The Java™ applet on this page is a frequentist exact (but non-deterministic) freeware Monte Carlo program to work two-dimensional contingency tables with structural zeroes, testing quasi-independence of rows against columns. The algorithm is due to Besag and Clifford (1989.) I wrote and uploaded this applet merely because I could not find such an applet on the Web.

The AWT controls in order are a single-line TextField to hold the paths integer, a single-line TextField to hold the steps integer, a multi-line TextArea which I will call the upper text area, a Button called “goSwap,” a faded Button called “percent,” a faded Button called “stop,” and a multi-line TextArea which I will call the lower text area.

When loading is finished, path and steps are already set to their default values: one thousand and one thousand. Nothing prevents the user from changing these. The paths number is the total number of genuine and fake paths. The steps number is the number of steps to each path.

The values of paths and steps are up to the user. If lunch will take an hour, then paths can be made larger, so as possibly to get a better p-value, or maybe steps can be made larger, so as to get more power.

From Das (1945) and White (1963) I copy

Classification of Purum marriages
                             Sib of husband
Sib of wife      Marrim Makan Parpa Thao Kheyang
Marrim              [0]     5     1  [0]       6
Makan                 5   [0]     0   16       2
Parpa               [0]     2   [0]   10      11
Thao                 10   [0]   [0]  [0]       9
Kheyang               6    20     8    0       1

 -1   5  17  -1   6
  5  -1   0  16   2
 -1   2  -1  10  11
 10  -1  -1  -1   9
  6  20   8   0   1

 pValue of this run is 0.001

 time to run was 0.782 seconds

The present program sometimes fails. Here is an example to select and copy to the clipboard and paste into the upper text area and run with the “goSwap” button:

-1   2  30
 4  -1   5
 6  70  -1

 pValue of this run is 1.0

 time to run was 0.766 seconds

 pValue is 1.196092889749022E-5

 time to run was 0.016 seconds

-1   2  30  3
 4  -1   5  4
 6  70  -1  5
 6   7   8 -1

 pValue of this run is 0.001

 time to run was 0.828 seconds

If on the other hand the percent is small, then just please click the mouse on the “stop” button. Then please change the paths and/or the steps to something smaller, and click the “goSwap” button again.
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Rules to keep in mind

The experimenter ought to click the “goSwap” button only once. (Running the program ten times and taking the smallest p-value is clearly cheating.) Students will perhaps be told by their teacher how many times they may click.
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Browsers and Java

However, the program can work only if Java is installed and Java is turned on. If there is no Java or if Java has been turned off, then the text fields and the text areas and the “goSwap” and “percent” and “stop” buttons will not even be visible. In that case, the user is respectfully requested to download and install Java and/or to turn Java back on. Users who have trouble doing this are respectfully asked to get help from their classmates, children, spouses, or teachers.
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Download

If the browser’s downloader renames the “jar” file to a “zip” file, please be sure to rename it back to a “jar”. I know a browser which takes too much on itself in this way.
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The algorithm

Besag and Clifford (1989) remembered that the Markov chain made by a Metropolis algorithm had the same probabilities in both directions. (We are, of course, supposing that the null hypothesis is true.) That is, we may move backwards in time from the genuine sample to the starting sample. Then we may move forward in time from the starting sample to each of the fakes.

My Java method to do this is called “backwardForward.” This method is called twice, the first time to find the expected values, and the second time to use those expected values to get chi-squares. The same random number seed is used both times.
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Advantages and disadvantages

However, the test on this page is not deterministic. Since it uses random numbers, the p-values can differ from run to run. This is why the experimenter may run only once. Students, of course, may run as many times as their teacher permits.
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A note to developers

final boolean debugging=false;

		try
		{
		parse();
		}

		catch( Throwable thro )
		{
		String temp="";
		temp+=thro.getClass().getCanonicalName();
		temp+="\n\n";
		temp+=thro.getMessage();
		temp+="\n";
		lowerTextArea.setText( temp );

			if( debugging )
			{
			StackTraceElement[] ste=thro.getStackTrace();
			int n=ste.length;
	
				for( int j=0;j<n;j++ )
				{
				lowerTextArea.append( "\n"+ste[j] );
				}

			}

		}

Besag, J., Clifford, P. “Generalized Monte Carlo significance tests,” Biometrika 76 (1989), 633-642.

Das, T. (1945). The Purums: An Old Kuki Tribe of Manipur. Calcutta, University of Calcutta.

White, H. C. (1963). An Anatomy of Kinship, p. 138. Englewood Cliffs, N. J., Prentice-Hall.
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Revision date, licenses, and e-mail address

       at     dot
smtw2gh  gmail   com