Statistical and Social Significance
A researcher wants to see if urban, suburban and rural communities differ in terms of the support for food banks. The researcher randomly chose 4000 food banks from around the country and interviewed the director of each. Food banks were classified by community (urban, suburban, rural) and how much support the director said they received from the community (high, medium and low). Here is the table (this data is fictitious).
|
|
Urban
|
Suburban
|
Rural
|
Total
|
|
High Support
|
500
|
250
|
350
|
1100
|
|
|
26.40%
|
27.80%
|
29.20%
|
27.50%
|
|
Medium Support
|
700
|
300
|
350
|
1350
|
|
|
36.80%
|
33.30%
|
29.20%
|
33.80%
|
|
Low Support
|
700
|
350
|
500
|
1550
|
|
|
36.80%
|
38.90%
|
41.60%
|
38.70%
|
|
|
1900
|
900
|
1200
|
4000
|
|
|
Expected Frequency
|
fo - fe
|
(fo - fe)2
|
(fo - fe)2/fe
|
|
Urban-high
|
(1100*1900)/4000
|
500 - 522.5 = -22.5
|
-2.252 = 506.25
|
506.25/522..97
|
|
Urban-medium
|
(1350*1900)/4000
|
700 - 641.25= 58.75
|
3451.6
|
3451.6/641..38
|
|
Urban-low
|
|
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|
|
|
Suburban-high
|
|
|
|
|
|
Suburban-medium
|
|
|
|
|
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Suburban-low
|
|
|
|
|
|
Rural-high
|
|
|
|
|
|
Rural-medium
|
|
|
|
|
|
Rural-low
|
|
|
|
|
Complete the table to calculate chi square.
Calculate the degrees of freedom for the table.
Can you reject the null hypothesis at the alpha = 0.05 level?
Write an paragraph in which you report your results regarding the hypothesis test. Include statements of the null and research hypothesis, the chi square value, degrees of freedom and your conclusions.
Write another paragraph in which you discuss and compare the social significance of the differences compared to the statistical significance.