**Log-Linear Analysis for a 2x2x2 Table of Cross- Categorized Frequency Data**

Log-linear analysis is a version of chi-square 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 3-way contingency table, since it allows all chi-square values to be derived through simple addition and subtraction of various combinations of the weighted logarithms. The second advantage is that the chi-square values thus derived are linear, which allows for more complex analyses not readily available through the conventional chi-square computational procedure. When a chi-square value is calculated by the log- linear method, it is typically designated as G

This page will calculate the values of G

Log-linear analysis, which is essentially a variation on the logic and procedures of chi-

A
_{1} | A
_{2} | |||||

C
_{1} | C
_{2} | C
_{1} | C
_{2} | |||

B
_{1} | B
_{1} | |||||

B
_{2} | B
_{2} |

df [ABC] = 4 |
Note that G^{2} is distributed approximatelyas chi- referring calculated values of G ^{2} to theappropriate sampling distributions of chi-square. |

AB Table
| AC Table
| BC Table
| |||||||||||

B
_{1} | B
_{2} | C
_{1} | C
_{2} | C
_{1} | C
_{2} | ||||||||

A
_{1} | A
_{1} | B
_{1} | |||||||||||

A
_{2} | A
_{2} | B
_{2} | |||||||||||

df [AB] = 1 | df [AC] = 1 | df [BC] = 1 | |||||||||||

df [ABC-AB] = 3 | df [ABC-AC] = 3 | df [ABC-BC] = 3 | |||||||||||

df [ABC-AC-BC] = 2 | df [ABC-AB-BC] = 2 | df [ABC-AB-AC] = 2 | |||||||||||

AB(C) Tables | AC(B) Tables | BC(A) Tables | |||||||||||

AB(C
_{1}) | AC(B
_{1}) | BC(A
_{1}) | |||||||||||

B
_{1} | B
_{2} | C
_{1} | C
_{2} | C
_{1} | C
_{2} | ||||||||

A
_{1} | A
_{1} | B
_{1} | |||||||||||

A
_{2} | A
_{2} | B
_{2} | |||||||||||

df [AB(C_{1})] = 1 | df [AC(B_{1})] = 1 | df [BC(A_{1})] = 1 | |||||||||||

AB(C
_{2}) | AC(B
_{2}) | BC(A
_{2}) | |||||||||||

B
_{1} | B
_{2} | C
_{1} | C
_{2} | C
_{1} | C
_{2} | ||||||||

A
_{1} | A
_{1} | B
_{1} | |||||||||||

A
_{2} | A
_{2} | B
_{2} | |||||||||||

df [AB(C_{2})] = 1 | df [AC(B_{2})] = 1 | df [BC(A_{2})] = 1 |

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©Richard Lowry 2001-

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