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Chapter 3

ECO220Y1 Chapter 3 Notes

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University of Toronto St. George
Jennifer Murdock

ECO220Y1 Textbook Notes Chapter 3: Surveys and Sampling 3.1 Three Features of Sampling 1. Examine a Part of the Whole o Population: the entire group of individuals or instances about whom we hope to learn. o Sample: a subset of a population, examined in the hope of learning about the population. o Sample survey: a study that asks questions of a sample drawn from some population in hopes of learning something about the entire population. o Biased: said to occur when the summary characteristics of a sample differ from the corresponding characteristics of the population it is trying to represent. o In order to make a sample as representative as possible, individuals should be selected at random. 2. Randomize o Randomizing protects us by giving us a representative sample even for effects we were unaware of (i.e. peas in soup).  It makes sure that, on average, the sample looks like the rest of the population. o Randomization: a defence against bias in the sample selection process, in which each individual is given a fair, random chance of selection. o Pseudorandom: numbers generated by a computer program; they are not technically random. o Sampling variability: the differences that exist from sample to sample. 3. The Sample Size is What Matters o The size of the sample determines what we can conclude from the data regardless of the size of the population.  I.e. too small a sample will yield less accurate data. 3.2 A Census – Does It Make sense?  Census: an attempt to collect data on the entire population of interest (sample becomes the population).  Problems with attempting a census: o May be difficult to complete (i.e. hard to contact every single person in the population). o The population may change (i.e. births/maturity/deaths and changes in tastes/preferences).  A sample done in a shorter time frame can virtually eliminate this issue. o Double counting (i.e. someone has a primary and a secondary residence). 3.3 Populations and Parameters  Models of data can give us summaries that we can learn from and use even though they don’t fit each data value exactly.  Parameter: a numerically valued attribute of a model for a population. o The value is rarely known; rather the hope is to estimate it from sampled data.  Population parameter: a parameter used in a model for a population.  Statistic: a value calculated from sampled data, particularly one that corresponds to, and thus estimates, a population parameter. o Sample statistic: usually used to parallel the term “population parameter.”  Representative sample: a sample from which the statistics computed accurately reflect the corresponding population parameters. 3.4 Simple Random Sampling (SRS)  Simple random sampling (SRS): a sample in which each set of n individuals in the population has an equal chance of selection.  Sampling frame: a list of individuals from which the sample is drawn. Individuals in the population of interest but who are not in the sampling frame cannot be included in any sample.  Possible methods: o Assigning sequential numbers to each individual in the population and then randomly selecting numbers and finding the person they correspond to. o Generating random numbers for each individual in the population and then sorting numerically and then picking a random sample of any size off the top of the sorted list. 3.5 Other Random Sample Designs  Strata: subsets of a population that are internally homogeneous but may differ from one another.  Stratified random sample: a sampling design in which the population is divided into several homogeneous subpopulations, or strata, and random samples are then drawn from each stratum. o Allows for information to be obtained about each stratum as well as the population as a whole. o When samples are unable to be obtained in
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