In statistical analysis, a two-sample proportion test is used to compare the proportions of a particular outcome between two groups. Conducting a power analysis helps researchers determine the sample size needed to detect a significant difference between these proportions with a specified level of confidence. In this article, we present three diverse examples of power analysis for a two-sample proportion test, providing clarity and insight into its practical applications.
In a clinical trial, researchers aim to evaluate the effectiveness of a new medication in reducing symptoms of a specific disease compared to a placebo. They hypothesize that the drug will result in a higher proportion of patients experiencing symptom relief compared to those receiving the placebo.
The researchers decide to conduct a power analysis to determine the sample size needed to detect a significant difference in proportions with a power of 0.80 and a significance level of 0.05. They expect that 60% of patients in the treatment group will experience symptom relief, while only 40% in the placebo group will.
Using a power analysis calculator, they input the following parameters:
The calculator indicates that a total sample size of 132 participants is required (66 in each group) to achieve the desired power.
A marketing team is interested in understanding customer satisfaction levels between two demographic groups: millennials and baby boomers. They want to know if there is a significant difference in the proportion of satisfied customers across these groups after using a new product.
The team anticipates that 75% of millennials are satisfied, while 65% of baby boomers report satisfaction. They wish to determine the sample size needed for their survey with a power of 0.85 and a significance level of 0.05.
Using a power analysis formula or software, the team inputs the following:
The results show that they need at least 318 participants in total (159 from each demographic group) to confidently detect a significant difference in proportions.
An educational researcher is investigating the impact of a new teaching method on student performance in mathematics. They hypothesize that students using the new method will show a higher success rate (passing the exam) compared to those using traditional methods.
The researcher believes that 80% of students using the new method will pass, while 70% of students using the traditional method will pass. To confirm this hypothesis, the researcher conducts a power analysis with a target power of 0.90 and a significance level of 0.01.
In the power analysis tool, the following values are entered:
The analysis indicates that a total sample size of 576 students is needed (288 from each method) to achieve sufficient power for detecting the difference in proportions.