Oddsformat
We often use the odds ratio and relative risk when performing an analysis on a 2-by-2 table, which takes on the following format:
Fractional odds are stating the same thing, in a different format. In fractional odds, whatever the second number is, can be seen as the stake, and whatever the first number is, is what the bettor will receive back should the bet be successful. For example, if the price is 15/2, the bettor will receive 15 'stakes' for every 2 they wager. Odds conversion. By Isaiah Founder & Editor of Betshoot.com Last updated on 23 April 2020 at 22:00. There are three types of odds, decimal, fractional and the US. The Europeans are very familiar with decimal odds (i.e., @2.05), and some of us aren't familiar with fractional or US odds. At the bottom of each page, just above the page footer, you find 'View odds as:' which enables you to toggle between 'Fractional' and 'Decimal' odds. Once set, the page will remember your preference the next time you enter the site.
The odds ratio tells us the ratio of the odds of an event occurring in a treatment group to the odds of an event occurring in a control group. It is calculated as:
Odds ratio = (A*D) / (B*C)
The relative risk tells us the ratio of the probability of an event occurring in a treatment group to the probability of an event occurring in a control group. It is calculated as:
Relative risk = [A/(A+B)] / [C/(C+D)]
This tutorial explains how to calculate odds ratios and relative risk in Excel.
How to Calculate the Odds Ratio and Relative Risk
Suppose 50 basketball players use a new training program and 50 players use an old training program. At the end of the program we test each player to see if they pass a certain skills test. The following table shows the number of players who passed and failed, based on the program they used:
The odds ratio is calculated as (34*11) / (16*39) = 0.599
We would interpret this to mean that the odds that a player passes the test by using the new program are just 0.599 times the odds that a player passes the test by using the old program. In other words, the odds that a player passes the test are actually lowered by 40.1% by using the new program.
The relative risk is calculated as [34/(34+16)] / [39/(39+11)] = 0.872
We would interpret this to mean that the ratio of the probability of a player passing the test using the new program compared to the old program is 0.872. Because this value is less than 1, it indicates that the probability of passing is actually lower under the new program compared to the old program.
We could also see this by directly computing the probability that a player passes under each program:
Probability of passing under new program = 34 / 50 = 68%
Probability of passing under old program = 39 / 50 = 78%
Odds Format
How to Calculate Confidence Intervals
Once we calculate the odds ratio and relative risk, we may also be interested in computing confidence intervals for these two metrics.
Odds Format
A 95% confidence interval for the odds ratio can be calculated using the following formula:
95% C.I. for odds ratio = exp(ln(OR) – 1.96*SE(ln(OR))) to exp(ln(OR) – 1.96*SE(ln(OR)))
where SE(ln(OR)) =√1/A + 1/B + 1/C + 1/D
The 95% C.I. for the odds ratio turns out to be (.245, 1.467). The image below shows the formula we used to calculate this confidence interval:
A 95% confidence interval for the relative risk can be calculated using the following formula:
Oddsformat Sverige
95% C.I. for relative risk = exp(ln(RR) – 1.96*SE(ln(RR))) to exp(ln(RR) – 1.96*SE(ln(RR)))
where SE(ln(RR)) =√1/A + 1/C – 1/(A+B) – 1/(C+D)
The 95% C.I. for the relative risk turns out to be (.685, 1.109). The image below shows the formula we used to calculate this confidence interval: