1. Exploratory Data Analysis
1.4. EDA Case Studies
1.4.2. Case Studies
1.4.2.10. Ceramic Strength

1.4.2.10.2.

Analysis of the Response Variable

Numerical Summary

As a first step in the analysis, a table of summary statistics is computed for the response variable. The following table, generated by Dataplot, shows a typical set of statistics.

 
                                SUMMARY
 
                     NUMBER OF OBSERVATIONS =      480
 
 
***********************************************************************
*        LOCATION MEASURES         *       DISPERSION MEASURES        *
***********************************************************************
*  MIDRANGE     =   0.5834740E+03  *  RANGE        =   0.4763600E+03  *
*  MEAN         =   0.6500773E+03  *  STAND. DEV.  =   0.7463826E+02  *
*  MIDMEAN      =   0.6426155E+03  *  AV. AB. DEV. =   0.6184948E+02  *
*  MEDIAN       =   0.6466275E+03  *  MINIMUM      =   0.3452940E+03  *
*               =                  *  LOWER QUART. =   0.5960515E+03  *
*               =                  *  LOWER HINGE  =   0.5959740E+03  *
*               =                  *  UPPER HINGE  =   0.7084220E+03  *
*               =                  *  UPPER QUART. =   0.7083415E+03  *
*               =                  *  MAXIMUM      =   0.8216540E+03  *
***********************************************************************
*       RANDOMNESS MEASURES        *     DISTRIBUTIONAL MEASURES      *
***********************************************************************
*  AUTOCO COEF  =  -0.2290508E+00  *  ST. 3RD MOM. =  -0.3682922E+00  *
*               =   0.0000000E+00  *  ST. 4TH MOM. =   0.3220554E+01  *
*               =   0.0000000E+00  *  ST. WILK-SHA =   0.3877698E+01  *
*               =                  *  UNIFORM PPCC =   0.9756916E+00  *
*               =                  *  NORMAL  PPCC =   0.9906310E+00  *
*               =                  *  TUK -.5 PPCC =   0.8357126E+00  *
*               =                  *  CAUCHY  PPCC =   0.5063868E+00  *
***********************************************************************

From the above output, the mean strength is 650.08 and the standard deviation of the strength is 74.64.

4-Plot

The next step is generate a 4-plot of the response variable.

This 4-plot shows:

1. The run sequence plot (upper left corner) shows that the location and scale are relatively constant. It also shows a few outliers on the low side. Most of the points are in the range 500 to 750. However, there are about half a dozen points in the 300 to 450 range that may require special attention.

   A run sequence plot is useful for designed experiments in that it can reveal time effects. Time is normally a nuisance factor. That is, the time order on which runs are made should not have a significant effect on the response. If a time effect does appear to exist, this means that there is a potential bias in the experiment that needs to be investigated and resolved.

2. The lag plot (the upper right corner) does not show any significant structure. This is another tool for detecting any potential time effect.

3. The histogram (the lower left corner) shows the response appears to be reasonably symmetric, but with a bimodal distribution.

4. The normal probability plot (the lower right corner) shows some curvature indicating that distributions other than the normal may provide a better fit.