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# Week 6 Notes Stat121! STAT 121

BYU

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This 6 page Class Notes was uploaded by Amanda Berg on Sunday October 11, 2015. The Class Notes belongs to STAT 121 at Brigham Young University taught by Dr. Christopher Reese in Fall 2015. Since its upload, it has received 44 views. For similar materials see Principles of Statistics in Statistics at Brigham Young University.

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Date Created: 10/11/15

Week 6 Notes Lesson 14 Designs of Experiments and Sample Surveys Randomized Block Design RBD o What is a block Same thing as a strata in observational studies Group of individuals that are similar with respect to some characteristic known before the experiment begins and that characteristic is expected to affect the response of treatments Often equal in number to the number of treatments Example testing the effects of a drug on rats separate rats into litters because genetically they are similar 0 What is randomized block design An experimental design where the random assignment of individuals to treatments is carried out separately within each block Note blocks are another form of control they control the effects of the variables that de nes the blocks Less lurking variables than RCE As many randomizations as we have blocks 0 As many subjects as treatments in block 0 Accounts for lurking variables makes experimental design more powerful by equalizing the effects of certain lurking variables 1 randomly classify subjects based on lurking variables 2 randomly assign subjects to treatments separately within each block o It is an experiment because there is comparison randomization and replication each block 0 Bene ts of RBD o RCE use when individuals are similar 0 RBD use when individuals are similar within a block but different from block to block RBD prevents confounding of lurking variables with response variable RBD reduces chance of variation by removing variation associated with the lurking variable RBD yields more precise estimates of chance variation which makes detection of statistical signi cance easier Matched Pairs o If all blocks have size 2 two individuals and the experiment involves two treatments this is a randomized block design called matched pairs de gn examples 0 Subjects are sets of identical twins each receiving a different treatment 0 quotsubjectsquot are left and right arms of the same individual 0 Before and after treatment measurements on the same individual Special case of randomized block designs Block pair of individuals or pairs of measurements Explanatory variable two treatments Matched pairs are experiments because Randomly assign the two treatments of the two individuals within each pair block OR randomize the order of applying the treatments to each individual Replication equals the number of pairs Compare the two treatments Each pair serves as its own control 0 Example Dieting with exercise and dieting without exercise are compared using 20 sets of identical twins Explanatory variable whether dieting includes exercise 0 Response variable cholesterol level 0 Block pair of identical twins 0 Comparison two treatments 0 Randomization randomly select one twin to diet with exercise and the other to diet without exercise 0 Replication 20 pairs of identical twins 0 Types of questions in sample surveys 0 Open questions allow for almost unlimited responses Ex what is your favorite type of music Advantages less restrictive so answers are a better representation of the actual opinions of the population Disadvantages harder to analyze 0 Closed questions limit response options Ex Which of these types of music do you prefer Rock classical pop or hiphop Advantages easier to analyze Disadvantages may be biased by the options provided 0 Closed questions should permit options such as quototherquot andor quotnot surequot if those options apply 0 Question wording o Wording of question leads miseads or confuses Examples Loaded words 0 Double negatives 0 quotDoes it seem possible or does it seem impossible to you that the extermination of the Jews by the Nazis never happenedquot Wordy questions 0 quotThe term Holocaust usually refers to the killing of millions ofJews in Nazi death camps during WW2 In your opinions did the holocaust de nitely OOOO happen probably not happen or de nitely not happenquot Probability What is probability 0 Taking an SRS from a population and calculating a summary statistic analogous to game of chance 1 do random procedure with many possible outcomes 2 end up with one particular outcome 3 distribution of outcomes for large number of plays can be characterized 0 Not redoing the experiment but predicting what would happen if you did 0 Probability theory 0 Components 1 speci c game including strategy if applicable 2 specify possible outcome sample space 3 specify probability distribution long run proportion associated with each possible outcome 0 Theory can guide decision on strategy for playing game Strategy that has higher probability longterm proportion of favorable results can be considered better strategy even in short run 0 Probability distribution 0 You can nd it in 2 ways Theoretical calculations are sometimes hard or even impossible Law of large numbers as the number of trials or repetitions increases the relative frequency of the event gets closer and closer to the theoretical probability of the event Empirical evaluation actually play the game or simulate it thousands of times Observing frequency of occurrence Often counterintuitive don39t trust intuition Terminology 0 Random phenomenon individual attempt unpredictable but outcomes from large number of reputations follow a regular power Probability tells us what could happen over large number of repetitions Sample space set of all possible outcomes Event a collection of possible outcomes Probability distribution probability of each outcome and outcome itself If we let quotAquot be an event the probability of A PA is the likelihood of that event happening For any event A PA is always in the interval 01 PAO means A will certainly NOT happen EVER OOOO PAO5 means that the chance of A occurring is equal to the chance that it won t PA1 means that A certainly WILL occur EVERY TIME 0 Probability must be between 01 0 Sum of probabilities of all possible outcomes must equal 1 o If two events occur simultaneously the probability either on or the other occurssum of their probabilities mutually exclusive 0 Probability that an even doesn39t occur equals 1probability it does occur Random Variables and Probability Distributions Random variable label on all possible values 0 Continuous variable that can take on any value in an interval so that all possible values cannot be listed ex time height temperature 0 Discrete variable whose possible values are a list of distinct variables ex gender opinion shoe size Categorical variable or quantitative variable that is not continuous shoe size can be 55 or 5 whereas height can be 52346236463 feet Two types categorical and numerical Can be graphed by percentage in decimal form 4545 categorical 0 DO compare percentages for outcomes 0 DON T calculate measures of center or spread Bar graph Hai rwur Fruit Eli 55ml Elt39l llit39 laeltlalta L pfil i ll 3 quota a l E It In 5 0 Numerical 0 DO compare percentages 0 DO calculate appropriate measures of center and spread swig 41352 mi H E E5 39i 5 rd a 0 Can be treated like a regular bar graph but with percentages hey that makes calculating the IQR and stuff even EASIER Probability density curve Often it makes more sense to model the probability distribution with a smooth curve called the probability density curve and calculate the area underneath the curve Curve is on or above horizontal line x axis Total area under curve1 Where the curve is high the data values are dense Does not describe the distribution exactly accurate enough for practical purposes Often uses more accurate estimates of probabilities than using a histogram of your sample data Probability that X has a value in any interval is equal to area under the curve for that interval DelquotLib IJDS IIL IIZI I115 I131 I135 EJJEI LE i EIIJEI IaiEIJI llllrnili SmellTH HE39S 55W FIEIllil EL lILiEIIJilE Dam Hllnrate rcmcentra m EL LILIJiIE Dam Hlbrate Emcem ra m I135 EJJEI I I131 I1 25 I PIKE if Nitrate 39u lUE ii 4 j g 235 Danquotnib IEIJE I EL IIII Fg litrata HEIIJEEP39 ME Hilliaif PM 5 nial Nikita PM 5 Mimi

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