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







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