Enter paired measurements of the same subjects (e.g. before and after treatment) to compute the mean and SD of differences and test whether the difference is non-zero, returning t, df and p.
对同一对象前后/配对测量的差值进行检验。
| Item | Formula / Note | Source / Standard |
|---|---|---|
| Difference scores | d_i = x1_i - x2_i (two measurements on the same unit) | Student (1908), The probable error of a mean, Biometrika 6(1) |
| Paired t statistic | t = dbar / (s_d / sqrt(n)), df = n - 1 | NIST/SEMATECH e-Handbook of Statistical Methods §1.3.5.4 |
| Standard deviation of differences | s_d = sqrt( sum(d_i - dbar)^2 / (n - 1) ) | NIST/SEMATECH e-Handbook of Statistical Methods §1.3.5.4 |
| Effect size | Cohen's d_z = dbar / s_d | Cohen J., Statistical Power Analysis for the Behavioral Sciences (1988) |