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r - Sort data frame column by factor

Supose I have a data frame with 3 columns (name, y, sex) where name is character, y is a numeric value and sex is a factor.

sex<-c("M","M","F","M","F","M","M","M","F")
x<-c("MARK","TOM","SUSAN","LARRY","EMMA","LEONARD","TIM","MATT","VIOLET")
name<-as.character(x)
y<-rnorm(9,8,1)
score<-data.frame(x,y,sex)
score
     name      y     sex
1    MARK  6.767086   M
2     TOM  7.613928   M
3   SUSAN  7.447405   F
4   LARRY  8.040069   M
5    EMMA  8.306875   F
6 LEONARD  8.697268   M
7     TIM 10.385221   M
8    MATT  7.497702   M
9  VIOLET 10.177969   F

If I wanted to order it by y I would use:

score[order(score$y),]
        x         y sex
1    MARK  6.767086   M
3   SUSAN  7.447405   F
8    MATT  7.497702   M
2     TOM  7.613928   M
4   LARRY  8.040069   M
5    EMMA  8.306875   F
6 LEONARD  8.697268   M
9  VIOLET 10.177969   F
7     TIM 10.385221   M

So far, so good... The names keep the correct score BUT how could I reorder it to have M and F levels not mixed. I need to order and at the same time keep factor levels separated.

Finally I would like to take a step further to involve character, the example doesn't help, but what if there were tied y values and I would have to order again within factor (e.g. TIM and TOM got 8.4 and I have to assign alphabetical order).

I was thinking about by function but it creates a list and doesn't help really. I think there must be some function like it to apply on data frames and get data frames as return.

TO MAKE CLEAR THE POINT:

sep<-split(score,score$sex)
sep$M<-sep$M[order(sep$M[,2]),]
sep$M
x         y sex
1    MARK  6.767086   M
8    MATT  7.497702   M
2     TOM  7.613928   M
4   LARRY  8.040069   M
6 LEONARD  8.697268   M
7     TIM 10.385221   M

sep$F<-sep$F[order(sep$F[,2]),]
sep$F
x         y sex
3  SUSAN  7.447405   F
5   EMMA  8.306875   F
9 VIOLET 10.177969   F

merged<-rbind(sep$M,sep$F)
merged
x         y sex
1    MARK  6.767086   M
8    MATT  7.497702   M
2     TOM  7.613928   M
4   LARRY  8.040069   M
6 LEONARD  8.697268   M
7     TIM 10.385221   M
3   SUSAN  7.447405   F
5    EMMA  8.306875   F
9  VIOLET 10.177969   F

I know how to do that if I have 2 or 3 factors. But what if I had serious levels of factors, say 20, should I write a for loop?

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order takes multiple arguments, and it does just what you want:

with(score, score[order(sex, y, x),])
##         x        y sex
## 3   SUSAN 6.636370   F
## 5    EMMA 6.873445   F
## 9  VIOLET 8.539329   F
## 6 LEONARD 6.082038   M
## 2     TOM 7.812380   M
## 8    MATT 8.248374   M
## 4   LARRY 8.424665   M
## 7     TIM 8.754023   M
## 1    MARK 8.956372   M

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