ORDINAL DESCRIPTIVE MULTIVARIATE DISTRIBUTION
Partial gamma:
Where: fa 12.3 = fa between variable #1 and variable #2 for a subtable of variable #3.
fi 12.3 = fi between variable # 1 and #2 for a subtable
of variable #3.
Note: Compute fa and fi same as for gamma.
Variable #3 is always the variable held constant.
Variable #3 is assumed to be nominal; variables #1 and #2 must
be at least ordinal.
Interpretation of partial gamma: just like regular gamma,
but add the information from the 3rd variable.
Example:
| College Education | High School Ed. | Less than High School Ed. | |||||||||
| Income | Income | Income | |||||||||
| Age | Hi | Lo | Hi | Lo | Hi | Lo | |||||
| 45+ | 104 | 36 | 45+ | 159 | 179 | 45+ | 54 | 335 | |||
| 45- | 163 | 46 | 45- | 290 | 327 | 45- | 24 | 133 | |||
Q: What is the relationship between age and income, with
education held constant?
A: First, check level of measurements: age and income (variables
#1 and #2) are both ordinal in this case, and education (variable
#3) is nominal.
| COLLEGE | 104(46)= 4,784 | 36(163)= 5,868 |
| HIGH SCHOOL | 159(327)=51,993 | 179(290)=51,910 |
| LESS THAN HIGH SCHOOL | 54(133)= 7,182 | 335(24)= 8,040 |
| fa12.3= 63,959 | fi12.3= 65,818 |
Interpretation: A very small negative association between
age and income with education held constant. 1% more disagreement
than agreement in rank order between age and income with education
held constant.
Q2: What is the relationship between income and education
with age held constant?
A2: First, make new tables to get the data in the form
needed.
| 45+ | Under 45 | ||||||
| Income | Income | ||||||
| Education | Hi | Lo | Education | Hi | Lo | ||
| C | 104 | 36 | C | 163 | 46 | ||
| HS | 159 | 179 | HS | 290 | 327 | ||
| <HS | 544 | 335 | <HS | 24 | 133 | ||
| VARIABLE #3 AGE | fa12.3 | fi12.3 |
| 45+ | 104(179 + 335) + 159(335) = 106,721 | 36(159 + 54) + 179(54)= 17,334 |
| 45 | 163(327 + 133) + 290(133)= 113,550 | 46(290 + 24) + 327(24) = 22,292 |
| fa12.3 = 220,271 | fi12.3 = 39,626 |
Interpretation: " There is a moderately high positive
association between income and education with age held constant."
Or "There is 70% more agreement than disagreement
in rank order between income and education with age held constant".