Inferential Statistics I: Basic concepts of statistical inference / Estadística Inferencial I: Conceptos básicos de inferencia estadística

Resumen

This document presents the theoretical and methodological foundations of hypothesis testing in the field of research. In statistical inference, a statistical test is a procedure that allows us to decide whether a claim about a population parameter should be accepted or rejected using data obtained from a sample. To carry out the analysis, two complementary scenarios are formulated: the null hypothesis (H0), which assumes the absence of changes, differences, or effects, and the alternative hypothesis (H1), which postulates the existence of an effect and represents the claim that the researcher seeks to prove. The result of the test is based on analyzing population parameters (such as the mean or variance) and on the use of probability distributions (such as the Normal, Student's t, or Chi-square distributions) to define the regions of acceptance or rejection of H0. Decision-making assumes the possibility of committing errors: Type I Error (rejecting a true H0) and Type II Error (accepting a false H0). To determine if a result is valid, the p-value is calculated, which measures the probability of obtaining the observed results assuming the null hypothesis is true. If the p-value is less than the established significance level (α), H0 is rejected, and the result is considered statistically significant. The five steps for performing a statistical test are: formulating the hypotheses, defining the margin of error (α), choosing the test statistic, calculating the p-value, and issuing a well-founded conclusion with the defined confidence level.