The formula to calculate the Minimum Detectable Effect (MDE) is:
\[ MDE = (Z_c \times \sqrt{\frac{p \times (1 - p)}{n}}) + (Z_p \times \sqrt{\frac{p \times (1 - p)}{n}}) \]
Where:
The minimum detectable effect (MDE) is a statistical term used in hypothesis testing and experimental design. It represents the smallest effect size that a study is designed to detect with a given level of statistical power and significance. In the context of A/B testing or clinical trials, the MDE is the smallest difference between the control and treatment groups that the experiment is capable of identifying as statistically significant. Understanding the MDE helps researchers design experiments with adequate sample sizes to detect meaningful differences, ensuring that the study’s findings are both reliable and actionable.
Let's assume the following values:
Using the formula to calculate the Minimum Detectable Effect (MDE):
\[ MDE = (Z_c \times \sqrt{\frac{p \times (1 - p)}{n}}) + (Z_p \times \sqrt{\frac{p \times (1 - p)}{n}}) = (1.96 \times \sqrt{\frac{0.1 \times (1 - 0.1)}{1000}}) + (0.84 \times \sqrt{\frac{0.1 \times (1 - 0.1)}{1000}}) \approx 0.027 \]
The Minimum Detectable Effect (MDE) is approximately 0.027.
