CORRELATION

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• Session 1
• Topic Correlation Analysis
• Faculty Ms Prathima Bhat K
• Department of Management Studies
• Acharya Institute of Technology
• Bangalore 90
• Contact prathimabhatk_at_gmail.com
• 9242187131

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CORRELATION

• Correlation analysis is used as a statistical
  tool to ascertain the association between two
  variables. The problem in analyzing the
  association between two variables can be broken
  down into three steps

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• Try to know whether the two variables are related
  or independent of each other.
• If there is a relationship between the two
  variables, then know its nature strength.
  (i.e., positive/negative how close is that
  relationship)
• Know if there is a causal relationship between
  them. i.e., variation in one variable causes
  variation in another.

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CORRELATION CAUSATION

• Correlation may be due to chance particularly
  when the data pertain to a small sample.
• It is possible that both the variables are
  influenced by one or more other variables.
• It may be that case, where both the variables may
  be influencing each other - we cannot say which
  is the cause and which is the effect.

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TYPES OF CORRELATION

• Positive and negative
• Linear and non-linear
• Simple, partial and multiple

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DIFFERENT METHODS OF CORRELATION
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ALGEBRAIC METHOD (COVARIENCE METHOD)
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PROCESS OF CALCULATION

• Calculate the means of the two series, X Y.
• Take deviations - from their respective means,
  indicated as x and y. The deviation should be
  taken in each case as the value of the individual
  item minus () the arithmetic mean.
• Square the deviations in both the series and
  obtain the sum of the deviation. This would give
  S x2 and S y2.

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PROCESS (Contd..)

• Take the product of the deviations, that is, Sxy.
  This means individual deviations are to be
  multiplied by the corresponding deviations in the
  other series and then their sum is obtained.
• The values thus obtained in the preceding steps
  Sxy, Sx2 and Sy2 are to be used in the formula
  for correlation.

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SHORT-CUT METHOD

• Choose convenient values as assumed means of the
  two series, X and Y.
• Deviations (now dx and dy instead of x and y) are
  obtained from the assumed means in the same
  manner as in the earlier.
• Obtain the sum of the dx and dy columns, that is,
  S dx and S dy.

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SHORT-CUT METHOD (Contd)

• Deviations dx and dy are squared up and their
  totals Sdx2 and S dy2 are obtained.
• Finally, obtain S dxdy, which is the sum of the
  products of deviations taken from the assumed
  means in the two series.