P-values and confidence intervals

The P value, or probability value, is a cornerstone in statistical hypothesis testing. It quantifies the probability of observing data as extreme as, or more extreme than, what was actually observed, assuming that the null hypothesis (a hypothesis of no effect or no difference) is true.

• Definition: The P value is defined as the probability of obtaining a result equal to or more extreme than what was actually observed, under the assumption that the null hypothesis is true.
• Interpretation: A low P value (typically ≤ 0.05) suggests that the observed data is unlikely under the null hypothesis, leading to its rejection in favor of the alternative hypothesis. It does not, however, confirm the truth of the alternative hypothesis or the magnitude of the effect.
• Misconceptions: A common misconception is equating a P value with the probability that the null hypothesis is true. It is crucial to understand that the P value does not measure the probability of hypotheses but rather the probability of the data given a hypothesis. P-value does not prove the alternative hypothesis. It simply means that the data are unlikely to be explained by chance. A low p-value does not necessarily mean that the...