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25 Nov 2022

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Chi-Square Goodness of Fit Test

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Observed  Expected  (Observed-Expected)  (Observed - Expected)^2  /Expected 

18 

24.2234 

-6.2234 

38.7308 

1.5989 

15 

8.776596 

6.2234 

38.7308 

4.4130 

51 

44.7766 

6.2234 

38.7308 

0.8650 

10 

16.2234 

-6.2234 

38.7308 

2.3873 

Chi-square Statistic 

9.2642 

Chi-square = 9.2642 

Degrees of freedom = (row-1) (column -1) = (2-1) (2-1) = 1 

Probability= 0.0023 

Decision 

Since probability, 0.0023 is less than 0.05, gender is a significant factor. 

Age and VIOLENT2 

 

Violent 2 

 
Age  1 (Yes)  2 (No)  Total 

1 

0 

2 

2 

2 

23 

13 

36 

3 

24 

7 

31 

4 

17 

2 

19 

5 

5 

1 

6 

Total 

69 

25 

94 

Expected = (row total/column total)/ Grand total 

Expected 

Age  1 (Yes)  2 (No) 

1 

1.4680851 

0.531914894 

2 

26.425532 

9.574468085 

3 

22.755319 

8.244680851 

4 

13.946809 

5.053191489 

5 

4.4042553 

1.595744681 

Observed  Expected  (Observed-Expected)  (Observed - Expected)^2  /Expected 

0 

1.4681 

-1.4681 

2.1553 

1.4681 

23 

26.4255 

-3.4255 

11.7343 

0.4441 

24 

22.7553 

1.2447 

1.5492 

0.0681 

17 

13.9468 

3.0532 

9.3220 

0.6684 

5 

4.4043 

0.5957 

0.3549 

0.0806 

2 

0.5319 

1.4681 

2.1553 

4.0519 

13 

9.5745 

3.4255 

11.7343 

1.2256 

7 

8.2447 

-1.2447 

1.5492 

0.1879 

2 

5.0532 

-3.0532 

9.3220 

1.8448 

1 

1.5957 

-0.5957 

0.3549 

0.2224 

Chi-square Statistic 

10.2618 

Chi-square = 10.2618 

Probability = 0.0362 

Degrees of freedom = (row-1) (column -1) = (5-1) (2-1) = 4 

Decision 

Since probability, 0.0362 is less than 0.05, age is a significant factor. 

Married and VIOLENT2 

 

Violent 2 

 
Marital status  1 (Yes)  2 (No)  Total 
Married (1) 

35 

11 

46 

Single or Divorced (2) 

34 

14 

48 

Total 

69 

25 

94 

Expected = (row total/column total)/ Grand total 

Expected 

   
 

Violent 2 

   
Marital status  1 (Yes)  2 (No)     
Married (1) 

33.7660 

12.2340 

   
Single or Divorced (2) 

35.2340 

12.7660 

   
         
Observed  Expected  (Observed-Expected)  (Observed - Expected)^2  /Expected 

35 

33.76596 

1.2340 

1.5229 

0.0451 

11 

12.23404 

-1.2340 

1.5229 

0.1245 

34 

35.23404 

-1.2340 

1.5229 

0.0432 

14 

12.76596 

1.2340 

1.5229 

0.1193 

Chi-square Statistic 

0.3321 

Probability = 0.5644 

Degrees of freedom = (row-1) (column -1) = (2-1) (2-1) = 1 

Decision 

Since probability, 0.5644 is greater than 0.05, marital status is NOT a significant factor. 

Children and VIOLENT2 

 

Violent 2 

 
Have Children  1 (Yes)  2 (No)  Total 
Yes (1) 

30 

3 

33 

No (2) 

39 

22 

61 

Total 

69 

25 

94 

Expected = (row total/column total)/ Grand total 

Expected 

 

Violent 2 

Have Children  1 (Yes)  2 (No) 
Yes (1) 

24.2234 

8.776596 

No (2) 

44.7766 

16.2234 

Observed  Expected  (Observed-Expected)  (Observed - Expected)^2  /Expected 

30 

24.2234 

5.7766 

33.3691 

1.3776 

3 

8.7766 

-5.7766 

33.3691 

3.8021 

39 

44.7766 

-5.7766 

33.3691 

0.7452 

22 

16.2234 

5.7766 

33.3691 

2.0568 

Chi-square Statistic 

7.9817 

Degrees of freedom = (row-1) (column -1) = (2-1) (2-1) = 1 

Probability = 0.004725 

Decision 

Since p-value, 0.0047 is less than 0.05, having children is a significant factor. 

