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Chapter

Lecture 3: Probabilities

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Department
Biology
Course
Biology 2244A/B
Professor
Ben Rubin
Semester
Winter

Description
PROBABILITIESRare Event Rule for Inferential Statistics If under a given assumption the probability of a particular observed event is extremely small we conclude that the assumption is probably not correctNote This concept is widely misunderstood but is essential to the logic of statistical inferenceThe probability described here is calculated in many statistical techniques and reported as a p valueMuch more on p values later in the courseeventany collection of results or outcomes of a proceduresimple eventan outcome or an event that cannot be further broken down into simpler componentssample spacefor a procedure consists of all possible simple eventsy That is the sample space consists of all outcomes that cannot be broken down any furtherNotation for Probabilities P denotes probability A B and C denote specific events PAthe probability of event A occurring Rule 1 Relative Frequency Approximation of Probability Conduct or observe a procedure and count the number of times that event A actually occurs Based on these actual results PA is estimated as follows PA number of times A occursnumber of times trial was repeatedNote Obtain an approximation instead of exact numberRequires Equally Likely Rule 2 Classical Approach to ProbabilityOutcomesAssume that a given procedure has n different simple events and that each of those simple events has an equal chance of occurring If event A can occur in s of these n ways then PA number of ways A can occur s number of different simple events n
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