生物統計研讀筆記 - Establish Hypothesis 建立假設

正在研讀中的生物統計中，如何建立基本假設的步驟

• Typical steps of making hypothesis

  • State the problem
  • Formulate the null and alternative hypotheses
    • Null hypothesis 等號方向與情境描述方向相反，Greater than -> $\leq$
  • Choose the level of significance
    • the probability of rejecting a true null hypothesis
  • Determine the appropriate test statistic $\alpha: level$
  • Calculate the appropriate test statistic
  • Determine the critical values for the sampling distribution and appropriate level of significance, (or Determine the $P :value$ of the test statistic)
  • Compare the test statistic to the critical value
  • Based on the comparison, accept or reject hypothesis
    • $Z : value$ : c.v.’s = ±1.960, -1.960 < 1.8 < 1.960 -> Not extreme enough to reject null hypothesis
    • $P :value$ : 0.0718 > 0.05, which is the level of significance. -> Not rare enough to reject the null hypothesis
    • Above are two-taills, *how are the left-tail and right tail conditions? *

• Type I and Type II error

  • Type I error:
    • When $H_0$ is really true, but we reject $H_0$ based on the statistic result
    • P(Type I error) = the probability of rejecting a true null hypothesis.
  • Type II error:
    • When $H_0$ is really false, but we accept $H_0$ based on the statistic result
    • P(Type II error) = the probability of accepting a false null hypothesis.