Editing Final Report/Thesis 2015 (section)

======Non-Parametric Testing Initial Results And Evaluation======
Initially, a result was unable to be computed for the Chi-Squared value or ''p-value'' using the ''chi-squared test'' method.  It was soon discovered that in the calculation of the Chi-Squared value, if the frequency of a letter in the reference text (a particular language from the Declaration of Human Rights) was 0, this caused the denominator of the Chi-Squared value equation to be 0 and thus the equation became invalid (See Figure 10).  

[[File: Task_1_Chi-squared_Formula.png |thumb|1000px|centre|'''Fig. 10:''' Chi-Squared Formula]]

An assumption in the method of the ''chi-squared testing'' had to be made in an attempt to rectify the issue.  The count for letters in the reference text that appeared 0 times, were altered to 1, a small number chosen to be the closest integer value to 0 in the hope that it would not have significant enough effect on the results to cause a skew in the data.  This assumption was made since the sample size for the reference text was too small, and so not every letter appeared at least once.  After doing this, and computing all results, it was realised by the group that despite the initial results when changing the count from 0 to 1 looking promising, the frequencies of letters that actually appeared once had the same frequency as letters that did not appear at all and thus reduced the accuracy of the data used for the analysis.  This was rectified by altering the frequencies of letters appearing 0 times to 0.0001, since the frequencies for letters occurring 1 time had a frequency of approximately 0.0005, and so we had to select a number lower than the lowest occurrence.  The results of both methods are compared and contrasted in the following sections.

{|style="margin: 0 auto;"
| [[File: 0_to_1_Validation.png |thumb|400px|centre|'''Fig. 11:''' Initial Chi-Squared Test Results for English Declaration vs Sample Texts (Count from 0 to 1)]]
| [[File: 0_to_0.0001_Validaition.png |thumb|400px|centre|'''Fig. 12:''' Initial Chi-Squared Test Results for English Declaration vs Sample Texts (Frequency from 0 to 0.0001)]]
|}

The initial ''chi-squared test'' using both methods resulted in large chi-squared values that were brought about by a small text size sample of 44 letters (See Figures 11 and 12).  This effectively caused the ''p-value'' results to be very small numbers and therefore were unable to be used as a means of comparison and caused the null hypothesis to be rejected in every case.  However, this test could still be used as a measure of similarity since the Chi-Squared Values for each text comparison can be compared based on the fact that the smaller the Chi-Squared value, the more similar the two texts are.  Thus, despite being unable to obtain valid ''p-values'' and perform ''hypothesis testing'', the texts could still be ranked based on the Chi-Squared value in the full analysis.  Comparing the results from the count 0 to 1, versus the frequency 0 to 0.0001 shows that the chi-squared values were reduced overall in the second analysis, except for the chi-squared values calculated for the Somerton Man code.