Yorgi V. <[EMAIL PROTECTED]> asked:
> My question is -- can I somehow systematically compare the
> variability of two samples from different populations?
The short answer is "Yes". Your comments about the disparate shapes of
the two distributions, however, leads one to wonder whether the standard
method of comparison (F = variance1/variance2, with df1 and df2 degrees
of freedom) is appropriate.
On the other hand, what do you mean by "appears highly skewed on
both tails"? The usual meaning of "skewed" is that the distribution is
unsymmetrical, with a long tail in one direction (the direction of skew
-- if the tail points toward (larger) positive numbers, the skew is said
to be positive, and if it points toward negative numbers, the skew is
said to be negative. If both distributions are at least approximately
symmetrical, there should be no serious problems with the usual F ratio.
In any case, you have not reported the variances in question,
only the means of the two variables.
On Wed, 5 Apr 2000 [EMAIL PROTECTED] wrote:
> I am not experienced statistician but I have one simple question. I
> have 2 continuous variables from different populations. One has a mean
> of 50 one has a mean of 0.3. When I graph their distributions the
> first one (with 50 mean) appears to be less variable than the second
> (with mean of 0.3). It has a very gaussian appearance, whereas the
> other appears highly skewed on both tails. However, because the first
> has much larger magnitude, it has larger variance.
This sounds contradictory. How can the first variable (mean 50)
be less variable than the second (mean 0.3), if it has larger variance?
I infer that by "less (or more) variable" you refer to something other
than the variance of the variable in question. And your last sentence,
"because the first has larger magnitude, it has larger variance",
suggests that there are characteristics of the variables that are
important to know about, but that you have not mentioned.
1. Is there a reason why one would expect a variables with a large
mean to have a large variance?
2. Why, precisely, do you want to compare the variances (or, more
generally, the variabilities) of these variables?
3. If you want more specific help from us, it would help if you
could supply more information about the variables, and some kind
of display of the distributions (Minitab-style histograms,
dotplots, and stem-and-leaf diagrams spring to mind).
> My question is -- can I somehow systematically compare the
> variability of two samples from different populations? Perhaps there
> is some sort of method for standardizing variances? I would like to
> do better than simply say "the graphs suggest that one variable is
> more/less variable than the other" which is what I am doing now.
In what terms are you doing that? You have said above that
the variable that appears less variable is the one with the greater
variance. You can't be reporting _that_, or whoever you're reporting
to would surely wonder (with some justification) if you were out of
your mind.
------------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 603-535-2597
184 Nashua Road, Bedford, NH 03110 603-471-7128
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