1. Exploratory Data Analysis
1.4. EDA Case Studies
1.4.2. Case Studies
1.4.2.4. Josephson Junction Cryothermometry

## Graphical Output and Interpretation

Goal The goal of this analysis is threefold:
1. Determine if the univariate model:

$$Y_{i} = C + E_{i}$$

is appropriate and valid.

2. Determine if the typical underlying assumptions for an "in control" measurement process are valid. These assumptions are:
1. random drawings;
2. from a fixed distribution;
3. with the distribution having a fixed location; and
4. the distribution having a fixed scale.
3. Determine if the confidence interval

$$\bar{Y} \pm 2s/\sqrt{N}$$

is appropriate and valid where s is the standard deviation of the original data.

4-Plot of Data
Interpretation The assumptions are addressed by the graphics shown above:
1. The run sequence plot (upper left) indicates that the data do not have any significant shifts in location or scale over time.

2. The lag plot (upper right) does not indicate any non-random pattern in the data.

3. The histogram (lower left) shows that the data are reasonably symmetric, there does not appear to be significant outliers in the tails, and that it is reasonable to assume that the data can be fit with a normal distribution.

4. The normal probability plot (lower right) is difficult to interpret due to the fact that there are only a few distinct values with many repeats.
The integer data with only a few distinct values and many repeats accounts for the discrete appearance of several of the plots (e.g., the lag plot and the normal probability plot). In this case, the nature of the data makes the normal probability plot difficult to interpret, especially since each number is repeated many times. However, the histogram indicates that a normal distribution should provide an adequate model for the data.

From the above plots, we conclude that the underlying assumptions are valid and the data can be reasonably approximated with a normal distribution. Therefore, the commonly used uncertainty standard is valid and appropriate. The numerical values for this model are given in the Quantitative Output and Interpretation section.

Individual Plots Although it is normally not necessary, the plots can be generated individually to give more detail.
Run Sequence Plot

Lag Plot

Histogram (with overlaid Normal PDF)

Normal Probability Plot