2x2 Risk/Benefit Contingency Table

CountsOutcome
present		Outcome
absent		Totals
Experimental
group
Control
group
Totals
Parameters
Overall outcome rate Overall non-outcome rate
Experimental outcome rate Control outcome rate
Experimental outcome odds Control outcome odds
Absolute attributable effect
(absolute outcome difference)		 95% CI of attributable effect
Relative attributable effect
(relative outcome difference)
NNTB/NNTH
(Number needed to benefit/harm)		 95% CI of NNTB/NNTH
Attributable ratio
(relative outcome ratio)		 95% CI of attributable ratio
Odds ratio 95% CI of odds ratio
ProbabilitiesOutcome
present		Outcome
absent		Totals
Experimental
group
Control
group
Totals1.000
Definitions
Experimental outcome rate (EER)p(O+|E)/p(E)Probability of outcome in experimental group
Control outcome rate (CER)p(O+|C)/p(C)Probability of outcome in control group
If the experiment is an action/observation testing for increased likelihood of an outcome, then the hypothesis is EER > CER
If the experiment is an action/observation testing for decreased likelihood of an outcome, then the hypothesis is EER < CER
Experimental outcome oddsp(O+|E)/p(O-|E)Odds of outcome in experimental group
Control outcome oddsp(O+|C)/p(O-|C)Odds of outcome in control group
Absolute outcome differenceEER - CERAbsolute difference in the probabilities of outcomes between experimental and control groups
If the outcome is greater in the experimental group, this will be a positive number; if the outcome is greater in the control group, this will be a negative number
Relative outcome difference(EER - CER)/CERRelative difference in the probabilities of outcomes between experimental and control groups
If the outcome is greater in the experimental group, this will be a positive number; if the outcome is greater in the control group, this will be a negative number
Number needed (NN)1/(EER-CER)# of samples needed for a net change of 1 outcome