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Topic: Variance question
Replies: 1   Last Post: Jul 15, 1996 3:52 PM

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Richard Slater

Posts: 3
Registered: 12/12/04
Variance question
Posted: Jul 13, 1996 4:13 PM
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I've got 2 data sets - both of companies responding to a
questionnaire. The first set of 15 has a characteristic that the
second set of 27 does not.

The distribution is skewed, the whole sample population displayed a
high degree of skew. The sample was reasonably heavy tailed, the
first 200 companies' employee figures producing a mean of 67.89 and a
median of 57.5, indicating positive skew. The coefficient of
skewness is 1.05, and coefficient of kurtosis is 0.50. The 42
respondents data for numbers of employees produced a mean of 67.29, a
median of 61.5, again indicating positive skew. The coefficient of
skewness for the respondents is 1.23, the coefficient of kurtosis is 1.68.

My calculation of the variance for populations shows that there is a
significant between sample effect at the 0.05 significance level; the
F test statistic of 2.74 exceeds the 5% level of 2.1, and approaches
the 1% level of 2.9, therefore F test on variances shows that the
observed variance ratio is too large to support the null hypothesis
that the populations do not differ significantly.

Questions - data below.
A) Am I right so far ? or does the skewness / non normal distribution
invalidate a variance analysis ?
B) Does the fact that the population is skewed matter - or should I
correct using Bessel's ?
c) If I need to correct - how should I do it ?

F test on variances 2.7438
degrees of freedom 1 (greater) 14
degrees of freedom 2 (lesser) 26

Sample One = 15 respondents
73
181
25
42
49
138
67
48
55
87
30
187
89
72
25

and Sample 2 = 27 respondents

27
63
34
57
64
32
116
118
35
82
84
117
57
64
84
106
27
27
22
60
81
88
31
79
60
22
21

thanks, Richard.





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