Project Blue Book Special Report No. 14 (Analysis of Reports of Unidentified Aerial Objects)

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UNKNOWNS in each characteristic group showed the same general trend.
In other words, on the basis of these graphs, it looked as though there was
a good possibility that the UNKNOWNS were no different from the KNOWNS,
at least in the aggregate. It was decided to investigate this by the use of a
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statistical procedure called the "Chi Square Test".
The Chi Square Test is a statistical test of the likelihood that two
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distributions come from the same population, that is, it gives the proba­
bility that there is no difference in the make-up of the two distributions
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being measured.
The method is outlined as follows:
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( 1) Adjust the distributions by multiplying the KNOWNS in each
characteristic group by the ratio of the total number of
UNKNOWNS to the total number of KNOWNS. (The Chi
Square Test is applicable only to distributions which have
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the same total number of elements.)
(2) Take the difference between the number of UNKNOWNS and
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the adjusted number of KNOWNS in each characteristic
group.
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(3) Square the remainder from Step 2.
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(4) Divide the result of Step 3 by the corresponding number of
adjusted KNOWNS.
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This is the chi square for the particular group. Summing the indi­
vidual chi squares over the groups of a characteristic gives the chi square
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for that characteristic. This number is then compared with a table of the
distribution of chi square which can be found in many texts on elementary
s tatistics.
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It will be noted that chi square is tabulated in terms of degrees of
freedom which in this case is one less than the number of groups of sight­
ings for each characteristic.
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The tabulations of KNOWNS and UNKNOWNS against the six char­
acteristics and the Chi Square Test as it was applied are shown in Tables
II through VII. In each case, the number of degrees of freedom is given,
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as is the value of chi squares corresponding to probabilities of 5 per cent
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and 1 per cent that two distributions with this number of degrees of freedom
come from the same population. Since the greater the value of chi square
the smaller the probability of homogeneity of two distributions, a calculated
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value of chi square greater than either the 5 per cent or 1 per cent values
will indicate a probability less than 5 per cent or 1 per cent, respectively,
that the two distributions are homogeneous.
The term homogeneity is used
here to indicate that two distributions could have come from the same
population.
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