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Chapter 11Understanding Randomness Random
An event is random if we know what outcomes could happen but not which particular values did or will happen
Random Numbers “Hard to get”
Pseudorandom Table of random digits
Pick a number from the next slide
Simulation A simulation consist of a collection of things that
happened at random. Is used to model real-world relative frequencies using random numbers.
Component Situation that is repeated in the simulation. Each
component has a set of possible outcomes Outcome
An individual result of a simulated component of a simulation
Trial The sequence of events that we are pretending will
take place Step-by-step page 295
Chapter 12Sample Surveys
Idea 1: Examine a part of the whole Carefully select a smaller group from
the population (Sample) A sample that does not represent the
population in some important way is said to be biased
Sample Survey (cont.)
Idea 2: Randomize Randomizing protect us from the
influences of all the features of our population, even the ones that we may not have thought about.
Is the best defense against bias, in which each individual is given a fair random chance of selection
Sample Surveys (cont.) Idea 3: It’s the sample size
The fraction of the population that you have sampled doesn’t matter. It’s the sample size itself that’s important.
Census A Sample that consist of the entire population.
Difficult to complete. Not practical, too expensive Populations are not static Can be more complex
Populations and parameters Population parameter
Parameter (numerical value) that is part of a model for a population. We want to estimate this parameters from sampled data.
Sampling When selecting a sample we want it to be representative, that is that the statistics we compute from the sample reflect the corresponding parameters accurately
Simple Random Sample (SRS) Is a sample in which each combination of
elements has an equal chance of being selected
Sampling Frame A list of individuals from which the sample is
drawn
Other Sampling Designs Stratified random sampling
A sampling design in which the population is divided into homogeneous subsets called strata, and random samples are drawn from each stratum.
Cluster Sampling Random samples are drawn not directly
from the population, but from groups of clusters. (Convenience, practicality, cost)
Other Sampling Designs (cont.)
Systematic Sample Sample drawn by selecting individuals
systematically from a sampling frame. (ex. Every 10 people)
Multistage Sample Combining different sampling methods
How to Sample Badly Sample badly with volunteers
Voluntary response bias invalidates a survey Sample badly because of convenience
Convenience sampling: Simply include the individuals who are at hand
Sample from a bad sampling frame Undercoverage
Some portion of the population is not sampled at all or has a smaller representation in the sample than it has in the population.
How to Sample Badly Non response bias Response Bias
Influence arising from the design of the survey wording.
Look for biases before the survey. There is no way to recover from a biased sample or a survey that asks biased questions
Sampling Variability Difference from sample to sample, given that
the samples are drawn at random
Chapter 13Experiments Investigative Study
Observational Studies Researchers don’t assign choices No manipulation of the factors
Retrospective study Observational study in which the
researcher identifies the subject and then collect data on their previous condition or behavior
Prospective Study Identifies or selects the subjects and
follows the future outcomes
Experiment Random assignment of subjects to treatments. Explanatory Variable:
Factor (manipulate) Response variable :
Measurement Experimental units
Subjects Participants
Factor A variable whose levels are controlled by the
experimenter Levels of the factor
Treatments All the combinations of the factors with their respective
levels
The Four Principles of Experimental Design 1 - Control
We need to control sources of variation other than the factors being studied. (make the conditions similar for all treatment groups)
2 - Randomize Assign the subjects randomly to the
treatments to equalize the effects of unknown variation
The Four Principles of Experimental Design (cont.)
3 - Replicate Apply the treatments to several
subjects.
4 - Block Separate in blocks of identifiable
attributes that can affect the outcome of the experiment
Experiments Control Treatment
Baseline treatment level to provide basis for comparison.
Blinding There are two main classes of individuals
who can affect the outcome of the experiment
Subjects, treatment administrators Evaluators of the results
Single Blinding (one) Double Blinding (both)
Experiments Placebos
A null treatment to make sure that the effect of the treatment is not due to the placebo effect.
Blocking By blocking we isolate the variability due to the
differences between the blocks so that we can see the differences due to the treatment more clearly
Confounding When the levels of one factor are associated
with the levels of another factor, we say that these two factors are confounded