# 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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