## Friday, 17 April 2020

### Statistical Analysis of Irish Type III signature

Chi-squared test on Irish Type III Analysis

Dennis Wright’s paper from 2009 describes a four-fold greater frequency of the Irish Type III (IT3) signature among Dalcassian surnames compared to non-Dalcassian surnames … http://www.jogg.info/pages/51/files/Wright.pdf

This data is summarised in Tables 7 and 8 of the paper.

Thus, among men with Dalcassian surnames, 57 had the IT3 signature and 214 did not. Similarly, among men with non-Dalcassian surnames, 37 had the IT3 signature and 334 did not.

Chi-square test

I put these values into the 2x2 contingency table that forms part of the chi-square calculator at https://www.socscistatistics.com/tests/chisquare/default2.aspx.

The contingency table below provides the following information: the observed cell totals, (the expected cell totals) and [the chi-square statistic for each cell].

The chi-square statistic, p-value and statement of significance appear beneath the table. Blue means you're dealing with dependent variables; red, independent.

 IT3+ IT3- Marginal Row Totals Dalcasian 57   (39.68)   [7.56] 214   (231.32)   [1.3] 271 Non-Dalcassian 37   (54.32)   [5.52] 334   (316.68)   [0.95] 371 Marginal Column Totals 94 548 642    (Grand Total)

The chi-square statistic is 15.3283. The p-value is .00009. This result is significant at p < .01.

The chi-square statistic with Yates correction is 14.4561. The p-value is .000143. Significant at p < .01.
(There's probably a consensus now that the correction is over-cautious in its desire to avoid a type 1 error, but the statistic is there if you want to use it).

If we analyse only those Dalcassian surnames in bold in Table 7, we get the following results:

 IT3+ IT3- Marginal Row Totals Dalcasian 51   (22.04)   [38.03] 73   (101.96)   [8.22] 124 Non-Dalcassian 37   (65.96)   [12.71] 334   (305.04)   [2.75] 371 Marginal Column Totals 88 407 495    (Grand Total)

The chi-square statistic is 61.7173. The p-value is . This result is significant at p < .01.

The chi-square statistic with Yates correction is 59.6042. The p-value is . Significant at p < .01.

Fisher Exact Test

I also used another calculator on the website to do a Fisher Exact Test … https://www.socscistatistics.com/tests/fisher/default2.aspx

The Fisher exact test statistic and statement of significance appear beneath the table. Blue means you're dealing with dependent variables; red, independent.

 Results IT3+ IT3- Marginal Row Totals Dalcassian 57 214 271 non-Dalcassian 37 334 371 Marginal Column Totals 94 548 642  (Grand Total)

The Fisher exact test statistic value is 0.0001. The result is significant at p < .01.

If we analyse only those Dalcassian surnames in bold in Table 7, we get the following results:

 Results IT3+ IT3- Marginal Row Totals Dalcassian 51 73 124 non-Dalcassian 37 334 371 Marginal Column Totals 88 407 495  (Grand Total)

The Fisher exact test statistic value is < 0.00001. The result is significant at p < .01.

Conclusions

Both the chi-square test and Fisher exact test confirm that all comparisons are statistically significant, with p < 0.01 for all comparisons.

Maurice Gleeson
April 2020