Stats Test 2 notes.docx

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Statistical Sciences
Course Code
Statistical Sciences 1024A/B

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Chapter 9 SummaryWe can produce data intended to answer specific questions by OS or experimentsSample nsurveys that select a part of a pop of interest to represent the whole are one type of OS Experiments unlike observational studies actively impose some txt on the subjects of the experiment Variables are confounded when their effects on a response cant be distinguished from each other OS and uncontrolled experiments often fail to show that changes in exp variable actually cause changes in a resp variable bc the exp variable is confounded w lurking variables In an exp we impose one or more txts on indivs often called subjects Each txt is a ncombin of values of the exp variables which we call factors The design of an exp describes the choice of txts and the manner in which the subjects are assigned to txtsThe basic principles of stat design of exps are control and randomization to combat bias and using enough subjects to reduce chance variation The simplest form of control is comparison Exps should compare two or more txts in order to avoid confounding of the effect of a txt w other influences such as lurking variables nRandom uses chance to assign subjects to the txts Randomization creates txt group that nare similar except chance variation before the txts are applied Random and comparison together prevent bias or systematic favoritism in exps nYou can carry out random by using software or by using numerical labels to the subjects using a table of random digits to choose txt groups nApplying each txt to many subjects reduces the role of chance varia and makes the exp more sensitive to diffs among the txts Good exps need attn to detail and good stat designMany behavioral and med exps are ndouble blind Some give placebo to ctrl grp Random is then carried out separately in each block ndA 2 form of ctrl is to restrict random by forming blocks of indivs that are smiliar in some way that is imp to the response Random is then carried out separately in each block Matched pairs are a common form of blocking for comparing just two txts In some MPDs each subject receives both txts in a random order In others subjects are matched in pairs as closely as possible and each subject in a pair receives one of the txts Chapter 10 Introducing ProbabilityRandom samples eliminate bias from the act of choosing a sample but they can still be wrong bc of the variability that results when we choose at random Chance behavior is unpredictable in the short run but has a regular and predictable pattern in the long run There is a regular pattern but it emerges only after many repsBasis for idea of probability Figure 101 nRandom indiv outcomes are uncertain but there is a regular distribu of outcomes in a lot of reps Probability proportion of times the outcome would occur in a very long serious of repetitions Proportion in a small or moderation number of tosses can be far from probabilityProbability describes only what happens in the long run Pseudorandom numbers good for choosing samples and shuffling cards but they may have hidden patterns that can distort scientific simulations Coins obey law of physics A very small change in forcesmall changes in big changes out behavior is considered chaotic The description of coin tossing has two parts List of possible outcomes and a probability for each outcome This description is the basis for all probability models Sample space S of a random phenomenon is the set of all possible outcomes An event is an outcome or set of outcomes of a rp An event is a subset of the sample space A probability model is a mathematical description of a rp consisting of 2 parts a sample space S and a way of assigning probabilities to events Example 104 and 105Rolling diceCounting spots
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