STAT 104: Section 4 27 Feb, 2008 TF: Daniel Moon

Agenda of Today Observational Study vs. Design of Experiment Population vs. Sample Probability Rules Bayes’ Rule

Observational Study vs. Experimental Design Collects information from individuals making no attempt to influence the responses Various ways to collect information Simple random sampling, stratified random sampling, multi-stage sampling Imposes an intervention on individuals in order to observe their responses 3 principles Control Randomization Repetition Observational Study Experimental Design

Population and Samples Population Sample Parameter Statistic

Bias and Variability Bias Distance of the center of the sampling distribution from the true parameter Variability Variance of the sampling distribution Size doesn’t matter!

Agenda of Today Observational Study vs. Experimental of Design Population vs. Sample Probability Rules Bayes’ Rule

Sample Space & Event Sample Space A set of all possible outcomes for an activity or experiment. Examples Event a set of outcomes (a subset of the sample space) to which a probability is assignedsetsubsetsample space P(Event) = |Event| / |Sample Space|

Probability Rules P(A  B) = P (A & B) – intersection P(A  B) = P (A or B) – union P (A  B) = P(A) + P(B) - P(A  B) 0 ≤ P(A  B) ≤ P(A) or P(B) ≤ P(A  B) ≤ P(A) + P(B) P(A  B) = P(A|B) x P(B)

Probability Rules If Mutually Exclusive P(A  B) = 0 P(A|B) = 0 P (A  B) = P(A) + P(B) If Independent P(A|B) = P(A) P(A  B) = P(A) x P(B)

Problems DJ Shuffle Combination: Order doesn’t matter! N choose K Permutation: Order matters! Line-up M&M’s Probability Distribution describes the values and probabilities that a random event can take placeprobabilitiesrandom event total probabilities must sum to exactly 1, or 100%sum

Bayes Rule

Find the iPod!!! What is the probability you picked up friend A’s iPod given the first song you listened was Rock? Friend A listens to, 30% Rock, 70% Ballads Friend B listens to, 80% Rock, 20% Ballads Given a 50% chance you picked up friend A or friend B’s ipods

Drug Testing Many staff are falsely worried by a positive TB test From Lecture Note 12