Sum
Out of a sample of 120 persons in a village, 80 were administered a new drug for preventing influenza and out of them 18 were attacked by influenza. Out of those who were not administered the new drug, 10 persons were not attacked by influenza: Prepare to compute the χ^{2 }square statistic.
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Solution
The observed frequency table can be prepared as follows:
Drug administered | Drug not administered | Row total (R_{i}) | |
Attacked | 18 | 30 | 48 |
Not Attacked | 62 | 10 | 72 |
Column total (C_{j}) | 80 | 40 | 120 |
Expected frequencies are given by
E_{ij} = `("R"_"ij"xx"C"_"ij")/"N"`
E_{11} `(48xx80)/120` = 32
E_{12} = `(48xx40)/120` = 16
E_{21} = `(72xx80)/120` = 48
E_{22} = `(72xx40)/120` = 24
Table of expected frequencies.
Drug administered | Drug not administered | Total | |
Attacked | 32 | 16 | 48 |
Not Attacked | 48 | 24 | 72 |
Total | 80 | 40 | 120 |
Now.
χ^{2} = `sum[(("O"_"ij"- "E"_"ij")^2)/"E"_"ij"]`
= `(18-32)^2/32+(30-16)^2/16+(62-48)^2/48+(10-24)^2/24`
= `196/32+196/16+196/48+196/24`
= 6.125 + 12.25 + 4.083 + 8.167
= 30.625
Concept: Chi-Square Statistic ( χ2 )
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