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