Two selections from Bag A

All, I am looking at an example in Aliaga's Interactive Statistics.  
Bag A has
the following vouchers.

BagA <- c(-1000,10,10,10,10,10,10,
         10,20,20,20,20,20,20,30,
         30,40,40,50,60)

Bag B has the following vouchers.

BagB <- c(10,20,30,30,40,40,50,50,
         50,50,50,50,60,60,60,60,
         60,60,60,1000)

Two values are selected (from BagA or BagB) without replacement. In  
Table
1.1 on page 54 of the third edition, she lists all "Possible two  
values
selected" in columns one and two,

?unique
?expand.grid or ?combn

Perhaps spliting names from the tabulation below>

the "Average of the two selected values"

?mean

in column three and "BAG A Numbers of way of selecting the two  
values" in
column four, and "BAG B Number of ways of selecting the two values" in
column five.

Here are the first few rows:

-1000       -1000     -1000     0     0

Why is that combination even listed?

-1000             10      -495      7     0
-1000             20     -490       6     0
-1000            30      -485       2     0
-1000            40      -480       2     0
-1000            50      -475       1     0
-1000            60      -470       1     0
-1000       1000             0       0     0

What are the rules for listing a combination?

     10           10           10     21     0
     10            20           15    42      1

I can get that value if choosing just from BagA, but if the  
possibilities are for either bag to be selected, then an additional  
value would arise because 10 and 20 are in BagB.

?table

?apply
?paste

...

She then condenses the data in Table 1.2 on page 55, the first column
holding "Average of the two selected values', the second column  
holding "BAG
A Number of ways of selecting the two values," and third column  
holding "BAG
B Number of ways of selecting the two values."

Here are a few sample rows:

-1000     0     0
 -495     7     0
 -490     6     0
....

Can anyone help show me an efficient way of creating these two tables?

table( apply( combn(BagA,2), 2, function(x) paste( sort(x), sep=".",  
collapse=".") ) )

table( apply( combn(BagB,2), 2, function(x) paste( sort(x), sep=".",  
collapse=".") ) )


You should be able to take it from this illustration of how to get the  
BagA results:

cbind( do.call( rbind ,
             sapply(names(table( apply( combn(BagA,2), 2, function(x)  
paste( sort(x), sep=".", collapse=".") ) ) ) , strsplit, split= "\ 
\.") ),  # first 2 columns
        table( apply( combn(BagA,2), 2, function(x) paste( sort(x),  
sep=".", collapse=".") ) ) )
          [,1]    [,2] [,3]
-1000.10 "-1000" "10" "7"
-1000.20 "-1000" "20" "6"
-1000.30 "-1000" "30" "2"
-1000.40 "-1000" "40" "2"
-1000.50 "-1000" "50" "1"
-1000.60 "-1000" "60" "1"
10.10    "10"    "10" "21"
10.20    "10"    "20" "42"
10.30    "10"    "30" "14"
10.40    "10"    "40" "14"
10.50    "10"    "50" "7"
10.60    "10"    "60" "7"
20.20    "20"    "20" "15"
20.30    "20"    "30" "12"
20.40    "20"    "40" "12"
20.50    "20"    "50" "6"
20.60    "20"    "60" "6"
30.30    "30"    "30" "1"
30.40    "30"    "40" "4"
30.50    "30"    "50" "2"
30.60    "30"    "60" "2"
40.40    "40"    "40" "1"
40.50    "40"    "50" "2"
40.60    "40"    "60" "2"
50.60    "50"    "60" "1"

David.


David Winsemius, MD
Alameda, CA, USA

Here are the two tables from Aligaga. The first is table 1.1 and the second
is table 1.2.

http://r.789695.n4.nabble.com/file/n4641344/table1_1.jpg 

http://r.789695.n4.nabble.com/file/n4641344/table1_2.jpg 

David Arnold
College of the Redwoods



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View this message in context: http://r.789695.n4.nabble.com/Two-selections-from-Bag-A-tp4641327p4641344.html
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Here are the two tables from Aligaga. The first is table 1.1 and the  
second
is table 1.2.

http://r.789695.n4.nabble.com/file/n4641344/table1_1.jpg

My code from earlier today (that you have not included) showed you how  
to tabulate and construct the BagA entries. I actually did it  by way  
of makine a dataframe from the names of the table and a counts column  
with the table.  In Table 1.1 the two Bags combinations have been  
merge()-ed by their value columns.

 > merge(BagAcombs, BagBcombs, by=1:2, all=TRUE)
       X1   X2 counts.x counts.y
1  -1000   10        7       NA
2  -1000   20        6       NA
3  -1000   30        2       NA
4  -1000   40        2       NA
5  -1000   50        1       NA
6  -1000   60        1       NA
7     10   10       21       NA
8     10   20       42        1
9     10   30       14        2
10    10   40       14        2
11    10   50        7        6
12    10   60        7        7
13    10 1000       NA        1
  .... Rest of  output deleted

That object was assigned to "Combs".
I made the labels numeric. NA values were set to 0.

Combs$X1 <- as.numeric(as.character(Combs$X1))
Combs$X2 <- as.numeric(as.character(Combs$X2))

Calculate and average:

 > Combs$Average <- with( Combs, rowMeans(X1,X2) )

http://r.789695.n4.nabble.com/file/n4641344/table1_2.jpg

So the second table is aggregated (summed and sorted)  by the distinct  
values in the average-column of the first. (The 7 A 10 x 50 values are  
added to the 12 A 20 x 40 values and the single 1 A 30 x 30 to give 20  
in the 30 row for A). You should create a factor and aggregate in the  
usual manner.

 > aggregate(Combs[ , 3:5], list(Combs$Average), FUN=sum)
    Group.1 counts.x counts.y Average
1     -495        7        0    -495
2     -490        6        0    -490
3     -485        2        0    -485
4     -480        2        0    -480
5     -475        1        0    -475
6     -470        1        0    -470
7       10       21        0      10
8       15       42        1      15
9       20       29        2      40
10      25       26        4      50
11      30       20        9      90
... rest of output deleted.

The top and bottom rows of both tables appear to me to have no value.  
They are not really items in the sample space or the problem and their  
purpose remains a mystery.


(And ... Please do learn to include context.)

David Arnold
College of the Redwoods

David Winsemius, MD
Alameda, CA, USA