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 <math> H_0 </math> is true. It should not be used as a binary criterion (e.g., <math> p < 0.05 </math>) 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 <math> N </math> independent tests at threshold <math> \alpha </math>, the Family-Wise Error Rate (FWER) is <math> FWER = 1 - (1 - \alpha)^N </math>. Bonferroni correction divides the threshold by the number of tests, <math> p < \frac{\alpha}{N} </math>, 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: <math> \chi^2 = -2 \sum \ln(p_i) </math>. 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 name=":1">{{cita libro