Chi-square formula Once we have found the Chi square value, then we need to go to a Chi-square table...
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Transcript of Chi-square formula Once we have found the Chi square value, then we need to go to a Chi-square table...
![Page 1: Chi-square formula Once we have found the Chi square value, then we need to go to a Chi-square table of numbers for: At the Level of Significance we.](https://reader038.fdocuments.in/reader038/viewer/2022110400/56649dbe5503460f94ab1fd4/html5/thumbnails/1.jpg)
Chi-squareProcedures
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Observedis score we get
Expected
we would get if there were no differences.
Chi-square formula
![Page 4: Chi-square formula Once we have found the Chi square value, then we need to go to a Chi-square table of numbers for: At the Level of Significance we.](https://reader038.fdocuments.in/reader038/viewer/2022110400/56649dbe5503460f94ab1fd4/html5/thumbnails/4.jpg)
Once we have found the Chi square value, then we need to go to a Chi-square table of numbers for:
At the Level of Significance we set.
Chi-square value
Critical (or cut-off) value we must exceed
Chi-square formula
![Page 5: Chi-square formula Once we have found the Chi square value, then we need to go to a Chi-square table of numbers for: At the Level of Significance we.](https://reader038.fdocuments.in/reader038/viewer/2022110400/56649dbe5503460f94ab1fd4/html5/thumbnails/5.jpg)
![Page 6: Chi-square formula Once we have found the Chi square value, then we need to go to a Chi-square table of numbers for: At the Level of Significance we.](https://reader038.fdocuments.in/reader038/viewer/2022110400/56649dbe5503460f94ab1fd4/html5/thumbnails/6.jpg)
Director of recreation program wonders if there would be enough takers among his members to
warrant aBungee Cord Jumping program
He can ask all his customers. But what if 35 / 100 say yes. How will he decide if that’s a significant number.He decides to set up his inquiry as a scientific study, and so has a hypothetical question –There is not a significant difference between the yes and the nos. This is a null hypothesis, he assumes nothing.
His study will look something like this.
The Bungee Cord Jumping Dilemma
![Page 7: Chi-square formula Once we have found the Chi square value, then we need to go to a Chi-square table of numbers for: At the Level of Significance we.](https://reader038.fdocuments.in/reader038/viewer/2022110400/56649dbe5503460f94ab1fd4/html5/thumbnails/7.jpg)
![Page 8: Chi-square formula Once we have found the Chi square value, then we need to go to a Chi-square table of numbers for: At the Level of Significance we.](https://reader038.fdocuments.in/reader038/viewer/2022110400/56649dbe5503460f94ab1fd4/html5/thumbnails/8.jpg)
![Page 9: Chi-square formula Once we have found the Chi square value, then we need to go to a Chi-square table of numbers for: At the Level of Significance we.](https://reader038.fdocuments.in/reader038/viewer/2022110400/56649dbe5503460f94ab1fd4/html5/thumbnails/9.jpg)
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Determine the Chi-square statistic
from the data
Next Step
![Page 11: Chi-square formula Once we have found the Chi square value, then we need to go to a Chi-square table of numbers for: At the Level of Significance we.](https://reader038.fdocuments.in/reader038/viewer/2022110400/56649dbe5503460f94ab1fd4/html5/thumbnails/11.jpg)
Categories Observed Expected
YES 20 50
NO 80 50Total 100 100
Chi-square calculationsOur Chi-square value
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O- E O-E squared YES -30 900 NO 30 900
YES -30 900 900/50 = 18NO 30 900 900/50 = 18
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Categories
Observed
Expected
O - E (O – E) 2 (O – E) 2E
YES 20 50 -30 900 / 50 18
NO 80 50 30 900 / 50 18
100 100 Chi-sq value
36
Chi-square calculations
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1. Significance level was 0.52. Critical value at 0.5 is 3.85
3. Our Chi-square value is 364. This exceeds the critical value at the 0.5
level
5. We reject the null that there is no difference between the YES and NOs
Our Calculations
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Two types = One – way or Two –way
One –way = One Column or Row (df = C – 1)
Different Forms of Table
Category Observed Expected
Yes
No
Category 1 2 3 4 5
Observed
Expected
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Category 1 2 3 4 5
Observed 7 8 10 10 15
Expected 10 10 10 10 10
One-way calculations
N= 50
7-10 8-10- 10-10 10-10 10-10 10 10 10 10 10
9 4 0 0 25 .9 + .4 + 0 + 0 +25 3.8 10 10 10 10 10
O – E E
df = 5 - 1 = 4 Chi critical value = 9.49 No significant differences
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Two-way tableCategory
Natural Observed
Natural Expected
Artificial Observed
ArtificialExpected
Margin Total
Won 39 21 60
Lost 6 14 20
MarginTotal
45 35 Total=80
How do we find the expected?Col + Row Margin
Grand Total
Nat/won = (60x45) / 80 = 33.75Nat/lost = (20 x 45) / 80 = 11.25Art /won = (60 x 35) / 80 = 26.25Art/ lost = (20 x 35 ) / 80 = 8.75
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Two-way contCategory
Natural Observed
Natural Expected
Artificial Observed
ArtificialExpected
Margin Total
Won 39 33.75 21 26.5 60
Lost 6 11.25 14 8.75 20
MarginTotal
45 35 Total=80Nat/won = (60x45) / 80 = 33.75Nat/lost = (20 x 45) / 80 = 11.25Art /won = (60 x 35) / 80 = 26.25Art/ lost = (20 x 35 ) / 80 = 8.75Category Observed Expected (O – E) / E
Nat/ won 39 33.75 0.82
Nat/ lost 6 11.25 2.45
Art / won 21 26.25 1.05
Art / lost 14 8.75 3.15
Totals 80 80 X = 7.47
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Two-way cont
Category Observed Expected (O – E) / E
Nat/ won 39 33.75 0.82
Nat/ lost 6 11.25 2.45
Art / won 21 26.25 1.05
Art / lost 14 8.75 3.15
Totals 80 80 X = 7.47
How we get df?
(C-1)(R-1)(2 -1)(2 –
1) = 1
Critical value at 0.05, 1 df = 3.84Our Chi = 7.47There is a significant differences between surfaces
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Category 1 2 3 4 5
Observed 15 25 57 66 37
Expected 40 40 40 40 40
Homework One-way calculations
N= 50
15- 40 25-40 57-40 66-40 37-40 40 40 40 40 40
625 225 289 676 9 40 40 40 40 40
(O – E) 2 E
df = 5 - 1 = 4 Chi critical value = 9.49Reject NullThere are significant differences
45.6
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Two-way tableCategory
YesObserved
YesExpected
NoObserved
NoExpected
Margin Total
18-39 45 44.34 35 35.67 80
40 - 59 56 44.34 24 35.67 80
60 + 32 44.34 48 35.67 80
MarginTotal
133 107 240
Col + Row Margin Grand Total
YES - 80 x 133 / 240 = 44.34
NO - 80 x 107 / 240 = 35.67
Df = ? Df = (c-1)(r-1) = (2-1)(3-1)= 1 x 2 = 2
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YES45 - 44.34 /44.34 = (O. 66)2/44.34 = 0.01
56 - 44.34 /44.34 = 3.07 32 - 44.34 /44.34 =3.43
NO 35 - 35.67 / 35.67 = -(0.67)2/35.67 =
0.013 24 - 35.67 / 35.67 = 3.8 48 – 35.67 / 35.67 = 4.26 Sum all= 14.6 Critical value = 5.99 Reject Null
Chi value = (O – E) 2 E