1. ave 函数的论元

## function (x, ..., FUN = mean) 
## NULL

• x, 需要分析的数据

• ..., 用于分组的数据，如果空缺，则把函数应用于全部数据

• FUN, 应用于数据 x 的函数。

2. 一个例子

Score <- data.frame(
  RRR = c(2, 3,  8,  6,  5,  6),
  RPQ = c(5, 9, 10, 13,  8,  9),
  RCQ = c(8, 6, 12, 11, 11, 12)
  )
Score_long <- reshape(Score, direction = "long", 
  varying = list(names(Score)[1:3]), 
  timevar = "Condition", times = colnames(Score), v.names = "Score")
Score_long <- Score_long[, names(Score_long) != "id"]
row.names(Score_long) <- NULL
Score_long $ Group_Mean <- ave(Score_long $ Score, Score_long $ Condition)
Score_long $ Grand_Mean <- ave(Score_long $ Score)
Score_long

##    Condition Score Group_Mean Grand_Mean
## 1        RRR     2          5          8
## 2        RRR     3          5          8
## 3        RRR     8          5          8
## 4        RRR     6          5          8
## 5        RRR     5          5          8
## 6        RRR     6          5          8
## 7        RPQ     5          9          8
## 8        RPQ     9          9          8
## 9        RPQ    10          9          8
## 10       RPQ    13          9          8
## 11       RPQ     8          9          8
## 12       RPQ     9          9          8
## 13       RCQ     8         10          8
## 14       RCQ     6         10          8
## 15       RCQ    12         10          8
## 16       RCQ    11         10          8
## 17       RCQ    11         10          8
## 18       RCQ    12         10          8

SS_within <- sum((Score_long $ Score - Score_long $ Group_Mean) ^ 2)
SS_between <- sum((Score_long $ Group_Mean - Score_long $ Grand_Mean) ^ 2)
SS_total <- sum((Score_long $ Score - Score_long $ Grand_Mean) ^ 2)
c(SS_total, SS_between, SS_within)

## [1] 172  84  88

2. ave 函数的源代码

## function (x, ..., FUN = mean) 
## {
##     if (missing(...)) 
##         x[] <- FUN(x)
##     else {
##         g <- interaction(...)
##         split(x, g) <- lapply(split(x, g), FUN)
##     }
##     x
## }
## <bytecode: 0x7ff88ad07168>
## <environment: namespace:stats>

2. ave 函数的说明文档

## Group Averages Over Level Combinations of Factors
## 
## Description:
## 
##      Subsets of 'x[]' are averaged, where each subset consist of those
##      observations with the same factor levels.
## 
## Usage:
## 
##      ave(x, ..., FUN = mean)
##      
## Arguments:
## 
##        x: A numeric.
## 
##      ...: Grouping variables, typically factors, all of the same
##           'length' as 'x'.
## 
##      FUN: Function to apply for each factor level combination.
## 
## Value:
## 
##      A numeric vector, say 'y' of length 'length(x)'.  If '...' is 'g1,
##      g2', e.g., 'y[i]' is equal to 'FUN(x[j]', for all 'j' with 'g1[j]
##      == g1[i]' and 'g2[j] == g2[i])'.
## 
## See Also:
## 
##      'mean', 'median'.
## 
## Examples:
## 
##      require(graphics)
##      
##      ave(1:3)  # no grouping -> grand mean
##      
##      attach(warpbreaks)
##      ave(breaks, wool)
##      ave(breaks, tension)
##      ave(breaks, tension, FUN = function(x) mean(x, trim = 0.1))
##      plot(breaks, main =
##           "ave( Warpbreaks )  for   wool  x  tension  combinations")
##      lines(ave(breaks, wool, tension              ), type = "s", col = "blue")
##      lines(ave(breaks, wool, tension, FUN = median), type = "s", col = "green")
##      legend(40, 70, c("mean", "median"), lty = 1,
##            col = c("blue","green"), bg = "gray90")
##      detach()
##