Question

The table below shows data on the country of origin and worries about climate change for respondents of a survey.

Country: Country A Country B Country C Country D

No worries 124 99 32 53

Some worries 12 44 76 235

Big worries 0 12 41 555

Compute Cramer’s V for the association between country of origin and worries about climate change. Show your calculations and interpret your result.

Answer 1

Answer:

Step-1 :

Chi-square calculation as below;

I. Observed counts
	Country A	Country B	Country C	Country D	Column Total (CT)
No worries	124	99	32	53	308
Some worries	12	44	76	235	367
Big worries	0	12	41	555	608
Row Total (RT)	136	155	149	843	1283	Grand Total (GT)
II. Expected counts = ( RT x CT ) /GT
Expected frequency (E)	Country A	Country B	Country C	Country D	Total
No worries	32.65	37.21	35.77	202.37	308
Some worries	38.90	44.34	42.62	241.14	367
Big worries	64.45	73.45	70.61	399.49	608
Total	136	155	149	843	1283
III. Chi-square components
Chi-square calculations	Country A	Country B	Country C	Country D	Total
No worries	255.60	102.61	0.40	110.25	468.86
Some worries	18.60	0.00	26.14	0.16	44.90
Big worries	64.45	51.41	12.42	60.54	188.82
Total	338.66	154.02	38.95	170.95	702.58	<== Chi-square value

Step-2:

Nominal Measures: Cramer's V (V) Cramer's V is used for tables larger than 2x2. Formula for Cramer's V: x² V= V(N)(min r - 1,-1) Where (min -1, 6-1) is the minimum value of either the #rows-1 or the # columns-1.

Hence,

V=sqrt(702.58/(1283*2)) = 0.5233

Describing Strength of Association : Cramer's V

Characterizations

>.5                   high association

.3 to .5             moderate association

.1 to .3             low association

0 to .1              little if any association

Conclusion :

Since V = 0.5233 > 0.5 , it implies high association between country of origin and worries about climate change.

######## End of answer