How do you interpret a p-value of 0.03 in a hypothesis test?

How do you interpret a p-value of 0.03 in a hypothesis test?

• A. There is a 3% probability of observing the result if the null hypothesis is true; typically reject the null at 5% significance.
• B. There is a 3% chance the null is true.
• C. The result proves the alternative hypothesis.
• D. The probability that the alternative is true is 3%.

Answer: (A)

The p-value tells you how compatible the observed data are with the assumption that the null hypothesis is true. A p-value of 0.03 means that, if the null hypothesis were true, you'd expect to see results as extreme or more extreme as what you observed only about 3% of the time. Because this is below the common 5% significance threshold, the result is typically considered strong enough to reject the null at that level. It’s important to note that this does not mean there is a 3% chance the null is true, nor does it prove the alternative hypothesis. The p-value is about how surprising the data would be under the null model, not about the probabilities of the hypotheses themselves. Also, it doesn’t convey the size or practical importance of an effect, and its interpretation can be influenced by sample size.

The p-value tells you how compatible the observed data are with the assumption that the null hypothesis is true. A p-value of 0.03 means that, if the null hypothesis were true, you'd expect to see results as extreme or more extreme as what you observed only about 3% of the time. Because this is below the common 5% significance threshold, the result is typically considered strong enough to reject the null at that level.

It’s important to note that this does not mean there is a 3% chance the null is true, nor does it prove the alternative hypothesis. The p-value is about how surprising the data would be under the null model, not about the probabilities of the hypotheses themselves. Also, it doesn’t convey the size or practical importance of an effect, and its interpretation can be influenced by sample size.