2 x 2 Table Statistics


Values for Stratum 1
'Disease'
(+)(-)
(+)662894
70.2%29.8%100%
64.7%46.7% 
'Exposure'(-)363268
52.9%47.1%100%
35.3%53.3% 
10260162
63%37%100%
100%100%

Values for Stratum 2
'Disease'
(+)(-)
(+)13961200
69.5%30.5%100%
59.9%53% 
'Exposure'(-)9354147
63.3%36.7%100%
40.1%47% 
232115347
66.9%33.1%100%
100%100%

Unstratified (Crude) Values
'Disease'
(+)(-)
(+)20589294
69.7%30.3%100%
61.4%50.9% 
'Exposure'(-)12986215
60%40%100%
38.6%49.1% 
334175509
65.6%34.4%100%
100%100%


Chi Square and Exact Measures of Association

StratumTestValuep-value(1-tail)p-value(2-tail)

1Uncorrected chi square5.0470.012330.02466
Yates corrected chi square4.3340.018680.03736
Mantel-Haenszel chi square5.0160.012560.02511
Fisher exact0.9920(lower)
0.01881(upper)
0.03762
Mid-P exactlower=0.9866
upper=0.01341
0.02682

2Uncorrected chi square1.4860.11160.2233
Yates corrected chi square1.2180.13540.2708
Mantel-Haenszel chi square1.4820.11200.2239
Fisher exact0.9088(lower)
0.1349(upper)
0.2698
Mid-P exactlower=0.8869
upper=0.1131
0.2261

CrudeUncorrected chi square5.2090.011240.02247
Yates corrected chi square4.7870.014340.02868
Mantel-Haenszel chi square5.1990.011300.02260
Fisher exact0.9912(lower)
0.01448(upper)
0.02895
Mid-P exactlower=0.9883
upper=0.01166
0.02331

AdjustedMantel-Haenszel Summary Chi Sqr5.2110.02245
Fisher exact0.9912(lower)
0.01438(upper)
0.02876
Mid-P exactlower=0.9884
upper=0.01158
0.02316


All expected values (row total*column total/grand total) are >=5
OK to use chi square.


Risk-Based* Estimates and 95% Confidence Intervals
(Not valid for Case-Control studies)

Point EstimatesConfidence Limits

StratumTypeValueLower, UpperType

1Risk in Exposed70.2160.29, 78.55Taylor series
Risk in Unexposed52.9441.24, 64.33Taylor series
Overall Risk62.9655.3, 70.02Taylor series
Risk Ratio1.3261.023, 1.72¹ Taylor series
Risk Difference17.272.232, 32.31° Taylor series

2Risk in Exposed69.562.79, 75.47Taylor series
Risk in Unexposed63.2755.22, 70.63Taylor series
Overall Risk66.8661.74, 71.61Taylor series
Risk Ratio1.0990.9421, 1.281¹ Taylor series
Risk Difference6.235-3.837, 16.31° Taylor series

CrudeRisk in Exposed69.7364.24, 74.7Taylor series
Risk in Unexposed6053.33, 66.32Taylor series
Overall Risk65.6261.39, 69.62Taylor series
Risk Ratio1.1621.018, 1.327¹ Taylor series
Risk Difference9.7281.334, 18.12° Taylor series
Etiologic fraction in pop.(EFp)8.5631.099, 16.03
Etiologic fraction in exposed(EFe)13.951.75, 24.64

AdjustedDirectly Adjusted RR1.1531.011, 1.317¹ Taylor series
MH Adjusted RR1.1621.018, 1.327¹ Taylor series
Directly Adjusted RD9.6521.283, 18.02° Taylor series

Breslow-Day test for interaction of Risk Ratio over strata: chi square=1.495p=0.2219
p greater than 0.05 does not suggest interaction. Adjusted RR can be used.


Breslow-Day test for interaction of Risk Difference over strata: chi square=1.428 p=0.2326
p greater than 0.05 does not suggest interaction. Adjusted RD can be used.



Odds-Based Estimates and Confidence Limits

Point EstimatesConfidence Limits

StratumTypeValueLower, UpperType

1CMLE Odds Ratio*2.0851.088, 4.028¹ Mid-P Exact
1.04, 4.223¹ Fisher Exact
Odds Ratio2.0951.094, 4.012¹ Taylor series

2CMLE Odds Ratio*1.3220.8409, 2.078¹ Mid-P Exact
0.8213, 2.127¹ Fisher Exact
Odds Ratio1.3230.8432, 2.076¹ Taylor series

CrudeCMLE Odds Ratio*1.5341.06, 2.222¹ Mid-P Exact
1.043, 2.259¹ Fisher Exact
Odds Ratio1.5361.061, 2.221¹ Taylor series
Etiologic fraction in pop.(EFp|OR)21.415.495, 37.32
Etiologic fraction in exposed(EFe|OR)34.885.793, 54.98

AdjustedCMLE Odds Ratio*1.5351.06, 2.223¹ Mid-P Exact
1.044, 2.259¹ Fisher Exact
Directly Adjusted OR1.5361.061, 2.225¹ Taylor series
Mantel-Haenszel OR1.5361.062, 2.222¹ Robins,Greenland,Breslow

Breslow-Day test for interaction of Odds Ratio over strata: chi square=1.298 p=0.2554
p greater than 0.05 does not suggest interaction. Adjusted OR can be used.

*Conditional maximum likelihood estimate of Odds Ratio
Martin,D; Austin,H (1991) An efficient program for computing conditional maximum likelihood estimates and exact confidence limits for a common odds ratio. Epidemiology 2, 359-362.
° ¹ 95% confidence limits testing exclusion of 0 or 1, as indicated
P-values < 0.05 and confidence limits excluding null values (0,1, or [n]) are highlighted.
LookFirst items: Editor's choice of items to examine first.


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