Question

Find the expected count and the contribution to the chi-square statistic for the (Group 1, Yes) cell in the two-way table below. Yes No Group 1 711 263 Group 2 1159 313 Round your answer for the excepted 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

given data table is

	group 1	group 2
yes	711	263
no	1159	313

calculating row and column total or sum

	group 1	group 2	TOTAL
yes	711	263	974
no	1159	313	1472
TOTAL	1870	576	2446

For expected count, take sum of each row and column

then multiply the row and column total for individual value and divide by the grand total, we get

Table for expected count	group 1	group 2
yes	(1870*974)/2446 = 744.636	(576*974)/2446 = 229.364
no	(1870*1472)/2446 = 1125.364	(576*1472)/2446 = 346.636

Contribution to chi square is calculated (observed - expected)^2/(expected)

Observed	Expected	Contribution
711	744.636	(711-744.636)^2/744.636 = 1.519
263	229.364	(263-229.364)^2/229.364 = 4.933
1159	1125.364	(1159-1125.364)^2/1125.364 = 1.005
313	346.636	(313-346.636)^2/346.636 = 3.264

Chi square = 1.519 + 4.933 + 1.005 + 3.264

= 10.721