4.1. Crosstabulations and Scatter Diagrams

The crosstabulation (table) and the scatter diagram (graph) can help us understand the

relationship between two variables.

1. Crosstabulations

Example 1:

The following table is the crosstabulation of the quality rating (good, very good and excellent)

and the mean price ($10-19, $20-29, $30-39, and $40-49) data collected for a sample 300

restaurants located in the Los Angeles area.

Meal Price
Quality Rating	$10-19	$20-29	$30-39	$40-49	Total
Good	42	40	2	0	84
Very Good	34	64	46	6	150
Excellent	2	14	28	22	66
Total	78	118	76	28	300

The above crosstabulation provides insight abut the relationship between the variables,

quality rating and mean price. It seems higher meal prices appear to be associated with

the higher quality restaurants and the lower meal prices appear to be associated with

the lower quality restaurants. For example, for the most expensive restaurants ($40-49),

none of these restaurants is rated the lowest quality but most of them are rated highest quality.

On the other hand, for the least expensive restaurants ($10-19), only 2 of these restaurants

are rated the highest quality () but over half of them are rated lowest quality.

1. Scatter Diagram

Suppose we have the following scatter diagrams for two variables x and y:

The upper scatter diagram indicates the positive correlation between x and y

while the middle scatter diagram implies the negative correlation between the

two variables. The lower scatter diagram shows that there is no apparent relationship

between the weight and height.

JavaStatSoft:

Crosstabulations:

Statistics -> Exploratory Data Analysis -> Association Between Two Categorical Variables

Graphical Display:

Graph -> Scatter Plot