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Unformatted text preview: Unit Two: Decision Analysis; Comparing Population Means Decision Analysis In general, desirable features of decisionmaking include making assumptions explicit, thoroughly generating alternative courses of action (which we will call decision alternatives or, simply, alternatives) to “put on the table” for consideration, establishing a solid basis for evaluating the decision alternatives, and—throughout the process—having evidencebased reasoning trump unsubstantiated opinions. The term decision analysis typically refers to methods of evaluating decision alternatives whose outcomes (which when numerical quantities, such as profits or costs, we will call payoffs) cannot be anticipated with certainty but rather depend on which of multiple possible future events (which we will call states of nature) occur. Methods for choosing one of multiple mutually exclusive decision alternatives Setting Method for choosing one decision alternative: Know the payoff of each decision alternative under each possible state of nature, but do not know the probabilities of those states of nature occurring. (This setting is classified as decisionmaking under uncertainty.) Optimistic approach: choose the decision alternative whose best possible payoff is the best. Note : For some payoffs (e.g., profits or revenues), larger is better; for some payoffs (e.g., costs or fines), smaller is better. Conservative approach : choose the decision alternative whose worst possible payoff is the best. Minimax regret approach : choose the decision alternative whose maximum possible regret is the smallest, where the regret of (from choosing) decision alternative i should state of nature j occur = how much better a payoff you could have achieved under state of nature j had you chosen the decision alternative yielding the best payoff under state of nature j. Note: An alternative name for regret is opportunity loss. Know the payoff of each decision alternative under each possible state of nature, and know the probabilities of those states of nature occurring. (This setting is classified as decisionmaking under risk.) Expected value criterion : Choose the decision alternative having the best expected value, where (with d i denoting decision alternative i, S j denoting state of nature j, and EV(d i ) denoting the expected value of d i ): . occur) S should choosing from (payoff ) ( ) ( ∑ = j j i j i d S P d EV Note : The expected value of a decision alternative is the average payoff that would result by consistently choosing that decision alternative over an indefinite (infinite) number of replications of the identical decision situation. Note : Below, EV is to be read “expected value.” Elaborations related to the EV criterion With PI denoting perfect information (a perfect prediction of the future) and SI denoting sample information (an imperfect prediction of the future): EV with PI = ∑ ⋅ j j S P ) ( (best possible payoff under j S ) EVPI (EV of PI) = EV with perfect information – EV attainable without any additional information...
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 Fall '08
 STAFF
 Normal Distribution, Standard Deviation, Variance, Null hypothesis, Statistical hypothesis testing

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