事后检验（Post-hoc test）

  1. ANOVA无法说明哪个备择假设得到支持；
    • The ANOVA cannot indicate which alternative hypothesis is supported.
  2. 要进行事后检验以说明各组差异在什么地方；
    • Post-hoc tests are needed to show where the groups differ.
  3. 事后检验是比较每一个组和另一个处理组，一次比较两个，这称为成对比较。
    • Post-hoc test compares each group to another treatment group, two at a time; this is called a pairwise comparison.

族系（familywise）误差

  1. 每一个比较都是一个单独的假设检验，每一个都有犯I类错误的风险。所以，比较对数越多，作结论的风险越大。即容易发现实际不存在的差异。这称为实验导致的（experimentwise）alpha水平或族系（familywise）误差；
    • Each comparison is a separate hypothesis test, each with the risk of making a Type I error. So the more pairs of comparisons there are, the greater the risk of making a conclusion. That is, it is easy to find differences that do not actually exist. This is called the experimentwise alpha level or familywise error.
  2. 多次比较后犯I类错误的概率(Probability of making a Type I error after multiple comparisons)为αEW=1-(1-α）c，其中c为比较的次数(c=Number of comparisons)。

Tukey's HSD检验 (Tukey's HSD test)

  1. 此检验各组要有相同的样本容量;
    • This test requires the same sample size for each group.
  2. 可以计算出单一的值确定处理均值间的最小差异，考查此差异在统计上是否显著;
    • A single value can be calculated to determine the smallest difference between treatment means, to see if the difference is statistically significant.
  4. q可以查表得到。
    • q score can be obtained by looking up the table.

Scheffe检验 (Scheffe test)

  1. 适用于n不相等的情况;
    • Applies when n is not equal.
  2. 降低I类错误的风险，提高II类错误的风险。
    • Reduces the risk of Type I errors and increases the risk of Type II errors.