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1. Exploratory Data Analysis
1.4. EDA Case Studies
1.4.2. Case Studies
1.4.2.2. Uniform Random Numbers

1.4.2.2.4.

Work This Example Yourself

View Dataplot Macro for this Case Study This page allows you to repeat the analysis outlined in the case study description on the previous page using Dataplot . It is required that you have already downloaded and installed Dataplot and configured your browser. to run Dataplot. Output from each analysis step below will be displayed in one or more of the Dataplot windows. The four main windows are the Output window, the Graphics window, the Command History window, and the data sheet window. Across the top of the main windows there are menus for executing Dataplot commands. Across the bottom is a command entry window where commands can be typed in.
Data Analysis Steps Results and Conclusions

Click on the links below to start Dataplot and run this case study yourself. Each step may use results from previous steps, so please be patient. Wait until the software verifies that the current step is complete before clicking on the next step.


The links in this column will connect you with more detailed information about each analysis step from the case study description.

1. Invoke Dataplot and read data.
   1. Read in the data.


                              
 1. You have read 1 column of numbers 
    into Dataplot, variable Y.
2. 4-plot of the data.
   1. 4-plot of Y.


 1. Based on the 4-plot, there are no shifts
    in location or scale, and the data do not
    seem to follow a normal distribution.
3. Generate the individual plots.
   1. Generate a run sequence plot.


   2. Generate a lag plot.


   3. Generate a histogram with an
      overlaid normal pdf.

   4. Generate a histogram with an
      overlaid uniform pdf.

   5. Generate a normal probability
      plot.

   6. Generate a uniform probability
      plot.


 1. The run sequence plot indicates that
    there are no shifts of location or
    scale.
 2. The lag plot does not indicate any
    significant patterns (which would
    show the data were not random).
 3. The histogram indicates that a 
    normal distribution is not a good
    distribution for these data.
 4. The histogram indicates that a 
    uniform distribution is a good
    distribution for these data.
 5. The normal probability plot verifies
    that the normal distribution is not a
    reasonable distribution for these data.
 6. The uniform probability plot verifies
    that the uniform distribution is a
    reasonable distribution for these data.
4. Generate the bootstrap plot.
   1. Generate a bootstrap plot.






 1. The bootstrap plot clearly shows
    the superiority of the mid-range 
    over the mean and median as the
    location estimator of choice for
    this problem.
5. Generate summary statistics, quantitative
   analysis, and print a univariate report.
   1. Generate a table of summary
      statistics.

   2. Generate the mean, a confidence
      interval for the mean, and compute
      a linear fit to detect drift in
      location.


   3. Generate the standard deviation, a
      confidence interval for the standard
      deviation, and detect drift in variation
      by dividing the data into quarters and
      computing Barltetts test for equal
      standard deviations.

   4. Check for randomness by generating an
      autocorrelation plot and a runs test.



   5. Check for normality by computing the
      normal probability plot correlation
      coefficient.

   6. Print a univariate report (this assumes
      steps 2 thru 6 have already been run).



 1. The summary statistics table displays
    25+ statistics.

 2. The mean is 0.5078 and a 95%
    confidence interval is (0.482,0.534).
    The linear fit indicates no drift in
    location since the slope parameter is
    statistically not significant.

 3. The standard deviation is 0.29 with
    a 95% confidence interval of (0.277,0.314).
    Levene's test indicates no significant
    drift in variation.



 4. The lag 1 autocorrelation is -0.03.
    From the autocorrelation plot, this is
    within the 95% confidence interval
    bands.

 5. The uniform probability plot correlation
    coefficient is 0.9995.  This indicates that
    the uniform distribution is a good fit.

 6. The results are summarized in a
    convenient report.

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