Paird t-Test

1. Dependent sample \(t\)-test.
2. It determineds whether the mean difference between two sets of observations is zero.
3. One should measure each subject/entity twice, resulting in pairs of observations.
4. Common application: Case-control studies, Repeat-measures desgins.
5. Two competing hypotheses:
   • Null hypothesis.
     • assumes that the true mean difference between the paired samples is zero.
     • all ovservanle differences are explained by random variation.
   • Alternative hypothesis.
     • assumes that the true mean difference between the paired samples is not equal to zero.
     • explained:
       • two-tailed: the true mean difference is not equal to zero.
       • one-tailed:
         • upper-tailed alternative hypothesis: the true mean difference is greater than zero.
         • lower-tailed alternative hypothesis: the true mean difference is less than zero.

✅ 假设检验不是对你眼前这组数据下结论，而是试图推断产生这些数据的“背后机制”是什么。我们用数据去判断它更符合哪种假设：‘两组一样’还是‘有差异’。