A p-value represents the probability of obtaining data as extreme as, or more extreme than, what you actually observed, assuming that the null hypothesis is true. In simpler terms, it answers the question: "If our hypothesis is correct, how likely is it that we would collect data like what we actually got?"
The smaller the p-value, the less likely it is that we would observe our current data if the null hypothesis were true. This makes the null hypothesis less credible, suggesting that our observed results are not due to random chance alone.
To fully grasp p-values, we first need to understand what the null hypothesis is. The null hypothesis (often denoted as H₀) is a default assumption that there is no effect or no difference between groups being compared.
Example: Drug Trial
In a pharmaceutical study comparing two medications, the null hypothesis would typically state: "There is no difference in effectiveness between Drug A and Drug B." This is our starting assumption—that both drugs work equally well (or equally poorly).
When we calculate a p-value and find it to be very small (typically less than 0.05), we reject the null hypothesis. Rejecting "no difference" means we have statistical evidence that the two drugs actually do differ in their effectiveness.
Let's illustrate this concept with a concrete example that's easy to visualize.
Scenario: You suspect a coin might be biased (unfair).
Null Hypothesis (H₀): The coin is fair—the probability of getting heads is 50%.
Experiment: You flip the coin 100 times and observe 90 heads.
Analysis: Now we calculate the p-value, which is the probability of getting 90 or more heads in 100 flips if the coin were truly fair. Using statistical methods, we find this p-value is extremely small (much less than 0.05).
Interpretation: Since this p-value is so small, it means that if the coin were actually fair, it would be extremely unlikely to get 90 or more heads in 100 flips. Therefore, we reject the null hypothesis and conclude that the coin is likely biased.
The smaller the p-value, the stronger the evidence against the null hypothesis.
Remember, a p-value doesn't tell you the probability that the null hypothesis is true or false—it only tells you how compatible your data is with the null hypothesis being true.
