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1. Exploratory Data Analysis
1.2. EDA Assumptions


Techniques for Testing Assumptions

Testing Underlying Assumptions Helps Assure the Validity of Scientific and Engineering Conclusions Because the validity of the final scientific/engineering conclusions is inextricably linked to the validity of the underlying univariate assumptions, it naturally follows that there is a real necessity that each and every one of the above four assumptions be routinely tested.
Four Techniques to Test Underlying Assumptions The following EDA techniques are simple, efficient, and powerful for the routine testing of underlying assumptions:
  1. run sequence plot (Yi versus i)
  2. lag plot (Yi versus Yi-1)
  3. histogram (counts versus subgroups of Y)
  4. normal probability plot (ordered Y versus theoretical ordered Y)
Plot on a Single Page for a Quick Characterization of the Data The four EDA plots can be juxtaposed for a quick look at the characteristics of the data. The plots below are ordered as follows:
  1. Run sequence plot - upper left
  2. Lag plot - upper right
  3. Histogram - lower left
  4. Normal probability plot - lower right
Sample Plot: Assumptions Hold A 4-Plot which shows fixed location, fixed variation, fixed normal
 distribution, and no outliers

This 4-plot of 500 normal random numbers reveals a process that has fixed location, fixed variation, is random, apparently has a fixed approximately normal distribution, and has no outliers.

Sample Plot: Assumptions Do Not Hold If one or more of the four underlying assumptions do not hold, then it will show up in the various plots as demonstrated in the following example.

A 4-plot which shows fixed location, fixed variation,
 non-randomness, a non-normal U-shaped distribution, and
 several outliers

This 4-plot reveals a process that has fixed location, fixed variation, is non-random (oscillatory), has a non-normal, U-shaped distribution, and has several outliers.

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