2x2 Contingency Table with Odds Ratios, etc.

For a 2x2 Contingency Table:
·Rates, Risk Ratio, Odds, Odds Ratio, Log Odds
·Phi Coefficient of Association
·Chi-Square Test of Association
·Fisher Exact Probability Test

For two groups of subjects, each sorted according to the absence or presence of some particular characteristic or condition, this page will calculate standard measures for Rates, Risk Ratio, Odds, Odds Ratio, and Log Odds. It will also

calculate the Phi coefficient of association;_T
perform a chi-square test of association, if the sample size is not too small; and_T
perform the Fisher exact probability test, if the sample size is not too large. [Although the Fisher test is traditionally used with relatively small samples, the programming for this page will handle fairly large samples, up to about n=1000, depending on how the frequencies are arrayed within the four cells.]_T
For intermediate values of n, the chi-square and Fisher tests will both be performed.

To proceed, enter the values of X₀Y₁, X₁Y₁, etc., into the designated cells. When all four cell values have been entered, click the «Calculate» button. To perform a new analysis with a new set of data, click the «Reset» button.

The logic and computational details of the Chi-Square and Fisher tests are described in Chapter 8 and Subchapter 8a, respectively, of Concepts and Applications.

Data Entry_T

	Condition			Expected Cell Frequencies per Null Hypothesis
	absent	present	Totals	Expected Cell Frequencies per Null Hypothesis
Group 1
Group 2
Totals

	Rate	Risk Ratio	Odds	Odds Ratio	Log Odds
Group 1
Group 2

Rate = proportion in group with condition present
Risk Ratio = Rate[1]/Rate[2]
Odds[1] = present[1]/absent[1]
Odds[2] = present[2]/absent[2]
Odds Ratio = Odds[1]/Odds[2]
Log Odds = natural logarithm of Odds Ratio

		.95 Confidence Intervals
	Observed	Lower Limit	Upper Limit
Risk Ratio
Odds Ratio

	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

Fisher Exact Probability Test:_T

P	one-tailed
P	two-tailed

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