1. Bivariate Data – Contingency Tables

2. Objective
Construct Contingency Tables and Find the Requested Percentages.

3. Relevance
Learn ways to display qualitative data in a more useable format.

4. Bivariate Data
The values of 2 different variables that are obtained from the same population element.
Possible Arrangements:
A. 2 Qualitative Vars
B. 1 Qual 1 Quan
C. 2 Quantitative Var

5. Contingency Tables These are also called cross tabulation tables.
We use a contingency table to display bivariate data with 2 qualitative variables.

6. Example 1……2 Qualitative
30 college students were randomly identified and classified according to 2 variables; gender (M/F) and major (liberal arts-LA, business admin –BA, and technology - T). The results are shown.
M - LA
F-LA
F - LA
M - T
F - BA
M - BA
F - T

7. Organize into a Table
Let’s put the data into a table with frequencies for each group. LA BA T
Total M 5 6 7 18 F 4 2 12 11 10 9 30

8. Table based on % of GRAND TOTALLA BA T
Total M 5 6 7 18 F 4 2 12 11 10 9 30
For example: To find the percentage of males majoring in liberal arts from the entire population of students you divide 5 by 30 and multiply by 100.
Calculation:

9. Answers You do this for all the values in your contingency table.
Notice that the total % of the rows equal the total % of the columns. LA BA T
Total M
17%
20%
23%
60% F
13% 7%
40%
37%
33%
30%
100%

10. Table based on % of ROW TOTALSLA BA T
Totals M 5 6 7 18 F 4 2 12 11 10 9 30
For example: To find the percentage of females majoring in liberal arts from the population of all females you divide 6 by 12 and multiply by 100.
Calculations:

11. What about the other row?LA BA T
Total M 5 6 7 18 F 4 2 12 11 10 9 30
For example: To find the percentage of males majoring in technology from the population of all males you divide 7 by 18 and multiply by 100.
Calculations:

12. Answers You do this for all of the values in your contingency table.
Notice that the row percentages add up to 100%. LA BA T
Total M
28%
33%
39%
100% F
50%
17%

13. Table based on % of COLUMN TOTALSLA BA T
Total M 5 6 7 18 F 4 2 12 11 10 9 30
For example: To find the % of males majoring in business administration from the population of all business admin majors you divided 6 by 10 and multiply by 100.
Calculations:

14. What about another column?LA BA T
Total M 5 6 7 18 F 4 2 12 11 10 9 30
For example: To find the % of females majoring in technology from the population of all technology majors you divide 2 by 9 and multiply by 100.
Calculations:

15. Answers You do this for all of the values in your contingency table.
Notice that the column percentages add up to 100%. LA BA T
Total M
45%
60%
78% F
55%
40%
22%
100%

16. 1 Qualitative 1 Quantitative
When the data consists of one qualitative variable and one quantitative variable, it is easy to make comparisons by doing either a dot plot or box plot comparison.

17. Example Stopping distance for 3 tire tread designs.
Design A: 37, 36, 34, 40, 38, 32
Design B: 33, 35, 34, 42, 38, 34
Design C: 39, 40, 40 41, 41, 43

18. Assignment
Worksheet