Sampling and Measurement in Research

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Published Date:13-07-2017
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Unit 2: Sampling and Measurement Chapter 2 in the Text • Variables & Measurement • Collecting Data • Sampling • Sampling Bias In God we trust. All others must bring data. – W. Edmunds Deming 1 Variables and their Measurements • Variable: Any characteristic that takes different values for different individuals in a sample or population • Measurement scale: the type of measurements that the values of a variable take. 3 kinds: nominal, ordinal, and interval. • Two major Types of variables: categorical and quantitative • A categorical variable is a variable that can take on a few different values (categories) when measured. Sometimes called qualitative variables. • A quantitative variable is a variable that is measured on a numerical scale covering a large range of values. • Examples? Categorical: Quantitative: 2 Categorical Variables • Two types: Nominal and Ordinal • Nominal variable: a categorical variable in which the categories are unordered. • Ordinal variable: a categorical variable in which the categories have an order or hierarchy (and can possibly be numeric), but there is “no defined distance between levels on the measurement scale” • Examples? Nominal: Ordinal: 3 What a 1 + 1 = 3 Dummy Dummy Variables X Y • There is a special type of “nominal” categorical variable called a dummy variable or indicator variable. • These variables take on only 2 possible values: 0 or 1. The one usually stands for success or yes, while the zero usually stand for failure or no. • By convention, they are usually named after the category that is a success. • Example: to represent sex/gender, we could define a dummy variable named female, which would be 1 for all women, and 0 for all men: 1 if female  female  0 if male  4 In English please? Quantitative Variables • Two types: Discrete and Continuous. • Both are measured on an interval scale. That is there is a specific numerical distance between any two measurements. • Discrete variable: a quantitative variable that can take on only specific numbers, like 0, 1, 2, … • Continuous variable: a quantitative variable that can take an infinite number of possibilities within a range of numbers • Examples: Discrete: Continuous: 5 In summary: Variables Categorical Quantitative Nominal Ordinal Discrete Continuous (more common) (less common) Dummy (special case) Note: in this class (and most of statistics), the most important difference is that between categorical and quantitative variables. That differentiation will typical determine the type of statistics and analysis used. Nominal and ordinal variables will mostly be treated the same. Same goes for discrete and continuous variables. 6 Collecting Data • Data can be collected in many ways: The further down the list 1. Anecdotal information you go, the more reliable 2. Available data the information is. And the 3. Observational studies conclusions you can draw will 4. Randomized experiments typically then be stronger. 7 Anecdotal evidence • Anecdotal evidence is based on haphazardly selected individual cases, that often come to our attention because they are striking (probably not representative) • Example: Politicians often cite the case of a single individual to invoke a public response consistent with the politicians’ desire (a sample of size n = 1) • “Ask for averages, not testimonials” 8 Available data • Available data are data that were produced in the past for some other purpose but may help answer a present question • Many use available data because producing new data is expensive (nearly always most costly part of research). • There are lots of reliable available datasets on the web rich with information. Some examples: : : : 9 Observational Studies • An observational study is one in which data is collected by merely observing the measurements on the individuals in the sample. No attempt to influence or intervene with the subject is taken. • May be difficult to reach causal conclusions (that changing one variable causes another variable to change) since other variables may be muddling up (called confounding) this relationship. • Example: Does smoking cigarette increase your risk of heart disease? 