The ChiSquare Distribution

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The Chi-Square Distribution
Chi-Square Curve
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The Chi-Square Distribution
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The Chi-Square Goodness of Fit Test
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The Chi-Square Goodness of Fit Test
For a chi-square goodness-of-fit test, the test
statistic has approximately a chi-square
distribution if the null hypothesis is true. The
number of degrees of freedom is 1 less then the
number of possible values for the variable under
consideration.
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The Chi-Square Goodness of Fit Test
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The Chi-Square Goodness of Fit Test
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The Chi-Square Goodness of Fit Test
In the following cases we have given the relative
frequencies for the null hypothesis of a
chi-square-goodness-of-fit test and the sample
size. In each case decide whether assumptions 1
and 2 using that test are satisfied.
Sample size n 100. Relative frequencies .65,
.30, .05
Sample size n 50. Relative frequencies .65,
.30, .05
Sample size n 50. Relative frequencies .22,
.21, .25, .30, .02
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The Chi-Square Goodness of Fit Test
The following is statistics involving prisoners
on Death Row from 1980.
A frequency distribution of educational
attainment for 128 randomly sampled prisoners
sentenced to death in 1998 is as follows
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The Chi-Square Goodness of Fit Test
Identify the population and variable under
consideration.
Do the data provide sufficient evidence to
conclude that the educational attainment of
prisoners sentenced to death differs from that of
1980 death row inmates?
Create a table with the following Education,
observed, expected frequency, difference, square
of difference, Chi-square subtotal.
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The Chi-Square Goodness of Fit Test
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The Chi-Square Goodness of Fit Test
At the 5 significance level the data do provide
sufficient evidence to conclude that the
distribution level of education is different from
1980.
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The Chi-Square Independence Test
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The Chi-Square Independence Test
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The Chi-Square Independence Test
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The Chi-Square Independence Test
Following is a contingency table showing cross
classification of educational attainment for a
sample of 1273 Native Americans.
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The Chi-Square Independence Test
Expected frequencies are calculated by
Step 2Expected frequencies are in the table.
Step 3 Assumptions 1 and 2 are satisfied since
all E are 5 or greater.
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The Chi-Square Independence Test
Step 8 There is sufficient evidence to conclude
that education level and diabetes among rural
Native Americans in New Mexico are dependent.