# Odds ratio with 95% confidence interval

## The width and direction of the confidence interval is the primary inference with an odds ratio

The odds ratio with 95% confidence interval is the inferential statistic used in

If the confidence interval of an odds ratio

If the odds ratio and confidence interval are both entirely

If the odds ratio and confidence interval are both entirely

**retrospective case-control designs, chi-square analyses (unadjusted odds ratios with 95% confidence intervals), and in multivariate models predicting for categorical, ordinal, and time-to-event outcomes**. The**width of the confidence interval**of the odds ratio is the inference related to the**precision**of the treatment effect.If the confidence interval of an odds ratio

**crosses over 1.0**, the event is just as likely to occur as not occur, then researchers have a**non-significant**association between the variables.If the odds ratio and confidence interval are both entirely

**above 1.0**, then the outcome is**MORE LIKELY**to occur as a result of the treatment or exposure.If the odds ratio and confidence interval are both entirely

**below 1.0**, then the outcome is**LESS LIKELY**to occur as a result of treatment or exposure, denoting a "protective" effect.The research design of an odds ratio is set up like below.

**Research Design and the 2x2 table**

When researchers use a retrospective

**design, the odds ratio with 95% confidence interval is used as the primary inference. In the table below, one can see that the formula is (A*D) / (B*C).**__case-control__**Odds Ratio Calculation**

The 95% confidence interval of an odds ratio is the primary inference that dictates the precision of the statistical result. Here is the formula:

**95% confidence interval for an odds ratio**

### Confidence intervals of odds ratios and sample size

The width of the confidence interval associated with an odds ratio is the inference. Due to measurement error in categorical variables, a 95% confidence interval has to be wrapped around the odds ratio to understand where the true treatment effect may exist. Narrower confidence intervals allow for more precision and "believability" of the treatment effect. Wider confidence intervals decrease precision meaning that the true treatment effect may lie anywhere across a wide continuum.

An important concept to understand is that the width of the confidence interval for an odds ratio is 100% COMPLETELY DEPENDENT upon your sample size. Look at the example below:

An important concept to understand is that the width of the confidence interval for an odds ratio is 100% COMPLETELY DEPENDENT upon your sample size. Look at the example below:

**Sample size and 95% confidence interval for an odds ratio**

With the original sample size of 24, you find a significant association with an odds ratio of 10.0 with a 95% CI of 1.44 to 69.26. This means that people with the predictor are 10 times more likely to develop the outcome versus people without the predictor. The confidence interval is very wide, so you cannot be sure of where the true effect lies.

For purposes of presenting the reasoning of interdependency between sample size and confidence intervals, all that was done was to add a "0" to each of the frequencies in the above cross-tabulation table. The frequency of 10 in (A) became 100, 4 in (B) became 40, 2 in (C) became 20, and 8 in (D) became 80, for a new sample size of 240. With these new values, you find the EXACT same odds ratio of 10.0 as before, but look at the width of the confidence interval. It has constricted substantially and now you have more confidence that the true effect lies in the interval, 95% CI 5.42 - 18.44. This example shows that when conducting studies with categorical outcomes, a larger sample size is needed to yield precise measures of treatment effects.

For purposes of presenting the reasoning of interdependency between sample size and confidence intervals, all that was done was to add a "0" to each of the frequencies in the above cross-tabulation table. The frequency of 10 in (A) became 100, 4 in (B) became 40, 2 in (C) became 20, and 8 in (D) became 80, for a new sample size of 240. With these new values, you find the EXACT same odds ratio of 10.0 as before, but look at the width of the confidence interval. It has constricted substantially and now you have more confidence that the true effect lies in the interval, 95% CI 5.42 - 18.44. This example shows that when conducting studies with categorical outcomes, a larger sample size is needed to yield precise measures of treatment effects.

Click on the

**Prevalence**button to continue. Click on the**Download Database**button for a database structured for odds ratio data. Click on the**Download Calculator**button to download a free epidemiological calculator.## Statistician Services for Students

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