null hypothesis 虛無假設 H0
alternative hypothesis 對立假設 H1/Ha
analysis of variances (ANOVA) 變異數分析
E.g. 3 groups with one-way ANOVA
H0: μ1 = μ2 = μ3
H1: μ1 ≠ μ2 ≠ μ3
ANOVA的重點，是求F值：
F ＝MST/MSE = Mean Square Treatment/Mean Square Error
再和Critical Value CV=f(df1,df2)比較，CV可查f分佈表求得，當F值大於CV時，則拒絕H0
F值表示組間變異(variability between groups)較組內變異(variability within groups)多F倍，因此當F值越大，機率上組間的差異就越大，所以當F值增加至大於CV值時，組間有顯著異。
當F > CV時，組間有顯著差異，但不知道差異是在哪些組之間，因此需要事後檢定(post hoc test)
接著求p value，即在
可針對不同的α值查表求fα(df1,df2)，例如f0.05(df1,df2)和f0.01(df1,df2)等數值，即可粗略地得知p值所落在的範圍
p value:
<0 ---="" .05="" br=""><0 ---="" .01="" br=""><0 ---="" .001="" br="">
<0 ---="" .05="" br=""><0 ---="" .01="" br=""><0 ---="" .001="" br="">p<0.05 --- * statistically significant
<0 ---="" .05="" br=""><0 ---="" .01="" br=""><0 ---="" .001="" br="">p<0.01 --- ** statistically highly significant
<0 ---="" .05="" br=""><0 ---="" .01="" br=""><0 ---="" .001="" br="">p<0.001 --- *** statistically extremely significant
<0 ---="" .05="" br=""><0 ---="" .01="" br=""><0 ---="" .001="" br="">
test statistic 檢定統計量
significance level / level of significance 顯著水準 (通常α = 0.05)
- H0發生的機率、拒絕H0的機率、Type I error的機率(不太可能發生)
References
顯著水準 - 基礎統計名詞介紹網頁
Statistical significance (Wikipedia)
Foundations of ANOVA – Assumptions and Hypotheses for One-Way ANOVA (12-3) (Research By Design YouTube)
Mathematical statistics with applications in R, Ramachandran & Tsokos, 2nd edition (2015), p501,
