From the preceding data we have obtained population estimates for
certain of the California Athabascan groups. If these estimates are
judged reliable, it would be desirable to use them as a basis for
estimating the population of the remaining groups. When a detailed
analysis of the ecological or demographical factors involved is lacking,
it is sometimes necessary to fall back on rather simplistic assumptions
to attain the desired end. Cook goes rather far in this direction, using
simply the average population density per square mile of the known
groups to estimate the population of the unknown groups.
It appears to this writer that a somewhat more satisfactory method of
estimation would be based on simple linear regression theory. It is
a fact that pertinent relationships in population studies can often
be expressed in terms of simple exponential functions or in linear
combinations of logarithms. Thus we might propose a relationship such as
the following:
population = a + b (ln area)
or
population = a + b (ln fishing miles)
where a and b are constants to be determined and ln is the logarithm to
the base e.
Of course we would not expect these relationships to be precise.
The lack of exactness might be due to the crudeness of the various
measurements involved or perhaps to the fact that population depends on
more than one such factor. To account in some way for the uncertainty,
we might make a further assumption and propose the following
relationships:
population = a + b (ln area) + X
population = a + b (ln fishing miles) + X
where X has a normal probability distribution with mean = 0 and some
unknown variance = =s=^{2}. X is then, roughly speaking, the error
involved in each observation. That the error would be distributed
normally is quite reasonable under the circumstances. In situations
where the uncertainty of the observation is due to measurement error
or to a multiplicity of factors, the distribution obtained often
assumes a normal form or a form sufficiently normal so that the normal
distribution can be used as an approximation.
One additional assumption is necessary. We must assume that the sample
used is taken in a random fashion from the population to be studied. In
the present investigation, the sample is definitely not taken at random,
since we are using all groups for which we have population estimates
based on ethnographic information. The question is, then, whether this
selection of groups would result in some bias. For instance, the groups
for which we have ethnographic data might be the most numerous in the
first place and might thus cause us overestimate the population of
the remaining groups. On the whole, it would seem to me that there is
no such bias and that the assumption of a random sample is therefore
not misleading, at least in the direction of overestimation. If we now
consider each group for which we have no ethnographic data, we can see
whether the lack of such data is due to an initially small population or
to mere luck.
Kato: The reason Kato population is being estimated in gross
rather than from ethnographic data is that Goddard (1909, p. 67)
obtained a list of more than 50 villages which are not available
for calculation.
Bear River: Here the lack of information is due simply to the
fact that it was not collected. There have been several informants
living until recently (see Nomland, 1938).
Lassik: There was at least one good informant living until
recently (Essene, 1942), but Merriam worked with her only briefly.
Goddard evidently recorded a number of villages from this group,
but his notes are lost.
Nongatl: Goddard seems to have worked with at least two
informants from this group, but he spent a very brief time in the
area and some of his notes may have been lost.
Shelter Cove Sinkyone: Several informants from this group have
been alive until recently (see Nomland, 1935). No one saw fit to
collect the appropriate data.
It is obvious from this summary that the main reason for our lack of
information on these groups is the loss of Goddard's notes. If those
were at hand, we would probably have complete information on the Kato,
the Lassik, and probably the Nongatl. The absence of data on the Bear
River and Shelter Cove Sinkyone is due to the ethnographers' oversight.
None of these groups, therefore, seem to have been selected because of
their small aboriginal population. If the following estimates are in
error because the sample is not a random one, then the error is probably
one of underestimate rather than overestimate.
Given the foregoing assumptions, the least squares estimate of the
normal regression line may be obtained with the following formula.
P: population. A: area. F: fishing miles.
The equations of the lines are: