STAT2003 Chapter Notes - Chapter 9-11: Random Assignment, Stratified Sampling, Yellowcake
Ch 9. Understanding Randomness, Ch 10. Sample Surveys, Ch 11. Experiments and
Observational Studies
Covers: 9/18, 9/20, 9/22, 9/25, 9/27, 9/29, 10/2, 10/4, 10/6 (9 Lectures, Weeks 4, 5, & 6)
Ch 9. Understanding Randomness
https://www.random.org/analysis/
● Random procedure: a procedure whose outcome cannot be known in advance
● How can we determine the probability a random procedure will have a certain
outcome?
● Randomness: when the outcome of an event cannot be predicted exactly
● Random numbers: Think of them as a sequence of digits in the range 0 to 9, with each
digit picked randomly
● Questions:
○ If a coin is tossed 4 times, how many heads will it yield?
○ Is it possible that all 4 outcomes will be heads?
○ Do you think each individual outcome was random in this case?
● Even when individual outcomes are random, the totality of outcomes reveals the
underlying structure & behavior patterns.
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● Approach #1: Relative Frequency -- Approximation of Probability
○ Conduct/observe a procedure n times and count the # of times that an outcome
of interest occurs. Based on these results, the probability of the outcome is
estimated as follows:
=
#
#
○ This approach obtains an approximation (estimate) instead of an exact value
○ La of Large #’s: As the # of trials increases, the relative frequency probability
approaches the actual probability
● Approach #2: Classical Approach to Probability
○ Assume that a given procedure has n different outcomes and that each of these
outcomes has an equal chance of occurring. If a desired outcome can occur in s
of these n ways, then:
= #
# =
○ This approach requires equally likely outcomes
● Approach #3: Subject Probabilities
○ Poutoe is estiated usig oe’s o judget aout the likelihood of a
event
○ This approach is needed when there is no repeatable random experiment
available
■ Ex.
● What is probability it will rain the tomorrow?
● What is the probability the stock market will rise tomorrow?
● What is the probability that more than five students in this class
will get an A o the et ea?
● Simulation: An experiment conducted on computer or with pencil & paper.
○ Simulations model real-world situation by using random-digit outcomes to mimic
the uncertainty of a response variable of interest
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○ There are many situation when we would want to estimate the probability of an
outoe of a ado poedue ut…
■ The classical approach to probability is not possible
■ The relative frequency approach is unwieldy/expensive/infeasible/etc.
■ In these situations, we can simulate the random procedure in order to
estimate the probability of our outcome of interest
■ We need random numbers to simulate the randomness in real life
○ How to derive random numbers?
■ Random number tables from random sources in nature
■ Current statistics textbook (Appendix D)
■ Computer/calculator generation with pseudorandom numbers
● “tatCuh: Data → “iulate Data
● Use MATH → PRB → adItlo, high, utials to geeate a
set of random integers on your calculator
● Simulating by Hand.
○ Steps for Simulation.
■ 1. Identify the component to be repeated
■ . Eplai ho ou ill odel the eperiet’s outcoe
■ 3. Explain how you will combine the components to model the trial.
■ 4. State clearly what the response variable is.
■ 5. Run several trials
■ 6. Collect and summarize the results of the trials
■ 7. State your conclusion
○ Simulating a Dice Game
● Possible Problems
○ Do’t Oerstate Your Case
■ The simulation is not reality, it only indicates probability
○ Model Outcome Chances Accurately
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Document Summary
Covers: 9/18, 9/20, 9/22, 9/25, 9/27, 9/29, 10/2, 10/4, 10/6 (9 lectures, weeks 4, 5, & 6) Random procedure: a procedure whose outcome cannot be known in advance. Randomness: when the outcome of an event cannot be predicted exactly. Random numbers: think of them as a sequence of digits in the range 0 to 9, with each digit picked randomly. Even when individual outcomes are random, the totality of outcomes reveals the underlying structure & behavior patterns. Approach #1: relative frequency -- approximation of probability. Conduct/observe a procedure n times and count the # of times that an outcome of interest occurs. Based on these results, the probability of the outcome is estimated as follows: This approach obtains an approximation (estimate) instead of an exact value. La(cid:449) of large #"s: as the # of trials increases, the relative frequency probability approaches the actual probability.
