Question

The following data are for 30 observations involving two categorical variables, x and y. The categories...

The following data are for 30 observations involving two categorical variables, x and y. The categories for x are A, B, and C; the categories for y are 1 and 2.

Observation x y Observation x y
1 A 1 16 C 1
2 C 2 17 B 2
3 C 2 18 C 2
4 B 1 19 B 2
5 C 2 20 C 2
6 B 1 21 B 1
7 C 2 22 C 2
8 B 1 23 B 1
9 A 1 24 A 1
10 C 2 25 C 2
11 A 1 26 B 1
12 C 2 27 B 1
13 B 1 28 A 1
14 B 1 29 C 2
15 B 1 30 C 1


  1. Develop a crosstabulation for the data, with x as the row variable and y as the column variable.
  2. Compute the row percentages (to 1 decimal).
  3. Compute the column percentages (to 1 decimal).
  4. Describe the observed relationship between variables x and y.
    -Category A values for x are Selectalwaysusuallynot usuallyneverItem 30 associated with category 1 values for y.
    -Category B values for x are Selectalwaysusuallynot usuallyItem 31 associated with category 1 values for y.
    -Category C values for x are Selectalwaysusuallynot usuallyItem 32 associated with category 2 values for y.

Homework Answers

Answer #1

a). Develop a crosstabulation for the data, with x as the row variable and y as the column variable.

1   2 Total  
A 5 0 5
x B 10 2 12
C 2 11 13
Total 17 13 30

b) Row percentages:

y
1 2 Total
A 5/5 = 100% 0/5 = 0% 100%
x B 10/12 = 83.3 % 2/12 = 16.7% 100%
C 2/13 = 15.4% 11/13 = 84.6% 100%

c) Column percentages :

y
1 2
A 5/17 = 29.4% 0/13 = 0%
x B 10/17 = 58.8% 2/13 = 15.4%
C 2/17 = 11.8% 11/13 = 84.6%
Total 100% 100%

d) Category A values for x are always associated with category 1 values for y.

Category B values for x are usually associated with category 1 values for y.

Category C values for x are usually associated with category 2 values for y.

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