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Topic: standard deviation for 1-mean?
Replies: 7   Last Post: Jan 21, 2012 4:35 PM

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 Richard Ulrich Posts: 2,813 Registered: 12/13/04
Re: standard deviation for 1-mean?
Posted: Jan 21, 2012 4:35 PM

On Fri, 20 Jan 2012 23:41:42 -0800 (PST), Kerry <kbrownk@gmail.com>
wrote:

>On Jan 21, 1:12 am, Rich Ulrich <rich.ulr...@comcast.net> wrote:
>> On Fri, 20 Jan 2012 16:52:05 -0800 (PST), Kerry <kbro...@gmail.com>
>> wrote:
>>

...
>>
>> >On Jan 20, 6:00 pm, Kerry <kbro...@gmail.com> wrote:
>> >> I have a mean value for a sample of data that = 0.81 +/- 0.17 standard
>> >> deviation, where the value could have been between 0 and 1. I'd rather
>> >> present the mean as 1-mean = 0.19. But what would the standard
>> >> deviation be? I'd rather not have to go back to the original
>> >> individual values from the sample if possible. Is there a way to
>> >> derive the standard deviation without having to do this? For instance,
>> >> the coefficient of variation is 0.21. Can I assume the coefficient of
>> >> variation will be the same for 1-mean and find the standard deviation
>> >> that way (i.e. standard deviation = (1-mean)*(coef var) =
>> >> (0.19)*(0.21) = 0.04)?

>>
>> >> Thanks,
>>
>> >I just generated some fake data and found that the std dev is the same
>> >for mean and 1-mean. I guess that's not surprising, but it makes me
>> >question the usefulness of coefficient of variation for my data, which
>> >I planned on reporting.I guess because the data is naturally scaled by
>> >being between 0 and 1, coef var is not more informative, but it
>> >actually seems less informative in my case.

>>
>> The coefficient of variation is mainly useful for log-normal data.
>> I don't think of other cases where it says much.
>>
>> For log-normal data, it represents the error in a form that tends
>> to be constant and consistent across various samples, despite
>> variations in those means - even large variations.  It is sometimes
>> used for reporting the size of measured errors in drug concentrations.
>>
>>  - For data of that kind, the coefficient shows the same information
>> that you get from reporting the SD of the log of the data, if you
>> were presenting the data in the form of the logs.
>>
>> --
>> Rich Ulrich

>
>Coef Var is also useful for scaling variability in cases when you're
>comparing two groups, and you'd expect bigger values to naturally lead
>to more variance. For instance, if I wanted to see how weather
>conditions affect time to climb 2 different mountains, if one mountain
>is 10 times as big, then you expect the same weather conditions to
>cause more variance in the bigger mountain. Depending on what I'm
>interested in, coef var can be informative in in this case.

When you find yourself naturally and appropriately speaking of one
as "10 times as big" as the other, you ought to think of the log as
potentially being relevent.

If you are saying that reporting the c.o.v. can remind the reader
that variances will vary, that is probably true.

When your variable is bounded at both ends, and has lower
variance at either end, that is cause to consider a "folded"
transformation (I think that is what Tukey called them) like
the logistic.

> The
>original case that I provided above was a mean of a ratio b/t 0 and 1,
>
>Thanks,
>kb

Date Subject Author
1/20/12 Hosley
1/20/12 dvdavins@pobox.com
1/20/12 dvdavins@pobox.com
1/20/12 Hosley
1/21/12 Richard Ulrich
1/21/12 Hosley
1/21/12 Richard Ulrich
1/21/12 Ray Koopman