46 Lecture 10 - Goodness of Fit and Contingency Analysis

46 Lecture 10 - Goodness of Fit and Contingency Analysis -...

Info icon This preview shows pages 1–13. Sign up to view the full content.

View Full Document Right Arrow Icon
Lecture 10: Chi-Squared (Non-Parametric) Tests Goodness of Fit Contingency Analysis
Image of page 1

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

View Full Document Right Arrow Icon
2 Agenda 1. Goodness of fit tests Test of uniform distribution Test of normality Test of more than 2 proportions 2. Contingency analysis
Image of page 2
3 Announcements Quiz next week?
Image of page 3

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

View Full Document Right Arrow Icon
Goodness of Fit Test
Image of page 4
5 Introduction Remember one of the key ANOVA  assumptions: Each population is normally distributed This is also relevant to our use of the  Central Limit Theorem How do we test for this?  In general, how do we test whether  a population fits a particular  distribution? 
Image of page 5

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

View Full Document Right Arrow Icon
6 The Goodness of Fit Test The title describes this test very well We begin with a categorical variable This could be the classes of a frequency  distribution We will check whether the frequencies  in the  observed  frequencies conform to  what we would  expect  to see Here is a simple example
Image of page 6
7 Example 12.2 (p.484) The data on the following slide reflect`  the choices of majors by a sample of  200 incoming freshmen students. Using a significance level of  α  = 0.05, is  there sufficient evidence to conclude  that the distribution of major choices is  not uniform (i.e. not the same frequency  for all majors)?
Image of page 7

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

View Full Document Right Arrow Icon
8 Example 12.2 (cont’d) Just by looking at the data, do we think they  follow a uniform distribution? Should we draw this conclusion right away? Major # of Students Liberal Arts 44 Engineering 30 Education 26 Business 45 Sciences 55 200
Image of page 8
9 The Logic of Goodness of Fit At a first glance, the sample data do not  indicate a uniform distribution Nearly all categories are different! But  this may well be due to sampling error We need to check whether these differences  are  significant Once again we face the problem of inference : What sound judgment about the population can  we make based on sample data only?
Image of page 9

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

View Full Document Right Arrow Icon
10 The Logic… (cont’d) What we have in the table are the  observed  values for each category We will compare these to the  expected   values for each category  These are the values we would expect to  see if the data really did follow a uniform  distribution
Image of page 10
11 The Logic… (cont’d) Our test statistic will reflect the total  difference between  observed  and  expected  values If this difference is too large (relatively  speaking), we will conclude that the  data do not follow the said distribution
Image of page 11

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

View Full Document Right Arrow Icon
12 The Steps of Goodness of Fit 1.
Image of page 12
Image of page 13
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