Asian School of Business

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Asian School of Business PG Programme in
Management (2005-06) Course Quantitative
Methods in Management I Instructor Chandan
Mukherjee Session 4 Summarising a Distribution
(contd.) Changing the Shape of
a Distribution Power Transformation
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Log Transformation to Symmetry
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An Interpretation of Log Transformation
Try to place the following four countries on the
scale of Per Capita Gross National Income
COUNTRY
India
South Korea
New Zealand
Denmark
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An Interpretation of Log Transformation (contd.)
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An Interpretation of Log Transformation (contd.)
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An Interpretation of Log Transformation (contd.)
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Compare Wages of Permanent Casual Workers
(Sample from
Industries in Coimbatore)
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Outliers Indentified by Sex of the Worker
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Log Transformation to Symmetry
Weekly Earnings Data
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After Log Transformation Finding Out What Lies
Below the Pattern of Skewness
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Who Are The Outliers?
Women Always Loose Out to Men!
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Log Transformation to Symmetry It doesnt work
always
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Changing the Shape of a Distribution Ladder of
Transformation
Yp if p gt 0 reduces negative
skewness Log(Y) if p 0 reduces
positive -Yp if p lt 0 skewness Ladder of
Power p 3 Y3 reduces negative p 2 Y2
skewness p 1 Y no effect p
0.5 Y0.5 reduces p 0 Log(Y) positive p
-0.5 -Y-0.5 skewness
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Power Transformation