use ORs.

    Reply
  4. Asfaw says

    July 29, 2019 at 10:42 am

    Thanks a lot explained in an easy and understandable way

    Reply
  5. Dube G. says

    March 4, 2019 at 8:09 am

    Wonderful and easy way explanation. Thank u!

    Reply
  6. Sagnolep says

    February 17, 2019 at 5:03 am

    Thanks for the explanation

    Reply
  7. Shahzaib Bangash says

    December 22, 2018 at 10:46 am

    very well <3

    Reply
  8. Eskezeia says

    December 2, 2018 at 12:01 am

    Thank you. Easy and helpful explanation

    Reply
    • Shahzaib Bangash says

      December 22, 2018 at 10:49 am

      you have mean of OR ?
      if have then email plz.

      Reply
  9. ak says

    November 17, 2018 at 10:03 am

    thanks for this lucid explanation. this query is about the last sentence. do you mean to say the RRR is probability of an event occurring (a/a+b) among treatment group/the probability of the event occurring (c/c+d) among control group?

    Reply
    • Shivanand K says

      December 3, 2019 at 8:50 am

      I am also confused. Pleae explain

      Reply
    • Yeetey says

      February 3, 2020 at 3:31 am

      You sure are perfectly right…

      RR is the probability of an event occurring in the treatment group (a/a+b)/the probability of an event occurring in the control or comparison group (c/c+d).

      Reply
  10. max says

    October 26, 2018 at 3:46 am

    its good information.. thanks

    Reply
  11. Subhash says

    August 8, 2018 at 5:31 am

    Thank you! It was very helpful in understanding RR and OR. Examples were brilliant.

    Reply
  12. CHANDRARAJU DEEPIKA says

    July 11, 2018 at 9:18 pm

    Why can’t a probability ratio used instead of odds ratio.. is there any specific advantage…

    Reply
    • Karen Grace-Martin says

      October 12, 2018 at 10:17 am

      Chandraraju,

      Some people do use the probability ratio, aka the relative risk. The disadvantage of it is the RR is not a constant effect of X. Only the odds ratio is. The probability ratio changes depending on the value of X. So if you want to know how X affects Y, odds ratios are the best summary measure.

      Reply
  13. Shamel Addas says

    April 17, 2018 at 10:15 pm

    Great explanation, Audrey. What about if you do not have a control group in your data set. In a retrospective cohort study, how could one obtain an odds ratio?

    Reply
  14. Madeleine says

    February 19, 2018 at 5:52 pm

    Waoh! So nice explanations , they are very helpful to understand the OR and RR, Thank you

    Reply
  15. KS says

    December 21, 2017 at 10:36 am

    Thanks for giving very simple explanation , quick question is there any special application of OR in practical life where RR is not suitable?

    Reply
    • Audrey says

      January 15, 2018 at 5:22 pm

      The short answer, at least in classic epidemiological research, is that OR are used for retrospective studies/Case control studies and RR is used for prospective studies. When the ‘Rare Disease’ assumption holds (meaning very low prevalence which means few existing cases), the OR and the RR are very close to each other and the OR is considered a good surrogate for the RR

      Reply
  16. Behailu says

    November 20, 2017 at 8:24 am

    Thank you. a simple explanation to differentiate RR vs OR.

    Reply
  17. Sweta says

    October 17, 2017 at 11:49 am

    Thanks! This was very helpful to distinguish RR and OR.

    Reply
  18. Rafael says

    June 14, 2017 at 10:39 pm

    Really helpful. Thank

    Reply
  19. christine says

    February 20, 2017 at 12:12 pm

    your explanation was really helpful and clear. Thank you for posting

    Reply

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Please note that, due to the large number of comments submitted, any questions on problems related to a personal study/project will not be answered. We suggest joining Statistically Speaking, where you have access to a private forum and more resources 24/7.

Primary Sidebar

Free Webinars

Effect Size Statistics on Tuesday, Feb 2nd

This Month’s Statistically Speaking Live Training

  • January Member Training: A Gentle Introduction To Random Slopes In Multilevel Models

Upcoming Workshops

  • Logistic Regression for Binary, Ordinal, and Multinomial Outcomes (May 2021)
  • Introduction to Generalized Linear Mixed Models (May 2021)

Read Our Book



Data Analysis with SPSS
(4th Edition)

by Stephen Sweet and
Karen Grace-Martin

Statistical Resources by Topic

  • Fundamental Statistics
  • Effect Size Statistics, Power, and Sample Size Calculations
  • Analysis of Variance and Covariance
  • Linear Regression
  • Complex Surveys & Sampling
  • Count Regression Models
  • Logistic Regression
  • Missing Data
  • Mixed and Multilevel Models
  • Principal Component Analysis and Factor Analysis
  • Structural Equation Modeling
  • Survival Analysis and Event History Analysis
  • Data Analysis Practice and Skills
  • R
  • SPSS
  • Stata

Copyright © 2008–2021 The Analysis Factor, LLC. All rights reserved.
877-272-8096   Contact Us

The Analysis Factor uses cookies to ensure that we give you the best experience of our website. If you continue we assume that you consent to receive cookies on all websites from The Analysis Factor.
Continue Privacy Policy
Privacy & Cookies Policy

Privacy Overview

This website uses cookies to improve your experience while you navigate through the website. Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. We also use third-party cookies that help us analyze and understand how you use this website. These cookies will be stored in your browser only with your consent. You also have the option to opt-out of these cookies. But opting out of some of these cookies may affect your browsing experience.
Necessary
Always Enabled

Necessary cookies are absolutely essential for the website to function properly. This category only includes cookies that ensures basic functionalities and security features of the website. These cookies do not store any personal information.

Non-necessary

Any cookies that may not be particularly necessary for the website to function and is used specifically to collect user personal data via analytics, ads, other embedded contents are termed as non-necessary cookies. It is mandatory to procure user consent prior to running these cookies on your website.