The data shown include the selling price of the vehicle as well as the age of the purchaser. Is it likely that there is a relationship between the selling price of a vehicle and the age of the purchaser? Would it be reasonable to conclude that the more expensive vehicles are purchased by older buyers? Describing Relationship between Two Variables – Scatter Diagram Excel Example 119 Describing Relationship between Two Variables – Scatter Diagram Excel Example 120
Contingency Tables z A scatter diagram requires that both of the variables be at least interval scale . z What if we wish to study the relationship between two variables when one or both are nominal or ordinal scale ? In this case we tally the results in a contingency table. 120 Contingency Tables A contingency table is a cross-tabulation that simultaneously summarizes two variables of interest. Examples: 1. Students at a university are classified by gender and class rank. 2. A product is classified as acceptable or unacceptable and by the shift (day, afternoon, or night) on which it is manufactured. 3. A voter in a school bond referendum is classified as to party affiliation (Democrat, Republican, other) and the number of children that voter has attending school in the district (0, 1, 2, etc.). 120
Contingency Tables – An Example A manufacturer of preassembled windows produced 50 windows yesterday. This morning the quality assurance inspector reviewed each window for all quality aspects. Each was classified as acceptable or unacceptable and by the shift on which it was produced. Thus we reported two variables on a single item. The two variables are shift and quality. The results are tabulated into the table in the following manner: Afternoon Acceptable Night Acceptable Afternoon Defective Day Acceptable Day Defective Night Acceptable Day Acceptable Afternoon Acceptable Night Defective Defective Acceptable l l l l l l l l l Contingency Tables – Results Using the contingency table, the quality of the three shifts can be compared. For example: 1.On the day shift, 3 out of 20 windows or 15 percent are defective. 2.On the afternoon shift, 2 of 15 or 13 percent are defective and 3.On the night shift 1 out of 15 or 7 percent are defective. 4.Overall 12 percent of the windows are defective 121
GOALS - Chapter 4 1. Develop and interpret a dot plot . 2. Develop and interpret a stem-and-leaf display . 3. Compute and understand quartiles , deciles , and percentiles . 4. Construct and interpret box plots . 5. Compute and understand the coefficient of skewness . 6. Draw and interpret a scatter diagram . 7.Construct and interpret a contingency table.
- Spring '11
- Standard Deviation