#檢定多於兩組(多組)的觀察值之間是否有差異
#重複測量(Repeated measures): Friedman檢定、重複測量變異數分析
#Friedman檢定 (重複測量): 二因子變異數分析對應的無母數檢定。對資料分布沒有任何假設,只要求資料是可排序的。只有在每個因子值組合僅有一個觀察值時適用。
#Example: 選擇四天分別取出六個池塘的水樣計算藍藻數(個/mm3),每次取樣只取一個樣本,就可使用該檢定。
pondcells<- matrix(c(130,125,350,375,225,235,
115,120,375,200,250,200,
145,170,235,275,225,155,
200,230,140,325,275,215),
nrow=4,byrow = T,
dimnames = list(1:4,c("A","B","C","D","E","F"))) #此檢定要將資料整理成矩陣形式
friedman.test(pondcells) #自由度為池塘數減一
#重複測量變異數分析 (Repeated-measures ANOVA): 此種試驗設計下,每個因子值組合都只有一個才可以執行二因子變異數分析。在重複測量的設計下,影響因子需互相獨立或是得大量降低自由度。
pond<-c("A","A","A","A",
"B","B","B","B",
"C","C","C","C",
"D","D","D","D",
"E","E","E","E",
"F","F","F","F")
cells<-c(130,115,145,200,
125,120,170,230,
350,375,235,140,
375,200,275,325,
225,250,225,275,
235,200,155,215)
day<- c(rep(1:4,6))
summary(aov(cells~pond*day + Error(cells/(pond*day))))