Chi Square

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Chi Square

• Fr Chris - St Francis High School
• March 2006

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Two Applications

• Goodness of Fit (one way)
• Two-Way (Contingency) Table

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1-Way(Univariate) Data

• Observed frequencies are from a RANDOM SAMPLE
• Large Sample size (expect at least 5 in each
  category)

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Stolen Cars by Color
San Luis Obispo Telegram-Tribune 9/2/96
Null Hypothesis Color makes no difference
15 white, 15 blue, 35 red, 30 black, 5 other
Alternative Hypothesis Color makes a difference
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SRS, and All EXPECTED cells gt5 so large enough
sample
Since P(Chi-sq, df4 gt 18.46) lt .001 so we reject
the null hypothesis, and conclude certain colors
are more likely to be stolen
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Now you try According to SLO Trib, 12/15/99,
SRS of 200 purchases of California Lotto tix
California in 1999 had 35 18-34, 51 35-64, 14
over 65
Try a Chi-Sq Goodness of Fit Test
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2 way Chi-Square is even more Fun! According to
Research Quarterly for Exercise and Sport, (1990)
p 315-320, SRS of 1200 looked at hours of TV and
a cardiovascular test
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But we compute df(r-1)(c-1) and the expected
frequencies are computed with by the marginal
totals
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Expected Frequency (Row)(Col)/total
df(4-1)(2-1)3, So we reject the Null Hypothesis
at the .05 level for any Chi Square over 12.83
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less than 12.83, so there is not enough evidence
to reject the null hypothesis at the .05 level,
so there is little evidence here that would
suggest that the hours watching TV is associated
with ones cardiovascular fittness.
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