Bivariate Data – Contingency Tables

Objective Construct Contingency Tables and Find the Requested Percentages.

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

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

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

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

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

Table based on % of GRAND TOTAL 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 liberal arts from the entire population of students you divide 5 by 30 and multiply by 100. Calculation:

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%

Table based on % of ROW TOTALS LA 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:

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:

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%  

Table based on % of COLUMN TOTALS LA 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:

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:

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%

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.

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

Assignment Worksheet