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Sampling Techniques & Sources of Bias STT 2820 Reasoning with Statistics Mr. Caleb Marsh Types of Studies Observational Study – In an observational study, we observe and measure specific characteristics, but we don’t attempt to modify the subjects being studied. Experimental Study – In an experiment, we apply some treatment and then proceed to observe its effects on the subjects. Subjects in experiments are referred to as experimental units. To ensure a representative sample… Simple Random Sample – Members from the population are selected in such a way that each individual member has an equal chance of being selected. Probability Sample – Involves selecting members from a population in such a way that each member has a known, but not necessarily the same, chance of being selected. Simple Random Sample Population Sample Probability Sample Procedure - Select Purple twice as much as Green Population Sample Systematic Sampling We select some starting point then select every kth element (such as the 50th) in the population to sample. **Caution** this sampling technique can cause issues if the selection of k leads to improper sampling. Systematic Sampling Procedure – Select every 4th Element Population Sample Stratified Sampling We subdivide the population into at least two different subgroups (called strata) so that subjects within the same subgroup share the same characteristics. Then, from each subgroup, we select a simple random sample. Simple Random Sample Population Sample Cluster Sampling Divide the population area into sections (called clusters, usually done geographically). Randomly select some of those clusters and then choose all members from the selected clusters. Cluster Sampling Population Sample Lincoln’s Gettysburg Address Four score and seven years ago our fathers brought forth on this continent, a new nation, conceived in Liberty, and dedicated to the proposition that all men are created equal. Now we are engaged in a great civil war, testing whether that nation, or any nation so conceived and so dedicated, can long endure. We are met on a great battle-field of that war. We have come to dedicate a portion of that field, as a final resting place for those who here gave their lives that that nation might live. It is altogether fitting and proper that we should do this. But, in a larger sense, we can not dedicate -- we can not consecrate -- we can not hallow -- this ground. The brave men, living and dead, who struggled here, have consecrated it, far above our poor power to add or detract. The world will little note, nor long remember what we say here, but it can never forget what they did here. It is for us the living, rather, to be dedicated here to the unfinished work which they who fought here have thus far so nobly advanced. It is rather for us to be here dedicated to the great task remaining before us -- that from these honored dead we take increased devotion to that cause for which they gave the last full measure of devotion -- that we here highly resolve that these dead shall not have died in vain -- that this nation, under God, shall have a new birth of freedom -- and that government of the people, by the people, for the people, shall not perish from the earth. Experimental Design Cross-sectional Study – Data are observed, measured and collected at one point in time. Retrospective (or case control) Study – Data are collected from the past by going back in time (through examination of records, interviews and so on.) Prospective (longitudinal or cohort) Study – Data are collected in the future from groups sharing common factors. More Experimental Design Randomization – Subjects are assigned to different groups through a process of random selection. Replication – The repetition of an experiment on more than one subject. Blinding – A technique in which the subject does not know whether he or she is receiving a treatment or a placebo. Confounding Confounding occurs in an experiment when you are not able to distinguish among the effects of different factors. Types of Errors Sampling Error – The difference between a sample result and the true population result; such an error results from chance sample fluctuations. Non-sampling Error – Occurs when the sample data are incorrectly collected, recorded or analyzed. Bias Bias –The tendency of our sample to misrepresent our population either by sampling or non-sampling error. Our goal in using a variety of sampling procedures is to reduce bias. However, there are certain “abuses” that can exist within the confines of statistical research. 1. Voluntary Response Sample A sampling procedure in which the respondents themselves decide on whether or not to be included in the study. Problem – Typically individuals that are highly motivated to respond, do… those that are not, do not. 2. Small Samples Conclusions cannot be based on samples that are too small. Problem – Small samples put too much influence on a selected few. 3. Misleading Graphs KWH 845 840 INCORRECT 835 830 825 July August KWH CORRECT 1000 800 600 400 200 0 July August 4. Loaded Questions Example – When asked 97% believe that the President should be granted line item veto powers to eliminate waste. Example – When asked 57% believe that the President should be granted line item veto powers. 5. Non - Response Occurs when either a person in unavailable for a response or refuses to respond to a survey question. Problem – Typically people who refuse to respond are socialized to do so. These individuals opinion’s might differ from the typical respondent. 6. Self Interest Study Occasionally an individual or group of individuals will commission a study with which the outcomes greatly effect the status quo. Hey… Do you like m&ms? Final Issues 7. Precise Numbers – The total number of hairs on your head is 1,275,562. 8. Partial Pictures – Average class size at ASU is 27 students. 9. Deliberate Distortions – The Average American Salary is $75,627 per year.