1. Sampling is the other method of getting data, along with experimentation. It involves looking at a sample from a population with the hope of making inferences about the population from the sample. We can consider many different sample designs, the various methods of taking the sample from the population. –Ex. 3.23 (3.2, 1/5) shows an example of voluntary response samples, consisting of people who choose themselves to be part of the sample, often by responding to a general appeal for volunteers. These type samples are highly biased, since people with very strong opinions (esp. negative ones!) are most likely to respond…

2. The remedy for voluntary samples is to have chance involved in the choice … i.e., to involve random selection of sample points. A simple random sample (SRS) of size n consists of n individuals from the population of interest, chosen in such a way that every collection of n individuals is as equally likely to be picked as any other. Go over Ex. 3.24 (3.2, 2/5) Other types of samples are also in use: –Stratified random sample: first divide the population into strata, then choose a SRS from each stratum and combine them to form the full sample –Multistage sample: choose the sample in stages, as in national political samples…see p. 203 (3.2, 4/5)

3. There are many things to be concerned with in sample surveys… –Undercoverage occurs when some groups in the population are left out of the process of choosing the sample –Nonresponse occurs when an individual chosen for the sample can’t be contacted or decides not to cooperate - see Example 3.27, p. 205 (3.2, 5/5) –Response bias occurs when an individual in the sample lies; or when the interviewer has a manner that elicits a particular response; respondents often have bad memories or “telescope” events in the past; see Example 3.29 on page 206 (3.2, 5/5) –Wording of questions can influence answers on a sample survey; see Example 3.30 on page 207 (3.2, 5/5)

4. HW: Read section 3.2 and go over all the examples. Do #3.52-3.55, 3.57-3.59, 3.61,3.62, 3.68, 3.71-3.74. Read ahead to section 3.3 on inference from samples...

5. Inference from Samples… If a sample represents the population from which it is drawn, then we should be able to use the information in it to make inferences about its population – this is one example of statistical inference in action. A sample is to its population as a statistic is to its corresponding parameter. A simple example of the above is the parameter defined as the proportion of people in the population of US adults who approve of the job Pres. Obama is doing as president (call it p); now take a sample from this population and compute the proportion of people in the sample who approve of the job he's doing. This value is called

6. Population versus sample Sample: The part of the population we actually examine and for which we do have data. –How well the sample represents the population depends on the sample design. Population: The entire group of individuals in which we are interested but can’t usually assess directly. Example: All humans, all working-age people in California, all crickets A parameter is a number describing a characteristic of the population (like p ) A statistic is a number describing a characteristic of a sample (like ) Population Sample

7. exhibits sampling variability: different random samples will give rise to different ‘s But sampling variability is not bad; in fact we use this fact as the basis for many statistical inferential procedures… “what would happen if we took many samples” or “what would happen if we repeated a particular procedure many times?” Simulation is a way of illustrating sample variability and we’ll use Table B as an example… –Suppose 60% of the population approves of the job the president is doing. How would samples of size 20 vary if we asked each person in the sample: “Do you approve of the job the president is doing?” and require a “yes” or “no” answer ? Try it with Table B – how would you set up the simulation?

9. The sampling distribution of a statistic is the distribution of values taken on by the statistic in all possible samples of the same size from the same population. Many times, sampling distributions of statistics based on large sample sizes tend to be normally distributed. Check out the sampling distribution of … A statistic is unbiased if the mean of its sampling distribution equals the true value of the parameter being estimated The variability of a statistic is described by the spread of its sampling distribution. Statistics from samples with large sample sizes have smaller variability.

11. Definition, pg 217–218 Introduction to the Practice of Statistics, Sixth Edition © 2009 W.H. Freeman and Company

12. Read section 3.3. Do # 3.84-3.86, 3.89, 3.95. Make sure you understand the process of simulation done in these last two exercises and in Example 3.32, (page 214 or Section 3.3, 2/6) and how these lead to an estimate of the sampling distribution, as in Figures 3.11 and 3.12 on page 215 (3.3, 3/6) Definition, pg 215 Introduction to the Practice of Statistics, Sixth Edition © 2009 W.H. Freeman and Company

13. Definition, pg 225 Introduction to the Practice of Statistics, Sixth Edition © 2009 W.H. Freeman and Company

14. Institutional review boards The organization that carries out the study must have an institutional review board that reviews all planned studies in advance in order to protect the subjects from possible harm. The purpose of an institutional review board is “to protect the rights and welfare of human subjects (including patients) recruited to participate in research activities” The institutional review board:  reviews the plan of study  can require changes  reviews the consent form  monitors progress at least once a year

15. Informed consent All subjects must give their informed consent before data are collected. –Subjects must be informed in advance about the nature of a study and any risk of harm it might bring. –Subjects must then consent in writing.

16. Confidentiality All individual data must be kept confidential. Only statistical summaries may be made public. Confidentiality is not the same as anonymity. Anonymity prevents follow-ups to improve non-response or inform subjects of results. Separate the identity of the subjects from the rest of the data immediately! Example: Citizens are required to give information to the government (tax returns, social security contributions). Some people feel that individuals should be able to forbid any other use of their data, even with all identification removed.

17. Clinical trials Clinical trials study the effectiveness of medical treatments on actual patients – these treatments can harm as well as heal. Points for a discussion:  Randomized comparative experiments are the only way to see the true effects of new treatments.  Most benefits of clinical trials go to future patients. We must balance future benefits against present risks.  The interests of the subject must always prevail over the interests of science and society. In the 1930s, the Public Health Service Tuskegee study recruited 399 poor black men with syphilis and 201 without the disease in order to observe how syphilis progressed without treatment. The Public Health Service prevented any treatment until word leaked out and forced an end to the study in the 1970s.