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When the flawed test is used to compute the significance of this data, the p-value is 0.0085 (see Table 2 of the paper). This p-value is considered statistically significant. However, when the data is analyzed using a standard method (the chi-square test) the p-value is 0.19. This p-value is much larger than the one from the paper and indicates that there is no reason to reject the null hypothesis. The chi-square test p-value for experiment two is small (0.0004). However, experiment three is not statistically significant because its p-value is 0.22.

When the Monte Carlo test is used to compute the significance of this data, the p-value is 0.0085 (see Table 2 of the paper). This p-value is considered statistically significant. However, when the data is analyzed using the chi-square test the p-value is 0.19. This p-value is much larger than the one from the paper and suggests that there is no reason to reject the null hypothesis. The chi-square test p-value for experiment two is small (0.0004). Similarly, the p-value produced by a chi-square test on the data from the third experiment is 0.22, which would lead to rejection of the experimental hypothesis.

The chi-square test is a common statistical method.<ref>''Mathematical Statistics with Applications'' by Wackerly, Mendenhall, and Scheaffer, Section 14.4.</ref> It can be implemented in Microsoft Excel. If the numbers from the last four columns of the experiment one data table (excluding the “totals” row) are entered into Excel in rows 1-12 and columns A-D, then the p-value can be computed by entering “=CHITEST(A1:B12,C1:D12)” into any empty cell of the spreadsheet.

The chi-square test is a common statistical method but it is only considered a valid test if the data used in the calculation satisfy a number of assumptions. The chi-square test always produces an approximate p-value, which approaches the 'true' p-value when the numbers used in the calculation are large. When the assumptions are violated, for example when the numbers in the 'expected' cells are below threshold levels, it is considered a violation of good statistical practice to use the chi-square test. For small cell counts, the chi-square test has an unacceptably high type II error; that is to say that it produces approximate p-values that are higher than they should be, and thereby supports the null hypothesis when it is false. The chi-square test also assumes that there is no relationship between the categories into which the experimental data are dividided; therefore in situations in which the categories are linked (for example 'patients before treatment; and 'same patients after treatment' or 'IQ scores of the same study group at times A, B, and C'), the chi-square test is not to be used. In this article, the categories entered into the chi-square test are not independent, so the results of a chi-square test are not valid. Furthermore, the numbers in the cells are below the threshold for chi-square acceptability.<ref>http://www.okstate.edu/ag/agedcm4h/academic/aged5980a/5980/newpage28.htm

</ref><ref>http://www.basic.northwestern.edu/statguidefiles/gf-dist_ass_viol.html</ref><ref>''Mathematical Statistics with Applications'' by Wackerly, Mendenhall, and Scheaffer, Section 14.4.</ref>  

 

The chi-square test can be implemented in Microsoft Excel. If the numbers from the last four columns of the experiment one data table (excluding the “totals” row) are entered into Excel in rows 1-12 and columns A-D, then the p-value can be computed by entering “=CHITEST(A1:B12,C1:D12)” into any empty cell of the spreadsheet.

==Experiment Three Data==

==Experiment Three Data==