STATISTICS - CH 11, LECTURE
Lesson 11.3:
Contingency Tables
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CHI-SQUARE EXAMPLE |
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Contingency Table: |
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Totals |
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3 |
4 |
7 |
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df:
(2-1)(2-1)=1 |
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7 |
7 |
14 |
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If α= .05, |
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Totals |
10 |
11 |
21 |
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CV = 3.841 |
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Calculations: |
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observed |
row total |
col total |
expected |
(o-e)^2/e |
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3 |
7 |
10 |
3.333333 |
0.033333 |
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4 |
7 |
11 |
3.666667 |
0.030303 |
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7 |
14 |
10 |
6.666667 |
0.016667 |
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7 |
14 |
11 |
7.333333 |
0.015152 |
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0.095455 |
sum: chi sqr |
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30 |
70 |
100 |
33.33333 |
0.333333 |
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40 |
70 |
110 |
36.66667 |
0.30303 |
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70 |
140 |
100 |
66.66667 |
0.166667 |
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70 |
140 |
110 |
73.33333 |
0.151515 |
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0.954545 |
sum: chi sqr |
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300 |
700 |
1000 |
333.3333 |
3.333333 |
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400 |
700 |
1100 |
366.6667 |
3.030303 |
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700 |
1400 |
1000 |
666.6667 |
1.666667 |
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700 |
1400 |
1100 |
733.3333 |
1.515152 |
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9.545455 |
sum: chi sqr |
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The point: |
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The same proportions, with larger sample sizes, give
larger X^2 values |
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SAMPLE PROBLEM:
Perform a Chi-square (c2) test to determine (at the .05 significance level) whether there is a significant relationship between success in a Physics course and a proposed prerequisite; the following table breaks down the number of Physics students in a test group according to whether or not they had the proposed prerequisite, and whether or not they succeeded in Physics:
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Successful in Physics |
Not successful in
Physics |
Totals |
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Student had prerequisite |
54 |
11 |
65 |
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Student didn’t have prerequisite |
8 |
21 |
29 |
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Totals |
62 |
32 |
94 |
Return to: Merced College; Don Power Updated 05/07/08 by Don Power