How to use quantitative analysis methods (such as t-tests) for hypothesis verification?

Quantitative analysis employs statistical methods like t-tests to empirically verify research hypotheses concerning population parameters based on sample data. Specifically, t-tests assess whether observed differences between group means are statistically significant or likely due to random chance. Key principles involve formulating explicit null and alternative hypotheses, selecting the appropriate t-test type (e.g., independent samples, paired samples, one-sample), and verifying underlying assumptions. These crucial assumptions include data approximating normal distribution, homogeneity of variances (for independent t-tests), and independence of observations. The calculated t-statistic is compared against critical values from the t-distribution, considering the chosen significance level (α, e.g., 0.05) and degrees of freedom; a resulting p-value lower than α leads to rejecting the null hypothesis. Implementation involves several sequential steps. First, precisely define the null (H₀) and alternative (H₁) hypotheses based on the research question. Second, ensure data meet test assumptions, potentially using diagnostics or non-parametric alternatives if violated. Third, calculate the relevant t-statistic (often using statistical software like SPSS, R, or Python). Fourth, determine the p-value associated with the calculated t-statistic and degrees of freedom. Finally, interpret the result: rejecting H₀ suggests sufficient evidence for H₁, while failing to reject H₀ indicates insufficient evidence against it. T-tests are commonly applied in experiments comparing control and treatment groups or measuring pre-post interventions.