1. Exploratory Data Analysis
1.2. EDA Assumptions
1.2.5. Consequences

1.2.5.2.

Consequences of Non-Fixed Location Parameter

Location Estimate

The usual estimate of location is the mean

$$\bar{Y} = \frac{1}{N} \sum_{i=1}^{N}{Y_i}$$

from N measurements Y₁, Y₂, ... , Y_N.

Consequences of Non-Fixed Location

If the run sequence plot does not support the assumption of fixed location, then

1. The location may be drifting.

2. The single location estimate may be meaningless (if the process is drifting).

3. The choice of location estimator (e.g., the sample mean) may be sub-optimal.

4. The usual formula for the uncertainty of the mean:

   $$s(\bar{Y}) = \frac{1}{\sqrt{N(N-1)}} \sqrt{\sum_{i=1}^{N}{(Y_i - \bar{Y})^2}}$$

   may be invalid and the numerical value optimistically small.

5. The location estimate may be poor.

6. The location estimate may be biased.