Chi Square A nonparametric hypothesis test by nfk14697

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									  Chi Square:
A nonparametric
 hypothesis test
           Unit 12
        Homework
 Ch 16: 1, 3, 7, 9, 13, 15, 17
       (pp.500-503)
 Finals Schedule

    Section 1 (2 pm):
11 am, Thursday, Dec 14

   Section 2 (3 pm):
2 pm, Thursday, Dec 14
Parametric vs. Nonparametric Tests
   Parametric hypothesis test
     about population parameter (m or s )
                                        2

     z, t, F tests

     interval/ratio data

   Nonparametric tests
     do not test a specific parameter

     nominal & ordinal data

     frequency data ~
            Chi-square (C2)
 Nonparametric tests
   same 4 steps as parametric tests

 Chi-square test for goodness of fit
   single variable

 Chi-square test for independence
   two variables

 Same formula for both
   degrees of freedom different

   fe calculated differently ~
    Assumptions & Restrictions
 Independence of observations
    any score may be counted in only

     1 category
 Size of expected frequencies
    If fe < 5 for any cell cannot use C
                                         2

    More likely to make Type I error

    Solution: use larger sample ~
         C2 Test for Goodness of Fit
 Test about proportions (p) in distribution
 2 different forms of H0
    No preference

        category   proportions are equal
       No difference
        from  comparison population
        e.g., student population
        55% female and 45% male?

   H1: the proportions are different ~
       Null Hypotheses: C2

                    Coke     Pepsi

No preference: H0    ½        ½


                    Female   Male

No difference: H0   55%      45%
        Sample Data: C2
 Frequency
 Expected frequency (fe)
   fe = pn

 Observed frequency (fo)
   S fo = n

 Degrees of freedom:Goodness of fit
   C-1

   C = number of cells (categories)

   C cv from table B.7, page A-34 ~
      2
Chi-square (C2)


               fo  fe 
                        2

C   2 
                  fe
             Example
 Classes’s favorite: Coke or Pepsi?
 H 0: ?
 C2cv =
    = .05

   df =                          ~
Coke or Pepsi?
    o       o
        e       e
     C2 Test for Independence
   2 variables
      are   they related or independent
 H0: also 2 forms
   no relationship between variables

   distribution of 1 variable is the

    same for the categories of other
 Same formula as Goodness of Fit
      different   df ~
    C2 Test for Independence
 Differences from Goodness of Fit
 df = (R-1)(C-1)
   R = rows

   C = columns

 Expected frequency for each cell


                 fC f R
            fe 
                   n
             Example
 Does watching violent TV programs
  cause children to be more
  aggressive on the playground?
 Data: frequency data
    Violent program: yes or no

    Aggressive: yes or no ~
         C2 Test for Independence
               Aggressive
              Yes      No
Violent TV        o            o
             41       e   9        e
   Yes


                  o            o
             17       e   33       e
   No

								
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