Measure of Shape

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Measure of Shape

• (Lesson 02C)
• Seeing Details of Data in Numbers

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Measures of Shape

• The number of days a company takes to pay
  invoices are given on the left
• Do they pay more often late than early?
• To answer this question we need to measure the
  shape of distribution first.

Data St-CE-Ch02-x1-Examples-Slide 33
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Measures of Shape

• Normal Distribution
• Most frequently observed distribution of
  phenomenon in nature.
• Examples
• Coloration of leafs
• Wing span of flies etc.

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Measures of Shape

• Frequency distribution (histogram) of sample data
  can take on different shapes
• Skewness and
• Kurtosis
• are two widely used tools to measure the shape.

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Measures of Shape (Cont.)

• Skewness measures the degree of asymmetry of a
  distribution around the mean. (for meaningful
  results 30 obs. or above)
• Skewness of a distributions is considered
• high if the value is greater than 2ses
• moderate if the value is between (0.5 to 1)ses
  
• symmetric if the value is 0.

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Measures of Shape (Cont.)
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Measures of Shape (Cont.)

• Negatively skewed means longer tail on the left
• In a perfectly symmetric distribution, the mean,
  median, and mode would all be the same
• Comparing measure of central tendency reveal
  information about the shape
• (mean lt mode indicates negative skewness).

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Measures of Shape (Cont.)

• Kurtosis measures the relative peakedness or
  flatness of a distribution.
• Zero Kurtosis indicates normal distribution
• Positive kurtosis indicates a relatively peaked
  distribution. Negative kurtosis indicates a
  relatively flat distribution.

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Measures of Shape (Cont.)

• The following two distributions have the same
  variance approximately the same skew but differ
  in kurtosis.

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Example Measure of Shape (cont.)

• The number of days a company takes to pay
  invoices are given on the left
• 1. Compute skewness and kurtosis
• 2. Explain the meaning of the results.

Data St-CE-Ch02-x1-Examples-Slide 33
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Example Measure of Shape (cont.)

• Analyze/ Descriptive Statistics/Descriptive
• Select the variable move to the right pane
• Select Options, check Mean, Std.Dev, Kurtosis,
  Skewness.
• Continue / Ok

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Example Measure of Shape (cont.)
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Example Measure of C. T. (cont.)

• The the skewness and kurtosis of the data
  pertaining the number of days Tracway takes to
  pay invoices are the following
• Skewness 1.25
• Kurtosis - 0.17
• Explain the meaning of the results.

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Measures of Shape (Cont.)

• ses Standard error of skewness
• (could be obtained from the statistical output
  of SPSS)
• sek Standard error of kurtosis
• (could be obtained from the statistical output
  of SPSS)
• ses sek are measures for statistical
  significance

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Measures of Shape (Cont.)

• Skewness measures the degree of asymmetry of a
  distribution around the mean. (for meaningful
  results 30 obs. or above)
• Skewness of a distributions is considered
• high if the value is greater than 2ses
• moderate if the value is between (0.5 to 1)ses
  
• symmetric if the value is 0.

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Measures of Shape (Cont.)
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Measures of Shape (Cont.)

• Kurtosis measures the relative peakedness or
  flatness of a distribution.
• Kurtosis of a distributions is considered
• high if the value is greater than 2sek
• moderate if the value is between (0.5 to 1)sek
  
• symmetric if the value is 0.

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Example Measure of C. T. (cont.)
Data St-CE-Ch02-x1-Examples-Slide 33
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Meaning Measure of Shape (cont.)

• The skew value suggests that the number of days
  the company takes to pay invoices are highly
  asymmetric (greater than 2ses ). There are
  more occasions than one normally expect that the
  company is stretching its payments
  substantially. However most of the time the
  company is paying its invoices earlier than what
  the mean value suggests.

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Meaning Measure of Shape (cont.)

• In general this company pays its debt on the
  invoices, on average, within 7.5 days.
• This company pays the vast majority of its
  invoices earlier than 7.5 days (skew1.25 gt 2ses
  majority of obs. pmt.). However, when it pays
  late than the late payments are far late than one
  would normally expect (skew1.25 gt 2ses
  asymmetry of obs. pmt.).

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Next Lesson

• (Lesson 02D)
• Frequency Distribution Histogram