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