Income and VIOLENT2 

 

Violent 2 

 
Income  1 (Yes)  2 (No)  Total 

1 

17 

8 

25 

2 

31 

12 

43 

3 

14 

3 

17 

4 

5 

2 

7 

Total 

67 

25 

92 

Expected = (row total/column total)/ Grand total 

Expected 

Income  1 (Yes)  2 (No) 

1 

18.2065 

6.7935 

2 

31.3152 

11.6848 

3 

12.3804 

4.6196 

4 

5.0978 

1.9022 

Observed  Expected  (Observed-Expected)  (Observed - Expected)^2  /Expected 

17 

18.2065 

-1.2065 

1.45569470699433 

0.0800 

31 

31.3152 

-0.3152 

0.0994 

0.0032 

14 

12.3804 

1.6196 

2.6230 

0.2119 

5 

5.0978 

-0.0978 

0.0096 

0.0019 

8 

6.7935 

1.2065 

1.4557 

0.2143 

12 

11.6848 

0.3152 

0.0994 

0.0085 

3 

4.6196 

-1.6196 

2.6230 

0.5678 

2 

1.9022 

0.0978 

0.0096 

0.0050 

Chi-square Statistic 

1.0925 

Degrees of freedom = (row-1) (column -1) = (4-1) (2-1) = 3 

Probability = 0.7789 

Decision 

Since probability, 0.7789 is greater than 0.05, income is NOT a significant factor 

Education and VIOLENT2 

 

Violent 2 

 
  1 (Yes)  2 (No)  Total 
High school (1) 

3 

5 

8 

Some college (2) 

20 

11 

31 

College graduate (3) 

29 

4 

33 

Graduate school (4) 

17 

5 

22 

Total 

69 

25 

94 

Expected = (row total/column total)/ Grand total 

Expected 

Income  1 (Yes)  2 (No) 

1 

5.8723 

2.1277 

2 

22.7553 

8.2447 

3 

24.2234 

8.7766 

4 

16.1489 

5.8511 

Observed  Expected  (Observed-Expected)  (Observed - Expected)^2  /Expected 

3 

5.8723 

-2.8723 

8.2503 

1.4049 

20 

22.7553 

-2.7553 

7.5918 

0.3336 

29 

24.2234 

4.7766 

22.8159 

0.9419 

17 

16.1489 

0.8511 

0.7243 

0.0449 

5 

2.1277 

2.8723 

8.2503 

3.8777 

11 

8.2447 

2.7553 

7.5918 

0.9208 

4 

8.7766 

-4.7766 

22.8159 

2.5996 

5 

5.8511 

-0.8511 

0.7243 

0.1238 

Chi-square Statistic 

10.2472 

Degrees of freedom = (row-1) (column -1) = (4-1) (2-1) = 3 

Probability = 0.016578 

Decision 

Since probability, 0.016578 is less than 0.05, education is a significant factor 

Hours and VIOLENT2 

 

Violent 2 

 
Age  1 (Yes)  2 (No)  Total 

1 

24 

3 

27 

2 

23 

3 

26 

3 

13 

5 

18 

4 

7 

10 

17 

5 

2 

4 

6 

Total 

69 

25 

94 

Expected = (row total/column total)/ Grand total 

Expected 

Age  1 (Yes)  2 (No) 

1 

19.81915 

7.180851064 

2 

19.08511 

6.914893617 

3 

13.21277 

4.787234043 

4 

12.47872 

4.521276596 

5 

4.404255 

1.595744681 

Observed  Expected  (Observed-Expected)  (Observed - Expected)^2  /Expected 

24 

19.8191 

4.1809 

17.4795 

0.8820 

23 

19.0851 

3.9149 

15.3264 

0.8031 

13 

13.2128 

-0.2128 

0.0453 

0.0034 

7 

12.4787 

-5.4787 

30.0164 

2.4054 

2 

4.4043 

-2.4043 

5.7804 

1.3125 

3 

7.1809 

-4.1809 

17.4795 

2.4342 

3 

6.9149 

-3.9149 

15.3264 

2.2164 

5 

4.7872 

0.2128 

0.0453 

0.0095 

10 

4.5213 

5.4787 

30.0164 

6.6389 

4 

1.5957 

2.4043 

5.7804 

3.6224 

Chi-square Statistic 

20.3277 

Degrees of freedom = (row-1) (column -1) = (5-1) (2-1) = 4 

Probability = 0.0004 

Decision 

Since probability, 0.0004 is less than 0.05, hours is a significant factor 

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Reference

StudyBounty. (2023, September 16). Chi-Square Goodness of Fit Test.
https://studybounty.com/chi-square-goodness-of-fit-test-essay

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