Chapter 3: Producing Data Lecture Presentation Slides Macmillan Learning 2017 Chapter 3 Producing Data Introduction 3.1 Sources of Data 3.2 Design of Experiments 3.3 Sampling Design 3.4 Ethics 2 3.1 Sources of Data Anecdotal data Available data
Sample surveys and experiments Observation vs. experiment Confounding 3 Sources of Data The validity of the conclusions that we draw from an analysis of data depends not only on the use of the best methods to perform the analysis, but also on the quality of the data. There are many sources of data. Whatever the source, a good statistical analysis will start with a careful study of the source of the data. ANECDOTAL DATA Anecdotal data represent individual cases. These cases are not necessarily representative of any larger group of cases. AVAILABLE DATA
Available data are data that were produced for some other purpose but that may help answer a question of interest. The library and the Internet can be good sources of available data. Because producing new data is expensive, we all use available data whenever possible 4 Sample Surveys, Sampling Sample surveys are a special type of data collection that usually aim to discover the opinions of people on certain topics. In a sample survey, a sample of individuals is selected from a larger population of individuals. The idea of sampling is to study a small part of the population in order to gain information about the population as a whole. Conclusions drawn from a sample are valid only
when the sample is drawn in a well-defined way (to be discussed in Section 3.3). 5 Observation vs. Experiment Sample surveys are one kind of observational study. Experiments do not just observe individuals or ask them questions. They actively impose some treatment in order to measure the response. An observational study observes individuals and measures variables of interest but does not attempt to influence the responses. The purpose is to describe some group or situation. An experiment deliberately imposes some treatment on individuals to measure their responses. The purpose is to study whether the treatment causes a change in the response. 6
Confounding Observational studies of the effect of one variable on another often fail to establish cause and effect because of confounding between the explanatory variable and one or more lurking variables. A lurking variable is a variable that is not among the explanatory or response variables in a study but that may influence the response variable. Confounding occurs when two variables are associated in such a way that their effects on a response variable cannot be distinguished from each other. 7 3.2 Design of Experiments
Experimental units, subjects, treatments Comparative experiments Randomization Principles of experimental design Cautions about experimentation Matched pairs design Block design 8 Experimental Units, Subjects, Treatments An experiment is a study in which we actually do something (a treatment) to people, animals, or objects (the experimental units) to observe the response. Here is the basic vocabulary of experiments. An experimental unit is the smallest entity to which a treatment is applied. When the units are human beings, they are often called subjects. The explanatory variables in an experiment are often called factors.
A specific condition applied to the individuals in an experiment is called a treatment. If an experiment has several explanatory variables, a treatment is a combination of specific values of these variables. 9 Need for Comparative Experiments Experiments are the preferred method for examining the effect of one variable on another. By imposing the specific treatment of interest and controlling other influences, we can pin down cause and effect. Good designs are essential for effective experiments, just as they are for sampling. Example: A study designed to reduce test anxiety had students write an essay about their feelings concerning an upcoming exam. Students Write about feelings Observe exam scores The scores on this exam (the second exam of the semester) were compared with those on the first exam. The mean score on the second exam was higher
than the mean score on the first exam. Is the writing exercise effective? How can you tell? Are you certain the increase is due to the writing exercise? 10 Comparative Experiments The test anxiety experiment was poorly designed to evaluate the effect of the writing exercise. The lack of a comparison group is one problem with it. Another is the placebo effect. The end result is the study suffers from bias. The placebo effect occurs when people respond favorably to personal attention or to any treatment that they hope will help them.
In a comparative experiment, subjects are assigned to one of two or more groups. In many studies, two such groups are the control group and the treatment group. A study is biased if it systematically favors certain outcomes. 11 Need for Randomization 12 The remedy for confounding is to perform a comparative experiment in which some units receive one treatment and similar units receive
another. Most well-designed experiments compare two or more treatments. Comparison alone is not enough. If the treatments are given to groups that differ greatly, bias will result. The solution to the problem of bias is random assignment. In an experiment, random assignment means that experimental units are assigned to treatments at random, that is, using some sort of chance process. 13 Principles of Experimental Design 14 Randomized comparative experiments are designed to give good evidence that differences in the treatments actually cause the differences we see in the responses.
1. Control for lurking variables that might affect the response, most simply by comparing two or more treatments. 2. Randomize: Use chance to assign experimental units to treatments. 3. Replication: Use enough experimental units in each group to reduce chance variation in the results. In principle, experiments can give good evidence for causation. We take the above steps to ensure that the only reasonable explanation fr differences observed is due to the treatment imposed. How to Randomize One way to randomize an experiment is to rely on random digits to make choices in a neutral way. We can use a table of random digits (such as Table B) or the random sampling function provided by most statistical software. How How to to randomly
randomly choose choose n n individuals individuals from from aa group group of of N: N: We We first first label label each each of of the the N N individuals individuals with with aa number
number (typically (typically from from 11 to to N, N, or or 00 to to N N 1). 1). Imagine Imagine writing writing the the whole whole numbers numbers from from 11 to to N
N on on separate separate pieces pieces of of paper. paper. Now Now put put all all the the numbers numbers in in aa hat. hat. Mix Mix up up the the numbers
numbers and and randomly randomly select select one. one. Mix Mix up up the the remaining remaining N N 11 numbers numbers and and randomly randomly select select one one of of them. them.
