In the context of sociology, how does understanding the relationship between p-value, confidence interval, and experimental design enhance hypothesis testing?

In sociology, understanding the relationship between p-value, confidence interval, and experimental design is crucial for hypothesis testing because it helps researchers evaluate their findings more accurately. The p-value indicates the probability that the observed results happened by chance; a low p-value suggests strong evidence against the null hypothesis. Meanwhile, the confidence interval provides a range of values within which we can be fairly certain the true effect lies, offering more context about the data. When researchers design their experiments well, they can ensure that their sample is representative, which strengthens the reliability of both the p-value and the confidence interval. For example, if a sociologist studies the impact of a new teaching method on student performance and finds a low p-value along with a narrow confidence interval, they can confidently assert that the method has a real and measurable effect.