# [R] boxplot question

Antje niederlein-rstat at yahoo.de
Mon Nov 23 10:40:49 CET 2009

```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:
>
> 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
>
> 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

```