What Does the p-value Even Mean?

P-values are widely misunderstood, even by people who use them regularly. A p-value does not tell you the probability your hypothesis is true or that your result is due to randomness. Instead, it measures how surprising your data would be if there were no real effect — essentially a 'weirdness score' under the null hypothesis. Common misconceptions like 'p < 0.05 means it's true' or 'lower p-value = better result' are fundamentally wrong. The 0.05 threshold was popularized by Ronald Fisher as a practical convention, not a mathematically optimal cutoff. Understanding p-values correctly also means recognizing their limits: statistical significance doesn't imply practical significance, and multiple tests increase the chance of false positives.