2. Patterns in partial tables

Select the correct entries from the dropdown menus to complete the following table of possible results when analyzing the effect of a third variable Z on the relationship between two variables X and Y.

Compared with Bivariate Table, Partial Tables Show	Pattern	Implications for Further Analysis	Likely Next Step
Same relationship between X and Y (gammas for partial tables within 0.10 of bivariate gamma)	Spurious/Intervening	Disregard Z	Analyze another Z variable
Weaker relationship between X and Y (gammas from partial tables at least 0.10 weaker than bivariate gamma)			Focus on relationship between Z and X or among X, Y, and Z
Mixed (at least 0.10 difference in gammas between partial tables and between partial tables and bivariate table)			Analyze subgroups (categories of Z) separately

Consider the following bivariate table showing the relationship between the number of missed work days (frequency of absence: low or high) and the amount of monthly sales (classified as either low or high, based on company-wide averages) among sales personnel at a car dealership.

	Frequency of Absence (X)
Monthly Sales (Y)	Low	High	Totals
Low	61 (59.8%)	59 (35.5%)	120
High	41 (40.2%)	107 (64.5%)	148
Totals	102 (100.0%)	166 (100.0%)	268
	Gamma = +0.4592

The data in the table suggest that there is association between the number of missed work days (X) and the amount of monthly sales (Y).

Here are the partial tables showing the bivariate relationship between X and Y after controlling for age.

A. Below 40

	Frequency of Absence (X)
Monthly Sales (Y)	Low	High	Totals
Low	17 (54.8%)	4 (8.0%)	21
High	14 (45.2%)	46 (92.0%)	60
Totals	31 (100.0%)	50 (100.0%)	81
	Gamma = +0.8663

B. 40 or above

	Frequency of Absence (X)
Monthly Sales (Y)	Low	High	Totals
Low	44 (62.0%)	55 (47.4%)	99
High	27 (38.0%)	61 (52.6%)	88
Totals	71 (100.0%)	116 (100.0%)	187
	Gamma = +0.2876

Compared with the bivariate table, the partial tables show relationship between the number of missed work days and the amount of monthly sales. This is evidence of relationship between the X and Y variables and implies that you should the variable Z (age) in further analysis.