odds ratios pop up all the time in research papers particularly in medical and health research but to be honest they can be a bit odd so here's a quick guide to what they mean and how to communicate them effectively here's a common or garden ordinary die or dice okay what if i throw this what are the odds it's going to come up six now unless you're a gambler you might think that's a sixth but you'd be wrong and i'm going to show you why okay so here are the six different ways in which that dice could come up and the only one i'm interested in is this six and that's what came up what's the probability of this happening it's the number of ways in which a six can come up which is one divided by the total number of equally likely possible outcomes which is six so that's the sixth or around 17 percent the odds are different it's the number of ways in which a six can come up which is one divided by the number of ways in which a six might not come up the things we're not interested in the five other outcomes so there's five one over five or point two or twenty percent now if you're a gambler you might say that means the odds were one to five on or five to one against a six coming up now an odds ratio is just one odds divided by another odds but that's actually rather tricky and so i think we need to look at an example this study was published in 2020 and looked at the link between depression and cannabis use it's based on a reputable us survey and one of their findings was the odds ratio for depression and daily or near daily past month cannabis use in 2015 to 2016 was 3.16 right what on earth does that mean let's look at the data now the paper doesn't actually give the raw data but we've done our best to approximate the numbers and from our working out we think that there were 34 people who were depressed and were regular users of cannabis and 187 people who were depressed and weren't using cannabis regularly of the ones who were not depressed there were 132 who were regular cannabis users and 2 2366 who are not regular cannabis users now this enables us to calculate the odds of being a cannabis user within each group so to calculate the odds of among people who are depressed we just have to divide 34 by 187 and we get 0.182 to get the odds of being a regular cannabis user among those being non-depressed it's 132 divided by the people who are not regular cannabis users two three six six and when we make that division we get 0.056 so those are the odds in the two groups when we divide those we get the odds ratio which is about 3.3 okay a couple of points first of all that isn't the exact number in the abstract of the paper which is if you remember was 3.16 and this is because the 3.16 is a number an odds ratio that's been adjusted for some other factors the fact that the odds ratio is greater than one means that there's a positive association between depression and regular cannabis use however we can't conclude that that's a causal link that the depression is causing the cannabis use the authors of the paper are very careful to emphasize that this is an association a link and the actual mechanism that links these two is extremely complex so odds ratios are rather complicated so why do researchers use them as a way to compare two groups rather than simpler measures like relative risks or the differences in absolute risks well first of all they can be estimated from a range of different study designs whether these are randomized experiments or case control studies that look at what happened in the past but primarily they've got very good mathematical properties there's a technique called logistic regression which allows us to estimate odds ratios while adjusting for other factors that might influence the association that we're interested in so i'm afraid we're stuck with them okay so how do we communicate odds ratios the answer is simple we don't we turn them into something that people at least have some chance of understanding and for that we start with basic percentages so we look at all the depressed group 34 plus 187 and of those the percentage that were daily regular cannabis users is 15 if we look at the non-depressed group all of these the percentage that were daily or regular cannabis users was five percent we noticed 15 is three times five there are three times as many uh cannabis users within the um depressed group as non-depressed group and that's a relative risk and that in this case is rather similar to this odds ratio but that won't always be the case it only holds when we're talking about fairly rare events say that happen less than 20 of the time like people being daily cannabis users and so it can be very misleading to interpret an odds ratio as a relative risk if it's for more common events okay we've got percentages here which clarifies things a lot but we can go even further by turning them into what we call expected frequencies and that's what i'm going to show you now okay here are some sentences that show what we mean by expected frequencies assuming the results of this study are correct out of 100 u.s adults who are not depressed we would expect around five to use cannabis daily out of 100 u.s adults who are depressed we would expect around 15 to use cannabis daily now we've got a tool real risk that will take the odds ratio and turn it into phrases such as this and also provide suitable graphics to communicate the results even more clearly okay what we've done in this video is to go from a rather tricky odds ratio in the abstract of an academic paper and turn it into phrases that we think people will understand and if you want more help with this go to the link to real risk in the description of this video