Difference between revisions of "Introduction"

*'''P-value''': In medicine, for example, we rely on statistical inference to confirm experimental results, specifically the {{Tooltip|P-value|2=The p-value represents the probability that observed results are due to chance, assuming the null hypothesis \( H_0 \) is true. It should not be used as a binary criterion (e.g., \( p < 0.05 \)) for scientific decisions, as values near the threshold require additional verification, such as cross-validation. *p-hacking* (repeating tests to achieve significance) increases false positives. Rigorous experimental design and transparency about all tests conducted can mitigate this risk. Type I error increases with multiple tests: for \( N \) independent tests at threshold \( \alpha \), the Family-Wise Error Rate (FWER) is \( FWER = 1 - (1 - \alpha)^N \). Bonferroni correction divides the threshold by the number of tests, \( p < \frac{\alpha}{N} \), but can increase false negatives. The False Discovery Rate (FDR) by Benjamini-Hochberg is less conservative, allowing more true discoveries with an acceptable proportion of false positives. The Bayesian approach uses prior knowledge to balance prior and data with a posterior distribution, offering a valid alternative to the p-value. To combine p-values from multiple studies, meta-analysis uses methods like Fisher's: \( \chi^2 = -2 \sum \ln(p_i) \). In summary, the p-value remains useful when contextualized and integrated with other measures, such as confidence intervals and Bayesian approaches.}}, a "significance test" that assesses data validity. Yet, even this entrenched concept is now being challenged. A recent study highlighted a campaign in the journal "Nature" against the use of the P-value.<ref>{{cita libro