Loglinear
analysis is a version of chisquare analysis in which the relevant values are calculated by way of weighted natural logarithms. The first advantage of this procedure is that it is easier to program in the case of a complex 3way contingency table, since it allows all chisquare values to be derived through simple addition and subtraction of various combinations of the weighted logarithms. The second advantage is that the chisquare values thus derived are linear, which allows for more complex analyses not readily available through the conventional chisquare computational procedure.
When a chisquare value is calculated by the loglinear method, it is typically designated as G
^{2} as an indication of its computational origin. Since G
^{2} is distributed approximately as chisquare, its associated probability under the null hypothesis can be estimated through reference to the appropriate sampling distribution of chisquare, as defined by its degrees of freedom. Values of G
^{2} will usually be quite close to the corresponding values of chisquare that would be calculated using the conventional procedure.
For a 3way contingency table containing up to 5 rows (A), 5 columns (B), and 5 layers (C), the present page will calculate the following seven values of G
^{2}:
_{Q}
ABC
 Representing the 3way interaction between A, B, and C.

AB
 Representing the 2way interactions for AB, AC, and BC, respectively. These are the same measures that would be obtained from an AB table collapsed across the levels of C, an AC table collapsed across the levels of B, and a BC table collapsed across the levels of A.

AC

BC

AB(C)
 Representing the 2way interactions for each pair of variables, AB, AC, and BC, when the effects of the third variable are removed from the picture. Thus, AB(C) represents the AB interaction when the AC and BC interactions are removed. It is the same measure that would be obtained by constructing a separate AB table for each level of C, calculating a separate G^{2} measure for each, and then summing the results.

AC(B)

BC(A)

To begin, enter the numbers of rows, columns, and layers in the designated places, then click the «Setup» button and enter your data into the appropriate cells of the dataentry matrices. After all data have been entered, click one of the «Calculate» buttons.
Data Entry
Results:
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©Richard Lowry 2001
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