Question

Find the expected count and the contribution to the chi-square statistic for the (Control, Neutral) cell in the two-way table below.

Strongly Agree Agree Neutral Disagree Strongly Disagree

Control 38 49 5 15 11

Treatment 55 43 9 5 2

Round your answer for the expected count to one decimal place, and your answer for the contribution to the chi-square statistic to three decimal places.

Expected count=

Contribution to the chi-square statistic=

Answer 1

E: Expected frequency.
E = ( Row total*Column total) / Grand total

Strongly	Strongly agree	Agree	Neutral	Disagree	Strongly disagree	Total
Control	38	49	5	15	11	118
Treatment	55	43	9	5	2	114
Total	93	92	14	20	13	232

Expected counts are:

O	E
38	47.30172
49	46.7931
5	7.12069
15	10.17241
11	6.612069
55	45.69828
43	45.2069
9	6.87931
5	9.827586
2	6.387931

Test statistic is

O	E	(O-E)	(O-E)^2	(O-E)^2/E
38	47.30172	-9.30172	86.52207	1.829153
49	46.7931	2.206897	4.870392	0.104084
5	7.12069	-2.12069	4.497325	0.631586
15	10.17241	4.827586	23.30559	2.291058
11	6.612069	4.387931	19.25394	2.911939
55	45.69828	9.301724	86.52207	1.893333
43	45.2069	-2.2069	4.870392	0.107736
9	6.87931	2.12069	4.497325	0.653746
5	9.827586	-4.82759	23.30559	2.371446
2	6.387931	-4.38793	19.25394	3.014112
			Total	15.808

Contribution to the chi-square statistic = 15.808