1. Exploratory Data Analysis
1.2. EDA Assumptions

1.2.4.

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".