Statistics Assignment

 

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Statistics Assignment

First Scenario

Is there a relationship between trust in police and presence of democracy? The independent variable is presence of democracy (DEMOCRACY_DICH) while the dependent variable is trust in police (Q59h, trust in police). Both variables are categorical variables. The null and alternative hypotheses can be stated as follows:

Null: There is no relationship between trust in police and presence of democracy;

Alternative: There is relationship between trust in police and presence of democracy.

Results suggest that there is indeed a relationship between trust in police and presence of democracy, since the calculated p-value (0.000) is less than 0.05, the accepted level of significance (refer to Table 2 in the Appendix). This can also be indirectly inferred from Table 1. Note that trust in police is substantially higher in democratic states than in non-democratic states. The effect size is small (0.162).

Second Scenario

Here, the goal is to determine whether there is a relationship between trust in police and whether respondents reside in rural, urban, or semi-urban settings. The independent variable is urban or rural primary sampling unit (Urban or Rural Primary Sampling Unit) while the dependent variable is trust in police (Q59h, trust in police). Both variables are categorical variables. The null and alternative hypotheses can be stated as follows:

Null: There is no relationship between trust in police and whether respondents reside in rural, urban, or semi-urban settings;

Alternative: There is relationship between trust in police and whether respondents reside in rural, urban, or semi-urban settings.

Results suggest that there is indeed a relationship between trust in police and whether respondents reside in rural, urban, or semi-urban settings, since the calculated p-value (0.000) is less than 0.05, the accepted level of significance (refer to Table 5 in the Appendix). This can also be indirectly inferred from Table 4. Note that trust in police is substantially higher in rural areas than either in urban or semi-urban settings. The effect size is small (0.093).

Third Scenario

Is there a relationship between extent of democracy and presence of democracy? The independent variable is extent of democracy (Q42. Extent of Democracy) while the dependent variable is presence of democracy (DEMOCRACY_DICH). Both variables are categorical variables. The null and alternative hypotheses can be stated as follows:

Null: There is no relationship between extent of democracy and presence of democracy;

Alternative: There is relationship between extent of democracy and presence of democracy.

Results suggest that there is indeed a relationship between extent of democracy and presence of democracy, since the calculated p-value (0.000) is less than 0.05, the accepted level of significance (refer to Table 8 in the Appendix). This can also be indirectly inferred from Table 7. It is interesting to note that extent of democracy is substantially higher in democratic states than in non-democratic states. The effect size is large (1.000).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Appendix

Table 1. Democracy (dichotomous) * Q59h. Trust police Crosstabulation
Count
    Q59h. Trust police Total
    Not at all Just a little Somewhat A lot
Democracy (dichotomous) Not a Democracy 2143 1396 1074 756 5369
Democracy 8516 10588 11370 11586 42060
Total 10659 11984 12444 12342 47429

 

 

Table 2. Chi-Square Tests (Democracy, Trust in Police)
  Value df Asymp. Sig. (2-sided)
Pearson Chi-Square 1242.165a 3 .000
Likelihood Ratio 1173.593 3 .000
Linear-by-Linear Association 1125.520 1 .000
N of Valid Cases 47429    
a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 1206.61.

 

 

Table 3. Symmetric Measures (Democracy, Trust in Police)
    Value Approx. Sig.
Nominal by Nominal Phi .162 .000
Cramer’s V .162 .000
N of Valid Cases 47429  

 

 

 

 

 

 

 

 

 

Table 4. Urban or Rural Primary Sampling Unit * Q59h. Trust police Crosstabulation
Count
    Q59h. Trust police Total
    Not at all Just a little Somewhat A lot
Urban or Rural Primary Sampling Unit Urban 5216 5360 5130 3878 19584
Rural 5937 7082 7973 9237 30229
Semi-Urban 104 178 177 213 672
Total 11257 12620 13280 13328 50485

 

 

Table 5. Chi-Square Tests (Trust in Police, Urban or Rural Primary Sampling Unit)
  Value df Asymp. Sig. (2-sided)
Pearson Chi-Square 877.477a 6 .000
Likelihood Ratio 893.555 6 .000
Linear-by-Linear Association 794.593 1 .000
N of Valid Cases 50485    
a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 149.84.

 

 

Table 6. Symmetric Measures (Trust in Police, Urban or Rural Primary Sampling Unit)
    Value Approx. Sig.
Nominal by Nominal Phi .132 .000
Cramer’s V .093 .000
N of Valid Cases 50485  

 

 

 

 

 

Table 7. Democracy (dichotomous) * Q42. Extent of democracy Crosstabulation
Count
    Q42. Extent of democracy Total
    Not a democracy A democracy, with major problems A democracy, but with minor problems A full democracy
Democracy

(dichotomous)

Not a Democracy 5452 0 0 0 5452
Democracy 0 15200 18013 9439 42652
Total 5452 15200 18013 9439 48104

 

 

Table 8. Chi-Square Tests (Extent of Democracy, Presence of Democracy)
  Value df Asymp. Sig. (2-sided)
Pearson Chi-Square 48104.000a 3 .000
Likelihood Ratio 34003.500 3 .000
Linear-by-Linear Association 19883.756 1 .000
N of Valid Cases 48104    
a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 617.92.

 

 

Table 9. Symmetric Measures (Extent of Democracy, Presence of Democracy)
    Value Approx. Sig.
Nominal by Nominal Phi 1.000 .000
Cramer’s V 1.000 .000
N of Valid Cases 48104  

 

 

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