Interpret a statistically significant lift of 2% from an experiment

Question

An experiment shows a 3% lift with p=0.08. What conclusions can you draw? What are the caveats?

Codemia · Accepted Answer

To interpret the experiment showing a 3% lift with a p-value of 0.08, we need to set up the statistical framework clearly.

Let's denote:
- $ \mu_0 $: the mean outcome of the control group 
- $ \mu_1 $: the mean outcome of the treatment group 
- Lift: $ \mu_1 - \mu_0 = 0.03 $ 
- Null Hypothesis (H0): There is no effect (i.e., $ \mu_1 = \mu_0 $) 
- Alternative Hypothesis (H1): The treatment has an effect (i.e., $ \mu_1 > \mu_0 $)

The p-value of 0.08 indicates the probability of observing a lift of at least 3% under the null hypothesis. Since this p-value is greater than the common significance level of 0.05, it suggests that we do not have enough evidence to reject the null hypothesis.

To analyze the statistical significance of the 3% lift, we can follow these steps:
1. **Check the confidence level**: With a p-value of 0.08, we can construct a 92% confidence interval instead of the conventional 95%.
2. **Calculate the confidence interval**: If we assume a standard error (SE) for the treatment effect, the confidence interval can be calculated as:
   $$ \text{CI} = \text{Lift} \pm Z_{\alpha/2} \times SE $$
   where $ Z_{\alpha/2} $ corresponds to the critical value for a 92% confidence level.
3. **Interpret the interval**: If the confidence interval includes zero, it suggests that the observed lift may not be practically significant.

Assuming we have a standard error of 0.01 for the treatment effect, we can find the critical value for a 92% confidence level, which corresponds to a Z-score of approximately 1.75.

Now, calculating the confidence interval:
- Lift = 0.03
- SE = 0.01
- CI = 0.03 \pm 1.75 \times 0.01 = 0.03 \pm 0.0175
- This yields a confidence interval of (0.0125, 0.0475).

Since this interval does not include zero, we can interpret that although the effect is not statistically significant at the 5% level, it suggests a positive lift that might be worth exploring further.

The result indicates a 3% lift with a p-value of 0.08. While this suggests a potential positive impact of the treatment, the lack of statistical significance at the 0.05 level means we should be cautious in concluding that the lift is definitive. The practical interpretation is that there may be an effect, but it is not strongly supported by the data, and further investigation with a larger sample size or additional experiments may be warranted.

Understanding this situation can lead to discussions on:
- **Practical vs Statistical Significance**: A 3% lift may be small in practical terms for a large business.
- **Bayesian vs Frequentist Approaches**: How prior distributions could influence interpretations.
- **Potential Confounders**: Identifying factors that might influence the treatment's effectiveness, such as demographic variables, and how to control for them using regression analysis.
- **Power Analysis**: Evaluating if the sample size was adequate to detect a meaningful effect size.

Interpret a statistically significant lift of 2% from an experiment

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