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

## 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.
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```   1. Read in the data.

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

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```
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``` 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.
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```   1. Generate a run sequence plot.

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```   2. Generate a lag plot.

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```   3. Generate a histogram with an
overlaid normal pdf.

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```   4. Generate a histogram with an
overlaid uniform pdf.

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```   5. Generate a normal probability
plot.

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```   6. Generate a uniform probability
plot.

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```
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``` 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.
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```   1. Generate a bootstrap plot.

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``` 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.
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```   1. Generate a table of summary
statistics.

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

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```   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.

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

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

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```

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``` 1. The summary statistics table displays
25+ statistics.

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``` 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.

```