Ronny,
Kurtosis is poorly defined in almost every elementary stat textbook around.
"Tailedness" and "peakedness" are both components of kurtosis. It is
impossible to adequately explain kurtosis with just one component. A good
reference that discusses this in much more detail is:
DeCarlo, L.T. (1997). "On the meaning and use of kurtosis". Psychological
Methods, 2, 292-307.
And as far as using EXCEL's help menus as a stat reference, well EXCEL 2000
also claims the following about the two-sample t-test: "You can use t-tests
to determine whether two sample means are equal."
Hope this helps,
Chris
>===== Original Message From Ronny Richardson <[EMAIL PROTECTED]>
=====
>Several references I have looked at define skewness as follows:
>
> mean > median: positive, or right-skewness
> mean = median: symmetry, or zero-skewness
> mean < median: negative, or left-skewness
>
>Now, if I enter the following data into Excel:
>
>-125, -100, -50, -25, -1, 0, 0, 0, 0, 0, 0, 0, 25, 50, 75, 75, 100, 107,
>150, 150
>
>You get a mean of 21.55 and a median of 0 so the mean is larger than the
>median and the data is right-skewed. Excel returns a skewness of 0.028,
>with is positive but barely so.
>
>If I enter the second data set of:
>
>1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 9, 8, 7, 6, 25, 50, 75, 100, 125
>
>Excel returns a mean of 23.50 and a median of 8.00 so the mean and median
>are closer together than data set #1 but the skewness value is 2.035, much
>larger than #1. Why should a mean and median that are closer together
>generate a skewness measure that is so much larger? Does this mean that the
>magnitude of the skewness number has no meaning?
>
>Now, if I delete the two 150's on the end of data set #1 and change the
>ranges on the formulae, I get a mean of 7.28 and I still get a median of 0.
>Again, the mean is larger than the median so this should be positively
>skewed but Excel returns a value of -0.370.
>
>I have verified Excel's calculations manually and they appear to be correct
>so it would appear that the commonly used statement that:
>
> mean > median: positive, or right-skewness
> mean = median: symmetry, or zero-skewness
> mean < median: negative, or left-skewness
>
>is incorrect, or, am I overlooking something?
>
>Excel, and another reference I looked at, state that "The peakeness of a
>distribution is measured by its kurtosis. Positive kurtosis indicates a
>relatively peaked distribution. Negative kurtosis indicates a relatively
>flat distribution."
>
>If that is the case, what does it mean that data set #1 above has a
>kurtosis value of zero?
>
>I appreciate any comments you can supply.
>
>
>
>
>Dr. Ronny Richardson
>Associate Professor of Management
>Southern Polytechnic State University
>School of Management
>1100 South Marietta Parkway
>Marietta, GA 30060-2896
>
>Phone: (770) 528-5542
>Fax: (770) 528-4967
>
>
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Christopher Mecklin, PhD
Assistant Professor
Department of Mathematics and Statistics
Murray State University
Murray, KY 42071
Phone: 270 762-5437
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