Empirical/Normal CDF Plots

The Empirical/Normal CDF (Cumulative Distribution Function) Plot shows the data values sorted from lowest to highest on the X axis with the respective percentiles (percentages) on the Y axis and may be compared against the same for the fitted Normal Distribution. It is similar to the Normal Probability Plot but instead of a straight line it will form an "S-shaped" curve. The empirical data is plotted as a blue stepped line, whereas the fitted normal distribution is shown as a smooth red line. Large deviations between the two indicate that the data are not normally distributed.

1. We will repeat the examples used for Normal Probability Plots. Click SigmaXL Random Data (1) Sheet (if not available please do Steps 1 and 2 given in the example).
   
   
2. Click SigmaXL > Graphical Tools > Empirical/Normal CDF Plots. Ensure that the entire data table is selected. If not, check Use Entire Data Table. Click Next.
   
   
3. Select Normal Data, click Numeric Data Variables (Y) >>. Check Display Normal CDF Plots.
   
   
   
   Note that Empirical/Normal CDF Plots permit multiple Y variables. If more than one Y is selected Group Category (X) is greyed out.
   
   
4. Click OK. An Empirical/Normal CDF Plot of the simulated random data is produced (your plot will be slightly different due to the random number generation):
   
   
   
   The Empirical CDF plot follows the Normal CDFfairly well, indicating that the data is normally distributed.
   
   
5. Click Sheet 1 Tab of Customer Data.xlsx.
   
   
6. Click SigmaXL > Graphical Tools > Empirical/Normal CDF Plots. Ensure that the entire data table is selected. If not, check Use Entire Data Table. Click Next.
   
   
7. Select Overall Satisfaction; click Numeric Data Variables (Y) >>. Click OK. An Empirical/Normal CDF Plot of the Overall Satisfaction data is produced:
   
   
   
   The Empirical CDF plot does not follow the Normal CDF well, indicating that the data is not normally distributed. The Empirical curve hits 100% at Overall Satisfaction = 5 since that was the maximum possible survey value, resulting in a skewed left distribution as noted in the histogram.
   
   
8. Now we would like to stratify the customer satisfaction score by customer type and look at the Empirical/Normal CDF plots.
   
   
9. Click Sheet 1 of Customer Data.xlsx. Click SigmaXL > Graphical Tools > Empirical/Normal CDF Plots . Ensure that Entire Table is selected, click Next. (Alternatively, press F3 or click Recall SigmaXL Dialog to recall last dialog).
   
   
10. Select Overall Satisfaction, click Numeric Data Variables (Y) >>; select Customer Type as Group Category (X) >>.
    
    
    
    
11. Click OK. Empirical/Normal CDF Plots of Overall Satisfaction by Customer Type are produced:
    
    
    
    We can see that the Empirical CDF plot for Customer Type 2 does not follow the Normal CDF well, indicating that the data is not normally distributed. The Empirical curve hits 100% at Overall Satisfaction = 5 since that was the maximum possible survey value, resulting in a skewed left distribution as noted in the histogram.
    
    Customer Types 1 and 3 are harder to interpret, so we would use normal probability plots and normality tests to complement these plots to asses normality.
    
    Tip: Empirical CDF Plots may also be compared against each other by using Excel's copy/paste for the graphs. In this case, it is recommended to uncheck the Display Normal CDF Plots option when creating the plots. The Two Sample KS Test is a formal test used to compare two empirical CDFs. See Two Sample Mann-Whitney Test(with 2 Sample KS Option).