X |
Expected Cell Frequencies per Null Hypothesis
| 0 |
1 |
Totals |
| Y |
1 |
0 |
| Totals |
| |
Chi-Square |
Chi-square is calculated only if all expected cell frequencies are equal to or greater than 5. The Yates value is corrected for continuity; the Pearson value is not. Both probability estimates are non-directional. Phi |
Yates |
Pearson | |
P | one-tailed | |
two-tailed |
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0 | 1 | Totals
1
| a
| b
| a+b
| 0
| c
| d
| c+d
| Totals
| a+c
| b+d
| n
| |
which for computational purposes reduces to
Also, the degree of disproportion within any array of cell frequencies
For any particular observed array of cell frequencies, the programming embedded in this page calculates the probability of that particular array plus the probabilities of all other possible arrays whose degree of disproportion is equal to or greater than that of the observed array. Thus, for the observed array
2
7
9
8
2
10
10
9
19
the one-tailed probability would be the sum of the separate probabilities for the arrays
probability
2
7
8
2
0.01754
1
8
9
1
0.00097
0
9
10
0
0.00001
sum = 0.01852
(one-tailed probability)
And the two-tailed probability would be that sum plus the sum of the separate probabilities for the arrays of equal or greater disproportion at the other extreme:
probability
8
1
2
8
0.00438
9
0
1
9
0.00011
sum = 0.00449
two-tailed probability = 0.01852 + 0.00449 = 0.02301
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©Richard Lowry 1998-
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