If the confidence interval for the odds ratio includes the number 1 then the calculated odds ratio would not be considered statistically significant.
This can be seen from the interpretation of the odds ratio. An odds ratio greater than 1 implies there are greater odds of the event happening in the exposed versus the non-exposed group. An odds ratio of less than 1 implies the odds of the event happening in the exposed group are less than in the non-exposed group.
An odds ratio of exactly 1 means the odds of the event happening are the exact same in the exposed versus the non-exposed group. Thus, if the confidence interval includes 1 eg, [0. The odds ratio can be confused with relative risk. As stated above, the odds ratio is a ratio of 2 odds. As odds of an event are always positive, the odds ratio is always positive and ranges from zero to very large.
The relative risk is a ratio of probabilities of the event occurring in all exposed individuals versus the event occurring in all non-exposed individuals. If the disease condition event is rare, then the odds ratio and relative risk may be comparable, but the odds ratio will overestimate the risk if the disease is more common. In such cases, the odds ratio should be avoided, and the relative risk will be a more accurate estimation of risk.
The relative risk for the above hypothetical example of smokers versus non-smokers developing lung cancer is calculated as:. Thus in our example, the odds ratio is The odds ratio is the ratio of the odds of the event happening in an exposed group versus a non-exposed group. The odds ratio is commonly used to report the strength of association between exposure and an event.
The larger the odds ratio, the more likely the event is to be found with exposure. The smaller the odds ratio is than 1, the less likely the event is to be found with exposure.
It is important to look at the confidence interval for the odds ratio, and if the odds ratio confidence interval includes 1, then the odds ratio did not reach statistical significance. This book is distributed under the terms of the Creative Commons Attribution 4. Turn recording back on.
Int J Tuberc Lung Dis ;— To calculate the risk ratio, first calculate the risk or attack rate for each group. Here are the formulas:. Thus, inmates who resided in the East wing of the dormitory were 6.
Example B: In an outbreak of varicella chickenpox in Oregon in , varicella was diagnosed in 18 of vaccinated children compared with 3 of 7 unvaccinated children. Chickenpox outbreak in a highly vaccinated school population. Pediatrics Mar; 3 Pt 1 — The risk ratio is less than 1. The risk ratio of 0.
A rate ratio compares the incidence rates, person-time rates, or mortality rates of two groups. As with the risk ratio, the two groups are typically differentiated by demographic factors or by exposure to a suspected causative agent. The rate for the group of primary interest is divided by the rate for the comparison group. The interpretation of the value of a rate ratio is similar to that of the risk ratio.
That is, a rate ratio of 1. They recorded Calculate the rate ratio. Note: Of 58 viral isolates identified from nasal cultures from passengers, most were influenza A, making this the largest summertime influenza outbreak in North America. Literature Altman DG Practical statistics for medical research.
London: Chapman and Hall. Odds ratios should be avoided when events are common [letter]. BMJ ; Similarly, you may subtract the number of unfavorable outcomes from the total number of outcomes to find the number of favorable outcomes. Express odds numerically. Generally, odds are expressed as the ratio of favorable outcomes to unfavorable outcomes, often using a colon.
In our example, our odds of success would be 2 : 4 - two chances that we'll win versus four chances that we'll lose. Like a fraction, this can be simplified to 1 : 2 by dividing both terms by the common multiple of 2. This ratio is written in words as "one to two odds. You may choose to represent this ratio as a fraction. In fact, we have a one-third chance of winning. Remember when expressing odds that odds are a ratio of favorable outcomes to unfavorable outcomes - not a numerical measurement of how likely we are to win.
Know how to calculate odds against an event happening. What if we want to know the odds of losing, also called the odds against us winning? To find the odds against us, simply flip the ratio of odds in favor of winning. Remember, as above, that this isn't an expression of how likely you are to lose, but rather the ratio of unfavorable outcomes to favorable outcomes.
How do you like those odds? Know the difference between odds and probability. Probability is simply a representation of the chance that a given outcome will happen. This is found by dividing the number of desired outcomes over the total number of possible outcomes. It's easy to convert between probability and odds. The answer is the number of unfavorable outcomes. Odds can then be expressed as 5 : 8 - the ratio of favorable to unfavorable outcomes. The answer is the total number of outcomes.
Part 2. Differentiate between dependent and independent events. For example, if you have a jar full of twenty marbles, four of which are red and sixteen of which are green, you'll have 4 : 16 1 : 4 odds to draw a red marble at random. Let's say you draw a green marble. If you don't put the marble back into the jar, on your next attempt, you'll have 4 : 15 odds to draw a red marble. Then, if you draw a red marble, you'll have 3 : 15 1 : 5 odds on the following attempt. Drawing a red marble is a dependent event - the odds depend on which marbles have been drawn before.
Independent events are events whose odds aren't effected by previous events. Flipping a coin and getting a heads is an independent event - you're not more likely to get a heads based on whether you got a heads or a tails last time.
Determine whether all outcomes are equally likely. However, if we roll two dice and add their numbers together, though there's a chance we'll get anything from 2 to 12, not every outcome is equally likely. There's only one way to make 2 - by rolling two 1's - and there's only one way to make 12 - by rolling two 6's. By contrast, there are many ways to make a seven.
For instance, you could roll a 1 and a 6, a 2 and a 5, a 3 and a 4, and so on. In this case, the odds for each sum should reflect the fact that some outcomes are more likely than others. Let's do an example problem. To calculate the odds of rolling two dice with a sum of four for instance, a 1 and a 3 , begin by calculating the total number of outcomes.
Each individual dice has six outcomes. Next, find the number of ways you can make four with two dice: you can roll a 1 and a 3, a 2 and a 2, or a 3 and a 1 - three ways. Take mutual exclusivity into account. For instance, if you're playing poker and you have a nine, ten, jack, and queen of diamonds in your hand, you want your next card either to be a king or eight of any suit to make a straight , or, alternatively, any diamond to make a flush.
Let's say the dealer is dealing your next card from a standard fifty-two card deck. There are thirteen diamonds in the deck, four kings, and four eights. The thirteen diamonds already includes the king and eight of diamonds - we don't want to count them twice. Thus, the odds of being dealt a card that will give you a straight or flush are 19 : 52 - 19 or 19 : Not bad! In real life, of course, if you already have cards in your hand, you're rarely being dealt cards from a complete fifty-two card deck.
Keep in mind that the number of cards in the deck decreases as cards are dealt. Also, if you're playing with other people, you'll have to guess what cards they have when you're estimating your odds. This is part of the fun of poker. Part 3. Know common formats for expressing gambling odds.
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