is used when we have categorical (nominal) rather than interval / ratio data can also be used for measurement data, is less powerful and than typical tests such as means

1
is used when we have categorical (nominal) rather
than interval / ratio datacan also be used for
measurement data, is less powerful and than
typical tests such as means
CHI Square
2
Measurement dataeach number represents a score
along a continuumFrequency / Nominal /
Categorical DataEach score represents a
frequency in a category.
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Example Classify webpage as good or bad
Web page seen as
Good Bad Total 26 40 68
Question Is the number of good web pages (26)
significantly different than the number of bad
webpages (40)?
4
Expected and Observed Frequency
Web page seen as
Good Bad Total Observed 26 40 68 Expected 34 34
68
Question Is the number of good web pages (26)
significantly different than the number of bad
webpages (40)?
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The CHI square statistic
Good Bad Total Observed 26 40 68 Expected 34 34
68
CHI square or X2
N 1861.00
X2 2.94
Look up the appropriate degrees of freedom in the
X2 table E. If X2 bigger than the critical X2,
then it is significant
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CHI Square test has exactly the same logic as a
t-testThe only difference is that it is
computed on frequencies rather than scores
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CHI Square for a multicategory case
Good Bad Medium Total Observed 26 40 15 81 Expec
ted 27 27 27 81
CHI square or X2
X2 11.63
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SPSS output
NPar Tests Chi-Square Test Frequencies
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CHI Square for a Contingency Table Analysis
(when there is more than one variable)
Good Bad Medium Total Finance 26 (27) 40 (27)
15 (27) 81 Newspaper 21 (30) 27 (30) 42 (30)
90
The table shows that webpages in the Finance
category were more were more likely to be good
than were webpages in the Newspaper condition.
Thus, the column a webpage is in (Good, Bad, or
Medium) graduate) is contingent upon (depends on)
the row the webpage is in (Finance or newspaper
category)
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Contingency Table Analysis
Good Bad Medium Total Finance 36 (27) 25 (27)
20 (27) 81 Newspaper 21 (27) 27 (27) 33 (27)
81
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SPSSusing the Non Parametric tool
NPar Tests Chi-Square Test Frequencies
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SPSS using cross tabs
Crosstabs
Mean 393.2
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Issues with CHI Square
Problem of small expected frequencies Not a good
test when expected frequencies are small, i.e.,
less than 5 Use CHI Square on frequencies not
proportions. Convert proportions to frequencies
using sample size
Minimum 0
Maximum 4132
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How to obtain expected frequenciesUniform
DistributionNormal DistributionTheoretical
Reason
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Confidence Limits on Mean

• Sample mean is a point estimate
• We want interval estimate
• Probability that interval computed this way
  includes m 0.95

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For Our Data
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Confidence Interval

• The interval does not include 5.65--the
  population mean without a violent video
• Consistent with result of t test
• What can we conclude from confidence interval?