10 Sample Surveys (a special case of observational studies) • An sample survey is an example of an observational study in which individuals from a population are interviewed to collect data. • The General Social Survey is an example of a sample survey. Gallup and the Pew research center are two other common examples. • A good framework to talk about random sampling later in this unit • Potentially lots of issues in making claims about the population from the results seen in the sample if not done carefully 11 Sample Surveys: an example • What’s the most important subject in school? Gallup took a poll (aka, a sample survey) to look into this. • They asked: “Thinking about all the subjects you studied in school, which one, if any, has been the most valuable to you in your life?” • Results: 12 Sample Surveys: an example (cont.) Here are Gallup’s “technical details”: • Results for this Gallup poll are based on telephone interviews conducted Aug. 7-11, 2013, with a random sample of 2,059 adults, aged 18 and older, living in all 50 U.S. states and the District of Columbia. For results based on the total sample of national adults, one can say with 95% confidence that the margin of sampling error is ±3 percentage points. • Interviews are conducted with respondents on landline telephones and cellular phones, with interviews conducted in Spanish for respondents who are primarily Spanish- speaking. Landline and cell telephone numbers are selected using random-digit-dial methods. Landline respondents are chosen at random within each household on the basis of which member had the most recent birthday. • Samples are weighted to correct for unequal selection probability, nonresponse, and double coverage of landline and cell users. They are also weighted to match the national demographics of gender, age, race, Hispanic ethnicity, education, region, population density, and phone status (cellphone only/landline only/both, and cellphone mostly). • In addition to sampling error, question wording and practical difficulties in conducting surveys can introduce error or bias into the findings of public opinion polls. 13 Experiments • An experiment is a study in which an investigator imposes an intervention (e.g. treatment) on individuals in order to observe their response. • Clinical trials are a type of experiment • An Example: A comparison of different drugs for women with breast cancer, often with as few as 100 people. • The experimenter chooses women in the study receive the different levels of the drug (new therapy vs. old therapy). The levels of the drug are called the treatment. • The outcome of the study may be the measured amount of disease-free survival for each woman 14 Experiments: a few details • There has to always be at least two groups of the treatment to compare. The ‘default’ condition is often called the control group (standard-of-care in clinical trials). • The control group may receive a placebo treatment. This is a treatment that looks like the active treatment (classic ex: a ‘sugar pill’) • The subjects should be randomized to the treatment groups. That is, chance should decide which patients receive the treatments • This guarantees that all other variables are balanced across the treatment groups • To ensure this balance, the study needs to be replicated enough times. 15 Experiments • An experiment is the best (only?) way to determine if one variable (the treatment) causes another variable (the outcome) to vary. • However, they are not always ethical or plausible. You cannot knowingly do harm to human subjects by forcing them to take a dangerous treatment (ex: force to smoke) • Experiments may not mimic real life (the conditions in which an experiment is run are often too ‘perfect’ or unrealistic). So there is often some loss of generalization of them to the real world. • They are also the most expensive way to collect data 16 Sampling • Sampling is the method used to obtain a sample of individuals/subjects from a larger population. • Some form of randomization should be used. That is chance is used to determine which individuals in the population end up in the sample. • This ensures that the sample is representative of the population (similar make-up of individuals). • Using a ‘convenience sample’ is easy, but can cause all sorts of problems which any sort of fancy statistical analysis cannot fix. But sometimes it’s the only way. • What is the simplest way of collecting a random sample (instead of a ‘systematic sample’, which does not use chance)? 17 Simple random sample (SRS) • In a SRS of size n: • each individual in the population has an equal chance of being chosen • every set of n individuals has an equal chance of being the sample chosen • Small example: selection of a 3-member advisory committee at random from the 11 faculty members of the Stat Dept. • What is the population? What is the sample? • What’s the chance that any one specific member is selected for the committee? • (Stat 110 question): How many different 3-person committees can be formed? 18 Simple random sample example • If we were to draw a simple random sample n = 60 students from all Harvard undergrads, we could : 1) Write out the sampling frame: the list of all individuals in the population. 2) Assign each of the N members to a number from 1 to N. 3) Use a random numbers table or software to generate random numbers So if N is a 4-digit number, then we could just generate random sets of 4 digits numbers, and choose the individuals based on those numbers 19 Using Random Numbers • For Harvard, N ≈ 6700. So we look for 60 unique random numbers between 0001 and 6700 in a systematic fashion from a random numbers table. Below is part of a table of random numbers: 1922 9503 0575 2871 9640 7367 4715 9940 0192 2775 20

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