Continue Continue in in this this way way until until we we have have our our sample sample of of nn numbers. numbers. Statistical Statistical software software can can do do this this for
for you, you, so so you you do do not not actually actually need need aa hat! hat! 15 Cautions About Experimentation The logic of a randomized comparative experiment depends on our ability to treat all the subjects in exactly the same way, except for the actual treatments being compared. In a double-blind experiment, neither the subjects nor those who interact with them and measure the response variable know which
treatment a subject received. The most serious potential weakness of experiments is lack of realism. The subjects or treatments or setting of an experiment may not realistically duplicate the conditions we really want to study. Nonetheless, the random comparative experiment, because of its ability to give convincing evidence for causation, is one of the most important ideas in statistics. 16 Matched Pairs A common type of randomized block design for comparing two treatments is a matched pairs design. The idea is to create blocks by matching pairs of similar experimental units. A matched pairs design is a randomized blocked experiment in which each block consists of a matching pair of similar experimental units.
Chance is used to determine which unit in each pair gets each treatment. Sometimes, a pair in a matched pairs design consists of a single unit that receives both treatments. Because the order of the treatments can influence the response, chance is used to determine which treatment is applied first for each unit. 17 Blocked Designs A block is a group of experimental units that are known before the experiment to be similar in some way that is expected to affect the response to the treatments. In a block design, the random assignment of experimental units to treatments is carried out separately within each block. Form blocks based on the most important unavoidable sources of variability (lurking variables) among the experimental units. Randomization will average out the effects of the remaining lurking variables
and allow an unbiased comparison of the treatments. Control what you can, block what you cannot control, and randomize to create comparable groups. 18 19 3.3 Sampling Design Population and sample Voluntary response samples Simple random samples Probability samples Stratified random samples Multistage samples Cautions about sampling 20
Population and Sample The population in a statistical study is the entire group of individuals about which we want information. A sample is the part of the population from which we actually collect information. We use information from a sample to draw conclusions about the entire population. Population Collect data from a representative Sample... Sample Make an Inference about the Population. 21
How to Sample Badly The design of a sample is biased if it systematically favors certain outcomes. Choosing individuals simply because they are easy to reach results in a convenience sample. A voluntary response sample consists of people who choose themselves by responding to a general appeal. Voluntary response samples often show bias because people with strong opinions (especially negative opinions) may be more likely to respond. 22 Simple Random Samples (SRS) Random sampling, the use of chance to select a sample, is the central principle of statistical sampling. A simple random sample (SRS) of size n consists of n individuals
from the population chosen in such a way that every set of n individuals has an equal chance to be the sample actually selected. 23 How to Choose an SRS A table of random digits is a long string of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 with these properties: Each entry in the table is equally likely to be any of the 10 digits 09. The entries are independent of one another. That is, knowledge of one part of the table gives no information about any other part. How to Choose an SRS Using Table B Step 1: Label. Give each member of the population a numerical label of the same length. Step 2: Table. Read consecutive groups of digits of the appropriate length from Table B.
Your sample contains the individuals whose labels you find. 24 SRS Example 25 Use the random digits provided to select an SRS of four hotels. 01 Aloha Kai 02 Anchor Down 03 Banana Bay 04 Banyan Tree 05 Beach Castle 06 Best Western 07 Cabana 69051
08 Captiva 09 Casa del Mar 10 Coconuts 11 Diplomat 12 Holiday Inn 13 Lime Tree 14 Outrigger 15 Palm Tree 16 Radisson 17 Ramada 18 Sandpiper 19 Sea Castle 20 Sea Club 21 Sea Grape 22 Sea Shell
23 Silver Beach 24 Sunset Beach 25 Tradewinds 26 Tropical Breeze 27 Tropical Shores 28 Veranda 64817 87174 09517 84534 06489 87201 97245 69 05 16 48 17 87 17 40 95 17 84 53 40 64 89 87 20 Our SRS of four hotels for the editors to contact is: 05 Beach Castle, 16 Radisson, 17 Ramada, and 20 Sea Club. Probability Samples and Stratified Random Samples A probability sample is a sample chosen by chance. We must know what samples are possible and what chance, or probability, each possible sample has.
To select a stratified random sample, first classify the population into groups of similar individuals, called strata. Then choose a separate SRS in each stratum and combine these SRSs to form the full sample. 26 Probability Samples: Multistage Random Samples A multistage random sample uses probability samples in a series of stages. The final stage results in clusters of nearby households. 27 Cautions About Sample Surveys
Good sampling technique includes the art of reducing all sources of error and bias. 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 cannot be contacted or refuses to participate. A systematic pattern of incorrect responses in a sample survey leads to response bias. The wording of questions is the most important influence on the answers given to a sample survey. Insist on knowing the exact questions asked, the rate of nonresponse, and the date and method of the survey before you trust a poll result. 28 3.4 Ethics Basic data ethics
Institutional review boards Informed consent Confidentiality Clinical trials Behavioral and social science experiments 29 Basic Data Ethics The most complex issues of data ethics arise when we collect data from people. Basic Data Ethics 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. All individuals who are subjects in a study must give their informed consent before data are collected. All individual data must be kept confidential. Only statistical
summaries for groups of subjects may be made public. 30 Institutional Review Boards 31 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 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. Who cannot give informed consent? Prison inmates Very young children People with mental disorders 32 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 decrease nonresponse 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. 33 Clinical Trials 34 Clinical trials study the effectiveness of medical treatments on actual patientsthese 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 blacks 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. Behavioral and Social Science Experiments 35 Many behavioral experiments rely on hiding the true purpose of the
study. Subjects would change their behavior if told in advance what investigators were looking for. The Ethical Principles of the American Psychological Association require consent, unless a study merely observes behavior in a public space.
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