A data science team conducted an A/B test to compare the click-through rates (CTR) of two different recommendation algorithms: the existing algorithm (Control) and a new algorithm (Variant). The null hypothesis stated that there is no difference in the mean CTR between the two algorithms. After running the experiment and performing a two-sample t-test, the team calculated a p-value of 0.04. The pre-determined significance level (alpha) for this test was 0.05.
Based on this result, what is the correct interpretation of the p-value?
There is a 4% probability that the null hypothesis is true and the observed difference in CTR is due to random chance.
There is a 96% probability that the new algorithm (Variant) is more effective than the existing algorithm (Control).
The result is not statistically significant because the p-value of 0.04 is less than the significance level of 0.05.
Assuming the null hypothesis is true, there is a 4% probability of observing a difference in CTR as extreme or more extreme than what was measured.
The correct answer provides the precise definition of a p-value in the context of the scenario. A p-value is the probability of observing a test result at least as extreme as the one actually found, under the assumption that the null hypothesis is true. In this case, with a p-value of 0.04, it means there is a 4% chance of observing the measured difference in CTR (or an even larger one) if there were actually no difference between the algorithms. Since the p-value (0.04) is less than the pre-determined alpha (0.05), the result is statistically significant, and the team would reject the null hypothesis.
Incorrect interpretations often involve common fallacies. The p-value is not the probability that the null hypothesis is true, nor is it the probability that the results are due to random chance. Furthermore, a p-value less than the significance level indicates a statistically significant result, not an insignificant one.
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What does it mean if the p-value is less than the significance level (alpha)?
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What is the null hypothesis in the context of hypothesis testing?
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Why is the p-value not the same as the probability that the null hypothesis is true?