Understanding Randomness and Sampling Methods in Statistics

1. Part III Gathering Data

2. 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

3. 1 2 3 4

4. 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

5. 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

6. 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

7. 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

8. 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.

9. 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

10. 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)

11. 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

12. 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.

13. 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

14. Exercises • Page 325 • #8 • #14 • #15

15. 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

16. 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

17. 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

18. 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

19. Designing an Experiment • Step-by-Step Page 335

20. 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)

21. 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

22. Exercises • Page 351 • #10 • #12