boxplot question

Hi there,

I was wondering if anybody can explain to me why the boxplot ends up 
with different results in the following case:

I have some integer data as a vector and I compare the stats of boxplot 
with the same data divided by a factor.

I've attached a csv file with both data present (d1, d2). The factor is 
34.16667.

If I run the boxplot function on d1 I get the following stats:

0.848...
0.907...
0.936...
0.965...
1.024...

For d2 I get these stats:

29
31
32
33
36


If I convert the stats of d1 with the factor, I get

29
31
32
33
35

Obviously different for the upper whisker. But why???

Antje

------------------------------------------------------------------------

If there's been an answer to this, I've missed it.
Here's my take.

Antje wrote:

Hi there,

I was wondering if anybody can explain to me why the boxplot ends up 
with different results in the following case:

I have some integer data as a vector and I compare the stats of 
boxplot with the same data divided by a factor.

I've attached a csv file with both data present (d1, d2). The factor 
is 34.16667.

If I run the boxplot function on d1 I get the following stats:

0.848...
0.907...
0.936...
0.965...
1.024...

For d2 I get these stats:

29
31
32
33
36


If I convert the stats of d1 with the factor, I get

29
31
32
33
35

Obviously different for the upper whisker. But why???

Antje

Antje:

Three comments:
1. I think your 'factor' is actually 205/6, not 34.16667.

2. This looks like another case of FAQ 7.31:

# Let's take your d2 and create d1; I'll call them x and y:
x <- rep(c(29:38, 40), c(7, 24, 50, 71, 24, 12, 14, 7, 13, 5, 1))
y <- x * 6 / 205

# x is your d2, sorted
# y is your d1, sorted

# The critical values are x[202:203] and y[202:203];
x[201:204]
#[1] 35 35 36 36

# The boxplot stats are:
sx <- boxplot.stats(x)$stats
sy <- boxplot.stats(y)$stats

# Calculate potential extent of upper whisker:
ux <- sx[4] + (sx[4] - sx[2]) * 1.5  #36
uy <- sy[4] + (sy[4] - sy[2]) * 1.5  #1.053658536585366

# Is y[203] <= uy?
y[203] <= uy
#[1] FALSE  #!!!

y[202] <= uy
#[1] TRUE

# For x:
x[203] <= ux
#[1] TRUE

And there's your answer: for y the whisker
goes to y[202], not y[203], due to the inevitable
imprecision in machine calculation.

3. last comment: I would not use boxplots for data like this.

 -Peter Ehlers

Peter Ehlers wrote:

If there's been an answer to this, I've missed it.
Here's my take.

Antje wrote:

Hi there,

I was wondering if anybody can explain to me why the boxplot ends up 
with different results in the following case:

I have some integer data as a vector and I compare the stats of 
boxplot with the same data divided by a factor.

I've attached a csv file with both data present (d1, d2). The factor 
is 34.16667.

If I run the boxplot function on d1 I get the following stats:

0.848...
0.907...
0.936...
0.965...
1.024...

For d2 I get these stats:

29
31
32
33
36


If I convert the stats of d1 with the factor, I get

29
31
32
33
35

Obviously different for the upper whisker. But why???

Antje

Antje:

Three comments:
1. I think your 'factor' is actually 205/6, not 34.16667.

2. This looks like another case of FAQ 7.31:

# Let's take your d2 and create d1; I'll call them x and y:
x <- rep(c(29:38, 40), c(7, 24, 50, 71, 24, 12, 14, 7, 13, 5, 1))
y <- x * 6 / 205

# x is your d2, sorted
# y is your d1, sorted

# The critical values are x[202:203] and y[202:203];
x[201:204]
#[1] 35 35 36 36

# The boxplot stats are:
sx <- boxplot.stats(x)$stats
sy <- boxplot.stats(y)$stats

# Calculate potential extent of upper whisker:
ux <- sx[4] + (sx[4] - sx[2]) * 1.5  #36
uy <- sy[4] + (sy[4] - sy[2]) * 1.5  #1.053658536585366

# Is y[203] <= uy?
y[203] <= uy
#[1] FALSE  #!!!

y[202] <= uy
#[1] TRUE

# For x:
x[203] <= ux
#[1] TRUE

And there's your answer: for y the whisker
goes to y[202], not y[203], due to the inevitable
imprecision in machine calculation.

3. last comment: I would not use boxplots for data like this.

 -Peter Ehlers

Hi Peter,

thanks a lot for your explanation! Now I understand the difference. I 
was using the boxplot statistic to filter outliers from my data. Do you 
have any suggestion for me what to use instead? (I tried to improve the 
estimation of mean and sd, when iteratively removing outliers by boxplot 
stats...)

Antje