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Example Use of Odds Ratio (OR) and Confidence Interval

The Case Scenario

A freelance writing company has been receiving complaints from freelancers of severe headaches after long hours of exposure to their computers. The company delegated one of its research assistants to collect and analyse the necessary data and determine the right course of action. The researcher recruited 100 freelancers that visit site with reported cases of headaches and 100 freelancers without cases of headaches. He questioned the freelancers if they had been using antiglare glasses over the past 12 months. Only 21 freelancers with cases of headaches reported using antiglare glasses as did 93 freelancers without cases of headaches. What recommendation can the researchers draw from this data?

Statistical Analysis Procedure

Based on the above data provided by studydaddy the most appropriate statistical analysis method is determining the odds ratio (OR) about the data and its corresponding confidence interval at 95% significance level (Knol, Le Cessie, Algra, Vandenbroucke, & Groenwold, 2012). This statistical procedure expresses the association between the odds of having headaches and the odds of not having headaches following exposure to anti-glare lens.

Step 1: Construct a Contingency Table

Step 2: Calculate the Odds Ratio

The odds ratio is the cross product of the above quadrants as follows.

Step 3: Calculate the Confidence Interval

The confidence interval is a natural logarithm (Ln) of the odds ratio and the z-score distribution using the following formula (Fleiss, Levin, & Paik, 2013).

Below is the substitution of the formula with data from the above table.

Based on the above computations, the 95% confidence interval for Ln (OR) is (-4.304, -3.520). The antilog of (-4.304, -3.520), using the exponential function, is required in order to generate the lower and upper limits of the confidence interval of the odds ratio.

Interpretation and Conclusion

An odds ratio of 0.02 means that the use of anti-glare glasses among the freelancers reduces chances of headaches by 98 %, as computed in (1- 0.02 = 0.98). Since neither the lower nor the upper limit of the confidence interval is equal to 1.0, an inference drawn is that the findings are statistically significant at 95% confidence level (p ≤ 0.05). The writing company such as www.studydaddy.com/chemistry-homework-help/ should recommend the use of anti-glare glasses to all its writers to minimise reported incidences of severe headaches by 98%.


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