null hypothesis, alternative hypothesis
名称、
内涵
相互关系
null: 原假设，希望拒绝的假设 H0
alternative: 备择假设，希望的结论Ha
相互互补
one-tailed test
and
two-tailed test
Test statistic
equation
standarlization of Xbar
critical value:
definition
determin factors
即k
- 查哪张表：z, t, F, Chi Square
- level of confidence
- one-tailed or two-tailed
Hypothesis Testing
8 部曲
- set null/alternative hypothesis
- determine distribution
- draw regect region
- determine level of significance
- determin critical value
- sampling – test statistic z value
- compare z and k
- draw conclusion: reject or fail to reject
mean hypothesis testing
如何选择？ 表格
mean hypothesis testing
method selection
两个mean，独立
区分H0, test-statistic, critical value
注意assume same variance - pool variance
mean hypothesis testing
method selection
两个mean，不独立
方法，H0, test-statistics, critical value
d1 = mean1 - mean2
【分母更正】图中S☞standard error, 即：
Sd/根n
variance hypothesis testing
如何选择？ 表格
variance hypothesis testing
Chi-square
Ho, test-statistics, critical value
variance Hypothesis testing
F-distribution
Ho, test-statistic, critical value
差F表时注意
- 单双尾都只查一个值
- s/s，大者放分子
P-value
definition
rule
lower p-value,
stronger evidence to reject Ho
Type I error
definition
P (type I error)
- definition: reject the null hypothesis when it’s actually true
- 拒真，错杀好人
- P (type I error) = level of significance, α
Type II error
definition
- fail to reject the null hypothesis when it’s actually false
- 取伪，放走坏人
Power of test
definition
equation
关于 type I error & type II error
两个结论
- P(I)上升（level of significance 上升）， P(II)下降，两者反相关
- 要想P(I) P(II) 都下降：increase sample size
什么情况下使用nonparametric test?
- 不满足分布假设（如：非正态分布总体小样本）
- 数据为ordinal given in rank （第一，第二、、、）
- 检验的事项与参数无关（如股票+-）
- 单尾/双尾，哪一个tester 有stronger believe？
- p-value: less precise than rejection points?
- 单尾检验有stronger believe
- not less precise.
