Question

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.

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.