for ln OR and the lower and upper limits of the 1- alpha confidence interval. ODDS_RATIO(R1, lab, alpha): returns a column array with the odds ratio for the 2 × 2 contingency table in R1, s.e. Real Statistics Function: The following function is provided in the Real Statistics Resource Pack: The 95% confidence interval for the odds ratio of 2.52 in Example 1 is (1.15, 5.53), as shown in Figure 3.įigure 3 – 95% confidence interval for odds ratio Worksheet Functions Thus, an estimate of the 1 – α confidence interval is Observation: For a 2 × 2 contingency table with entries the standard error of the natural log of the odds ratio is (2000), the odds ratio can be reinterpreted as a Cohen’s effect size by using the formula The ratio 2.52 is the odds ratio.Īccording to Chinn, S. This means that the odds of remaining uncured is 2.52 times greater for therapy 2 than therapy 1. The odds of a person who took therapy 2 is 51 to 57 or. The odds of a person who took therapy 1 remaining uncured is 11 to 31 or. This is a meaningful measure of effect size, called the risk ratio or relative risk.Ī related measure of effect size is the odds ratio. This shows that those taking therapy 2 were 1.80 times as likely as those taking therapy 1 to remain uncured. In fact, 26.19% of the people who took therapy 1 were not cured, while 47.22% of those who took therapy 2 were not cured. Odds Ratioįor a 2 × 2 contingency table, we can also define the odds ratio measure of effect size as in the following example.Įxample 1: Calculate the odds ratio for the data in Example 2 of Independence Testing.Īs we saw in Example 2 of Independence Testing, there is a significant difference between those taking therapy 1 and those taking therapy 2. 21 (with df* = 2), which should be viewed as a medium effect. As we saw in Figure 4 of Independence Testing, Cramer’s V for Example 1 of Independence Testing is.