FW: Adjusting a mean to reflect variability
Locked
FW: Adjusting a mean to reflect variability
 
|
Subject: Adjusting a mean to
reflect variability In measuring customer satisfaction (Scale 1-10 1=Poor) it’s
possible to get the same mean from vastly different distributions. I want to adjust the mean to accommodate this. An example may best illustrate. Usually the mean score is shown. In this case both product
are equal. But instinctively I prefer Product B as it has the lower
Standard Deviation. I’m looking for a method to adjust the mean to reflect this. Not all my customers understand the relationship between the
mean & the standard deviation so I rarely include the StdDev. I’m looking for one number – an adjusted mean – if something
like this exists.
|
Re: FW: Adjusting a mean to reflect variability
|
|
At 10:01 PM 2/18/2009, Mark Webb wrote:
Subject: Adjusting a mean to reflect variability Um, Mark, IIRC, the characteristic of a normal distribution is that the mean and the variance are *independent*. If you want a distribution in which the mean and variance are related, then you want something like a Poisson distribution, and statistics that are based on that distribution. An example may best illustrate. Do you have some reason (other than instinct) why you think the mean and the variance *should* be related? I'm not saying that such instincts are necessarily wrong; your instinct may be based on an intuitive understanding of the phenomena you're dealing with, and perhaps your instinct is right. If so, I suggest exploring your instinct a bit more to see if you can understand why you think that the mean and standard deviation should be related, and how. Bob Schacht Im looking for a method to adjust the mean to reflect this. Robert M. Schacht, Ph.D., Research Director
Pacific Basin Research and Training Center
1268 Young Street, Suite #204
Research Center, University of Hawaii
Honolulu, HI 96814
E-mail <[hidden email]>
Phone 808-592-5904, FAX 808-592-5909
|
Re: FW: Adjusting a mean to reflect variability
|
|
Don't report means in this case. The means, absent distributional information, aren't particularly useful (as you already noticed). |
Re: FW: Adjusting a mean to reflect variability
|
|
In reply to this post by Mark Webb-3
Mark ... Both the mean and the sd are informative
for understanding respondents'' satisfaction with Product A and Product
B. Their average satisfaction was the same for both products,
but their satisfaction varied more widely with A than with B. It's
not clear why you would want to adjust that difference
away.
Art From: Mark Webb [mailto:[hidden email]] Sent: Thursday, February 19, 2009 12:01 AM To: [hidden email] Subject: FW: Adjusting a mean to reflect variability In measuring customer satisfaction (Scale 1-10 1=Poor) it’s
possible to get the same mean from vastly different
distributions. I want to adjust the mean to accommodate this.
An example may best illustrate. Usually the mean score is shown. In this case both product
are equal. But instinctively I prefer Product B as it has the lower
Standard Deviation. I’m looking for a method to adjust the mean to reflect
this. Not all my customers understand the relationship between the
mean & the standard deviation so I rarely include the StdDev. I’m looking for one number – an adjusted mean – if something
like this exists.
|
Re: Adjusting a mean to reflect variability
|
|
From your request, it sounds like you may want the coefficient of variation. It is a standardized measure (SD/Mean) that reflects the “true” variability is a frequency distribution. In general, lower values suggest greater stability (i.e., lower variance relative to the mean of the distribution) while higher values represent lower stability (i.e., higher variance relative to the mean of the distribution). In your case, the two sets of data yield very different coefficients. The first yields .551, while the second yields a much smaller value: .096. These values, since they are in the same “dimensionless” units can be express as a ratio. In your case, the ratio of the more stable/less stable distributions would be quite large: .551/.096 ~ 5.7. This would suggest that the mean of the second distribution is much more “representative” of all its scores than is the mean in the first distribution for all its scores. In your specific case, because the means are the same, you could simply calculate the ratio of the two SDs and get the same outcome (3.03/.53 ~ 5.7) Hope this gives you what you wanted. Harley . Dr. Harley Baker Associate Professor and Chair, Psychology Program California State University Channel Islands One University Drive Camarillo, CA 93012 805.437.8997 (p) 805.437.8951 (f) [hidden email] From: Arthur Burke <[hidden email]> Reply-To: Arthur Burke <[hidden email]> Date: Thu, 19 Feb 2009 11:29:27 -0800 To: <[hidden email]> Conversation: FW: Adjusting a mean to reflect variability Subject: Re: FW: Adjusting a mean to reflect variability Mark ... Both the mean and the sd are informative for understanding respondents'' satisfaction with Product A and Product B. Their average satisfaction was the same for both products, but their satisfaction varied more widely with A than with B. It's not clear why you would want to adjust that difference away. Art From: Mark Webb [[hidden email] Sent: Thursday, February 19, 2009 12:01 AM To: [hidden email] Subject: FW: Adjusting a mean to reflect variability Subject: Adjusting a mean to reflect variability In measuring customer satisfaction (Scale 1-10 1=Poor) it’s possible to get the same mean from vastly different distributions. I want to adjust the mean to accommodate this. An example may best illustrate. Usually the mean score is shown. In this case both product are equal. But instinctively I prefer Product B as it has the lower Standard Deviation. I’m looking for a method to adjust the mean to reflect this. Not all my customers understand the relationship between the mean & the standard deviation so I rarely include the StdDev. I’m looking for one number – an adjusted mean – if something like this exists. Respondent Product A Product B 1 1 5 2 2 5 3 3 6 4 4 5 5 5 5 6 6 6 7 7 5 8 8 6 9 9 6 10 10 6 Mean 5.5 5.5 Stdev 3.03 0.53 |
Re: FW: Adjusting a mean to reflect variability
|
|
In reply to this post by Arthur Burke
Mark, As Art says, both mean and SD are useful,
and they really measure different properties of the distribution. Apparently
you pay attention to both: you prefer a product with higher mean, AND with
lower SD. Both are independent of each other, and
each product can be described by both figures, like a point in a map can be
located by latitude and longitude: you cannot “correct for dispersion in
longitude” by adjusting the latitude. You will have to use both. What you apparently want is to figure out
a “preference score”, a single figure which is an increasing
function of the mean and a decreasing function of the SD, as in P=a(M)-b(SD), but
that would imply giving relative weights (a and b) to each dimension (the mean
and the SD), and there is really no conceptual basis for such weights. Changing
the weights would change the results. In the case of latitude and longitude,
such function is simply the distance between two points with different Lat and
different Long, both with the same weight. The distance formula, by Pythagoras
theorem, is the square root of the sum of the Lat squared plus the Long squared.
You can compare two distances (from a reference point) using the formula. But
in the case of Mean and SD you do not have any such formula. And any formula
you choose would be arbitrary. Hector From: SPSSX(r)
Discussion Mark ... Both the mean and the sd are
informative for understanding respondents'' satisfaction with Product A
and Product B. Their average satisfaction was the same for both products,
but their satisfaction varied more widely with A than with B. It's
not clear why you would want to adjust that difference away. Art From: Mark Webb
I want to adjust
the mean to accommodate this. An example may
best illustrate. Usually the mean
score is shown. In this case both product are equal. But instinctively
I prefer Product B as it has the lower Standard Deviation. I’m looking
for a method to adjust the mean to reflect this. Not all my
customers understand the relationship between the mean & the standard
deviation so I rarely include the StdDev. I’m looking
for one number – an adjusted mean – if something like this exists.
|
| Free forum by Nabble | Edit this page |