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# Chi Square Distribution

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### Chi Square Distribution

1. 1. The Chi-square distribution  ²
2. 2. Non Parametric Tests <ul><li>These are tests conducted where there is no assumption about the parameters of the population or population from which the draw of samples.  ² test of independence and goodness of fit is a permanent eg. of the use of non parametric tests.It is very popular in behavioral sciences . </li></ul>
3. 3. Formula <ul><li>In a contingency table with r rows and c columns </li></ul><ul><li> ² =  (O-E)² </li></ul><ul><li>E with (r-1) (c-1) degrees of freedom. Where o is the observed frequency and E is the expected frequency. </li></ul>
4. 4. Question no 1 <ul><li>The demand for a particular space part in a factory was found to vary from day to day.In a sample study the observations was obtained </li></ul><ul><li>Ans:H0 </li></ul>
5. 5. Question 1 <ul><li>In the course of antimalarial work in a certain city over a period of time Quinine was given to 606 adults out of a total population of 3540. The data regarding the incidence of malarial fever is given below </li></ul>d 2741 c 193 Quinine not used b 587 a 19 Quinine used Having no fever Having Fever
6. 6. Formula <ul><li> ² = (ad-bc)² * n </li></ul><ul><li>(c+d)(a+b)(a+c)(b+d) </li></ul>
7. 7. Answer 606 b 587 a 19 Quinine used 2934 d 2741 c 193 Quinine not used 3.84 Dof=1 Ans=10.57 3540 Having no fever Having Fever
8. 8. Answer <ul><li> ² = (ad-bc)² * n </li></ul><ul><li>(c+d)(a+b)(a+c)(b+d) </li></ul><ul><li>=10.57> 3.84 The difference is significant(reject H0) </li></ul>606 b 587 a 19 Quinine used 2934 d 2741 c 193 Quinine not used 3540 Having no fever Having Fever
9. 9. Formula <ul><li>In a contingency table with r rows and c columns </li></ul><ul><li> ² =  (O-E)² </li></ul><ul><li>E with (r-1) (c-1) degrees of freedom. Where o is the observed frequency and E is the expected frequency. </li></ul>
10. 10. Question 2 <ul><li>A movie producer is bringing out a new movie in order to map out its advertising campaign ,he wants to determine whether the movie will appeal to most to a particular age group or whether it will appeal equally to all age groups. The producer takes a random sample from the person attending preview of the new movie and obtain the following results. What inference you will draw from the data? </li></ul>20 10 10 20 In different 22 42 22 54 Unlike the movie 28 48 78 146 Like the movie 60&Above 40-59 20-39 Under 20
11. 11. Answer <ul><li>Expected Frequency </li></ul><ul><li>E1 = 300*220 =132 E2 = 300*110 =66 …. </li></ul><ul><li>500 500 </li></ul><ul><li> ² =  (O-E)² </li></ul><ul><li>E </li></ul><ul><li> ² = (146-132)² + (78-66)²+… .. =40.16 </li></ul><ul><li>132 66 </li></ul><ul><li>Degrees of freedom=(r-1)(c-1)= (4-1)(3-1)=6 </li></ul><ul><li>ie. 40.16>12.59 Diff is significant (reject H0) </li></ul>60 20 10 10 20 In different 500 70 100 110 220 140 22 42 22 54 Unlike the movie 300 28 48 78 146 Like the movie 60&Above 40-59 20-39 Under 20 22