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Chapter3print - STAT503 Spring 2009 Lecture Notes Chapter 3...

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STAT503 — Spring 2009 Lecture Notes: Chapter 3 1 Chapter 3: Random Sampling, Probability September 1, 2009 Read 3.1-3.8 3.2 Random Sampling Choosing a sample of size n at random from a population: every member of the population has the same chance of being chosen the choices of consecutive members to the sample are independent of each other How is it actually done? If the population size, say N , is known, assign a number from 1 to N to each member of the population, and get n random numbers between 1 and N from. To get random numbers use: a computer (in Excel e.g. RandBetween) a random number table (in the textbook: Table 1) www.randomizer.org. www.random.org/nform.html. Choose the members of the population corresponding to those numbers. This strategy satisfies our requirements. If the population size is not fixed or known, it may be harder. Sometimes (especially in biology) it is hard to enumerate the population or to choose at random. Exercise: Choose 5 random students in the class to stand up. Use Table 1. Consider the following challenges: self-selection / non-compliance (of people) problems with collection logistics In choosing a random sample, some things are very important: Chapter3.tex; Last Modified: September 1, 2009 (W. Sharabati)

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STAT503 — Spring 2009 Lecture Notes: Chapter 3 2 the selection criteria must not correspond to what we are studying, i.e. must not introduce any systematic bias we must try to maintain independence of the sample points we must be careful in making inference: the population might not be what you wish it were (beware of extrapolation!) Examples: Patients from clinics: a doctor/researcher may be stuck with sampling individuals only in one city. Probably OK unless systematic bias, e.g. common environmental contaminant. Better use several clinics; people might refer their friends to the same clinic, similar in age/income/ancestry. Capture-recapture studies; may be influenced by age/size/fearfulness. US Census is actually a sample; more representative of people with relatively stable or traditional lifestyles (not the whole population is such). Read articles (scientific, newspaper) critically and think about sampling and extrapola- tion. 3.3 Introduction to Probability Probability Defined by frequencies OR by the following properties : is always between 0 and 1, where 0 means impossible and 1 means certain probabilities of non-overlapping events add (think histograms) probabilities of all possible outcomes add up to 1 For a chance event E , we write Pr( E ) or Pr { E } , or P ( E ) to denote its probability. Reality check: probability Pr( E ) should be approached by the fraction of times that E would occur if the experiment were performed a large number of times. This is the long-term relative frequency.
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