Statistical Inference

Course page: https://www.coursera.org/learn/statistical-inference By Jeff Leek, PhD, Roger D. Peng, PhD, Brian Caffo, PhD

  • Formula for groups with unequal variances:

\[\begin{align}t_{interval} & = \bar{Y} - \bar{X} \pm t_{df} \times \left( \frac{s_x^2}{n_x} + \frac{s_y^2}{n_y} \right)^\frac12 \\ df & = \frac{\left(\frac{s_x^2}{n_x} + \frac{s_y^2}{n_y} \right)^2}{\left( \frac{s_x^2}{n_x} \right)^2 / (n_x-1) + \left( \frac{s_y^2}{n_y} \right)^2 / (n_y-1)}\end{align}\]