Transcript Nonparametric Tests: Chi Square  Lesson 16 Parametric vs. Nonparametric Tests Parametric hypothesis test about population parameter (m or s )  z, t, F.

Nonparametric Tests:
Chi Square

2
Lesson 16
Parametric vs. Nonparametric Tests
Parametric hypothesis test
2
 about population parameter (m or s )
 z, t, F tests
 interval/ratio data
 Nonparametric tests
 do not test a specific parameter
 nominal & ordinal data
 frequency data ~

Chi-square ( 2)
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 ~

Sample Data: 2
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)
2
  cv from table B.5, page 364 ~

Chi-square (2)

2 

 fo  fe 
2
fe
Assumptions & Restrictions
Independence of observations
 any score may be counted in only
1 category
 Size of expected frequencies
2
 If fe < 5 for any cell cannot use 
 More likely to make Type I error
 Solution: use larger sample ~

2 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: 2
No preference: H0
No difference: H0
Coke
Pepsi
½
½
Female
Male
55%
45%
SPSS: No Preference
Data in 1 column
 Analyze
Nonparametric

Legacy Dialogs
Chi square

Dialogue box

Test Variable List

Expected Values  All categories Equal

Options  Descriptives (frequencies) ~
SPSS: No Difference

Same menus as No Preference


But must specify proportions or frequencies
Dialogue box

Expected Values  Values

Specify & Add vales one at time

In same order as defined values for
variable in variable view ~
*Effect Size: 1 Variable
EffectSize 

2
N (df )
N = total sample size across all
categories
 df = #categories – 1
 zero = no difference
 1 = large difference ~
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2 Test for Independence

2 variables
are they related or independent
H0:
 distribution of 1 variable is the same
for the categories of other
 no difference
 Same formula as Goodness of Fit

different df ~
2 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 ~

2 Test for Independence
Aggressive
Yes
No
Violent TV
Yes
No
41
9
17
33
SPSS: Test for Independence
Two variables
 Two-Way Contingency Table Analysis
 Data: 1 column for each variable
 Analyze
Descriptives
Crosstabs
 Dialogue Box
 Variables  Rows or Columns
 Statistics  Chi Square, *Phi
~

Effect Size (): 2 Variables


2
N
N = total sample size across all
categories
 Phi values: 0-1
 Interpret similar to Pearson’s r
 Small = .1; medium = .3, large = .5 ~
