Interpret a statistically significant lift of 2% from an experiment

Question

An experiment shows conflicting results. What conclusions can you draw? What are the caveats?

Codemia · Accepted Answer

In this scenario, we are analyzing the results of an experiment that shows a statistically significant lift of 2%. The goal is to determine whether this lift is meaningful in a practical context, especially considering that the results are conflicting. We can approach this by setting up a hypothesis test where:

- **Null Hypothesis (H0)**: There is no lift (i.e., the lift is 0%).
- **Alternative Hypothesis (H1)**: There is a lift (i.e., the lift is greater than 0%).

To evaluate the significance of the 2% lift, we will need to look at the p-value obtained from the experiment, assess the confidence intervals, and consider factors like multiple testing corrections and the sample size to ensure that our findings are robust.

To analyze the results, we will follow these steps:
1. **P-value Evaluation**: Determine the p-value associated with the lift. A common threshold for significance is p < 0.05.
2. **Confidence Interval Calculation**: Calculate the confidence interval for the 2% lift to see if it includes zero.
3. **Multiple Testing Correction**: If multiple hypotheses were tested, apply corrections (e.g., Bonferroni or FDR) to adjust the significance thresholds.
4. **Power Analysis**: Evaluate the power of the experiment to understand the likelihood of detecting a true effect.
5. **Caveats Identification**: Discuss potential limitations and assumptions that could impact the validity of our conclusions.

Let's assume the p-value for the observed lift of 2% is 0.03, indicating significance since it is less than 0.05. We can also calculate a 95% confidence interval for the lift:

- **Confidence Interval**: Using the formula for a confidence interval:
  
  CI = lift ± Z * (standard error),
  
  where Z is the Z-score for 95% confidence (approximately 1.96). Assume the standard error for the lift is 0.5%.

CI = 2% ± 1.96 * 0.5% = 2% ± 0.98% = (1.02%, 2.98%).

Since the interval does not include 0, we can conclude that the lift is statistically significant.

Finally, if we tested 10 hypotheses, we apply a Bonferroni correction, adjusting our alpha level to 0.05/10 = 0.005, which means our p-value of 0.03 is no longer significant under this correction.

The 2% lift indicates that there is a positive change associated with the treatment or intervention tested. However, given the p-value of 0.03 and the confidence interval does not include zero, we must be cautious. The Bonferroni correction suggests that the lift may not be statistically significant if multiple hypotheses were tested. Thus, while a 2% lift may seem promising, we need to consider the possibility of Type I errors due to multiple testing and ensure that our findings are replicable before making any business decisions based on this result.

This problem connects to several important statistical concepts. If asked, we could discuss:
- **Multiple Testing Corrections**: Understanding how to apply corrections like FDR or the Bonferroni method to maintain the integrity of our results when testing multiple hypotheses.
- **Regression Analysis**: If the experiment included covariates, regression could provide insights into the relationship between the lift and other variables.
- **Power Analysis**: Discussing how to determine the necessary sample size for future experiments to ensure adequate power to detect meaningful effects without false positives.
- **Probability Distributions**: Exploring how the assumptions of normality and distribution impact hypothesis testing and the validity of our results.

Interpret a statistically significant lift of 2% from an experiment

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