308
18 Dating the Last Migration to New Zealand
18.3 Analysing Variation in the Lengths of Canoe Genealogies
In the 19th and early 20th centuries, crude dating was obtained by simply using
average lengths of genealogies. Arguments for a more sophisticated approach to
chronology were made 60 years ago by Kelly [5] to deal with discrepancies in line
lengths. Arguing the importance of studying genealogies in the light of other oral
sources, L.G. Kelly pointed out obvious factors distorting their line lengths: “The
presence of old chiefs with young women naturally tends to lengthen the line on the
female side. On the other hand, when lines descend from an elder and a younger
member of a family, that of the latter will usually be found to be shorter.” In
1956–1962 J.B.W. Roberton [6] used the concept of a feasible biological range
to test the credibility of certain genealogies. He attempted to chart a chronology
through matching parallel lines, placing known contemporaries at the same level on
the chart and making distinctions between short and long generations spatially. He
assigned a chronology based on biological estimates for maximum and minimum
values for the assigned spacings. Roberton’s method was convincing and sophisticated but it was not taken up by others or extended beyond the examples he chose.
For other work bearing on these issues see H.G. Fletcher [7], Andrew Sharp [8] and
J.F.C. Stokes [9].
In contrast with the concern of prehistorians about the variation in the number of generations occurring in different lines of descent from a given ancestor
or from contemporaneous ancestors down to the present, most statisticians would
feel uneasy if there were not a certain amount of variation. Not only would they
expect statistical variation but they would use it as a source of information and a
test of consistency for genealogies rather than thinking of it in terms of nuisance
parameters.
Simmons’ repudiation of the Heke has been largely responsible for modern historians’ rejection of the historical insights and evidence embedded in Heke traditions.
In the following pages we apply a rigorous statistical analysis to the data furnished
by Simmons and used in his repudiation of the historicity of the Heke. The analysis
shows that the claim that the canoes of the Heke were not contemporaneous must be
rejected at the usual 5% level of statistical significance. More precisely, we show at
the 5% level that there is no statistically significant evidence of difference between
the mean line lengths in the various canoe traditions associated with the Heke or
between the variances of the distributions of those lengths.
18.4 Basic Data
After discussion of genealogies associated with various canoe traditions, the
following summaries of line lengths (in generations) Simmons [10] gives.
1. Mataatua: 17, 22,18, 14, 20, 15, 17, 18, 15, 19, 18, 18, 16, 17. The whakapapa
were recorded from 1892 to the early 20th century.
18 Dating the Last Migration to New Zealand
18.3 Analysing Variation in the Lengths of Canoe Genealogies
In the 19th and early 20th centuries, crude dating was obtained by simply using
average lengths of genealogies. Arguments for a more sophisticated approach to
chronology were made 60 years ago by Kelly [5] to deal with discrepancies in line
lengths. Arguing the importance of studying genealogies in the light of other oral
sources, L.G. Kelly pointed out obvious factors distorting their line lengths: “The
presence of old chiefs with young women naturally tends to lengthen the line on the
female side. On the other hand, when lines descend from an elder and a younger
member of a family, that of the latter will usually be found to be shorter.” In
1956–1962 J.B.W. Roberton [6] used the concept of a feasible biological range
to test the credibility of certain genealogies. He attempted to chart a chronology
through matching parallel lines, placing known contemporaries at the same level on
the chart and making distinctions between short and long generations spatially. He
assigned a chronology based on biological estimates for maximum and minimum
values for the assigned spacings. Roberton’s method was convincing and sophisticated but it was not taken up by others or extended beyond the examples he chose.
For other work bearing on these issues see H.G. Fletcher [7], Andrew Sharp [8] and
J.F.C. Stokes [9].
In contrast with the concern of prehistorians about the variation in the number of generations occurring in different lines of descent from a given ancestor
or from contemporaneous ancestors down to the present, most statisticians would
feel uneasy if there were not a certain amount of variation. Not only would they
expect statistical variation but they would use it as a source of information and a
test of consistency for genealogies rather than thinking of it in terms of nuisance
parameters.
Simmons’ repudiation of the Heke has been largely responsible for modern historians’ rejection of the historical insights and evidence embedded in Heke traditions.
In the following pages we apply a rigorous statistical analysis to the data furnished
by Simmons and used in his repudiation of the historicity of the Heke. The analysis
shows that the claim that the canoes of the Heke were not contemporaneous must be
rejected at the usual 5% level of statistical significance. More precisely, we show at
the 5% level that there is no statistically significant evidence of difference between
the mean line lengths in the various canoe traditions associated with the Heke or
between the variances of the distributions of those lengths.
18.4 Basic Data
After discussion of genealogies associated with various canoe traditions, the
following summaries of line lengths (in generations) Simmons [10] gives.
1. Mataatua: 17, 22,18, 14, 20, 15, 17, 18, 15, 19, 18, 18, 16, 17. The whakapapa
were recorded from 1892 to the early 20th century.