{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

slide5 - Home Page Title Page STAT231 STATISTICS Paul...

Info icon This preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
Home Page Title Page Contents Page 1 of 16 Go Back Full Screen Close Quit First Prev Next Last Go Back Full Screen Close Quit STAT231: STATISTICS Paul Marriott [email protected] July 8, 2008
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Home Page Title Page Contents Page 2 of 16 Go Back Full Screen Close Quit First Prev Next Last Go Back Full Screen Close Quit Chapter 5: Model Assessment In this chapter we will look at the problem of fitting models to data Define the likelihood function and the method of maximum likelihood estimation After fitting we use the data to evaluate how good the model is for the Problem
Image of page 2
Home Page Title Page Contents Page 3 of 16 Go Back Full Screen Close Quit First Prev Next Last Go Back Full Screen Close Quit Association across categories One assumption that is often used in modelling is that data is independent. If the data is counts of categories then there is a simple χ 2 -test which we can use to test the hypothesis of independence. For simplicity suppose we are comparing two binary variates X and Y . Independence means that knowing the value of x for a ran- domly selected unit in the population does not affect the prob- ability that y equals 1 . In terms of probabilities we would want to check P ( Y = 1 | X = 1) = P ( Y = 1) .
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Home Page Title Page Contents Page 4 of 16 Go Back Full Screen Close Quit First Prev Next Last Go Back Full Screen Close Quit Association across categories Y/X X = 0 X = 1 Total Y = 0 a b a + b Y = 1 c d c + d Total a + c b + d n = a + b + c + d Table 1: Observed Frequencies for paired categorical variables If X and Y were independent we would expect that the num- ber of counts of units where X = 0 & Y = 0 would equal n × P ( X = 0) × P ( Y = 0) . Could be estimated via ( a + b + c + d ) a + b ( a + b + c + d ) a + c ( a + b + c + d ) = ( a + b )( a + c ) a + b + c + d
Image of page 4
Home Page Title Page Contents Page 5 of 16 Go Back Full Screen Close Quit First Prev Next Last Go Back Full Screen Close Quit Association across categories Y/X X = 0 X = 1 Total Y = 0 ( a + b )( a + c ) n ( a + b )( b + d ) n a + b Y = 1 ( c + d )( a + c ) n ( c + d )( b + d ) n c + d Total a + c b + d a + b + c + d Table 2: Expected Frequencies for paired categorical variables when independence is assumed
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Home Page Title Page Contents Page 6 of 16 Go Back Full Screen Close Quit First Prev Next Last Go Back Full Screen Close Quit Association across categories Denote the four cell counts in observed table by o i Denote the four counts in expected table by e i Calculate the following statistic. s = i ( o i - e i ) 2 e i . Under independence the random variable version of this has an approximate χ 2 1 distribution. Thus we can calculate a p -value for the hypothesis of inde- pendence between X and Y via P ( S s ) where S χ 2 1 .
Image of page 6
Home Page Title Page Contents Page 7 of 16 Go Back Full Screen Close Quit First Prev Next Last Go Back Full Screen Close Quit Association across categories
Image of page 7

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern