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1. Exploratory Data Analysis
1.2. EDA Assumptions


Interpretation of 4-Plot

Interpretation of EDA Plots:
Flat and Equi-Banded, Random, Bell-Shaped, and Linear
The four EDA plots discussed on the previous page are used to test the underlying assumptions:
  1. Fixed Location:
    If the fixed location assumption holds, then the run sequence plot will be flat and non-drifting.

  2. Fixed Variation:
    If the fixed variation assumption holds, then the vertical spread in the run sequence plot will be the approximately the same over the entire horizontal axis.

  3. Randomness:
    If the randomness assumption holds, then the lag plot will be structureless and random.

  4. Fixed Distribution:
    If the fixed distribution assumption holds, in particular if the fixed normal distribution holds, then
    1. the histogram will be bell-shaped, and
    2. the normal probability plot will be linear.
Plots Utilized to Test the Assumptions Conversely, the underlying assumptions are tested using the EDA plots:
  • Run Sequence Plot:
    If the run sequence plot is flat and non-drifting, the fixed-location assumption holds. If the run sequence plot has a vertical spread that is about the same over the entire plot, then the fixed-variation assumption holds.

  • Lag Plot:
    If the lag plot is structureless, then the randomness assumption holds.

  • Histogram:
    If the histogram is bell-shaped, the underlying distribution is symmetric and perhaps approximately normal.

  • Normal Probability Plot:
    If the normal probability plot is linear, the underlying distribution is approximately normal.
If all four of the assumptions hold, then the process is said definitionally to be "in statistical control".
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