Reading 5: Statistical Tests

Reading 5: Statistical Tests#

For the class on Monday, January 27th

Reading assignments#

Read the following sections in Chap. 5 of [WJ12]:

  • Sec. 5.1 “Methodology of classical hypothesis testing”

  • Sec. 5.3.1 “Chi-square test”

  • Sec. 5.3.2 “Kolmogorov–Smirnov one-sample test”

  • Sec. 5.6 “Statistical ritual” (not including Table 5.6)

Questions#

Submit your answer on Canvas. Due at noon, Monday, January 27th.

  1. List any concepts that confuse you from your reading. Explain why they confuse you. If nothing confuses you, briefly summarize what you have learned from this reading assignment.

  2. You have some data points \((x_1, x_2, \cdots, x_n)\), and you want to test if they come from a specific distribution. You know the exact form of the distribution’s PDF \(p(x)\). Describe the steps you would take to perform this test.

  3. Same as (2), but the said distribution’s PDF has a dependence on a parameter \(\theta\). You know the form of \(p_\theta(x)\), but you do not know the value of \(\theta\). Describe the steps you would take to test if the data points come from \(p_\theta(x)\).