What is a P-value?
In this mock interview, a senior data scientist defines p-value.
This is a conceptual question. The interviewer is testing your understanding of the concept as well as your ability to communicate clearly (ideally illustrate with an example).
The technical definition is the probability of obtaining test results at least as extreme as the result actually observed, under the assumption that the null hypothesis is correct.
In simpler terms, in hypothesis testing a smaller p-value indicates stronger evidence against the null hypothesis, while a larger p-value suggests weaker evidence against it.
In hypothesis testing, the null hypothesis represents a default assumption or a statement of no effect, while the alternative hypothesis represents the claim we are testing. The p-value helps in deciding whether to reject the null hypothesis based on the observed data.
We'll walk through an example scenario.
Null hypothesis: The mean weight of apples from Orchard A is equal to the mean weight of apples from Orchard B.
Alternative hypothesis: The mean weight of apples from Orchard A is different from the mean weight of apples from Orchard B.
We can collect a random sample of apples from each orchard and measure their weights. Then, we calculate the sample mean and standard deviation.
We can conduct a two-sample two-tailed t-test to compare the means of the two samples, and calculate the test statistic using the mean and standard deviation.
Now, we need to find the p-value associated with this test statistic. This involves looking up the t-distribution table or using statistical software. Let's assume we find that the p-value is approximately 0.112.
Since this is a two-tailed test, we're interested in whether the means are different, not just if one is greater than the other. We can compare the p-value to our significance level, often set at = 0.05. You would expect to find a test statistic as extreme as the one calculated by our test only 5% of the time.
Since p > (0.112 > 0.05), we fail to reject the null hypothesis. This means that we do not have sufficient evidence to conclude that the mean weight of apples from Orchard A is different from the mean weight of apples from Orchard B at the 0.05 significance level.