1	CLAST Statistics and Probability Populations, Sampling and Bias
2	Basic Definitions Statistics - the branch of mathematics that deals with the collection, presentation, analysis, and interpretation of numerical data Probability - the branch of mathematics that deals with chance and the likelihood of events
3	Selecting Unbiased Samples What is a Population? What is a Sample? What constitutes an Unbiased Sample? Unbiased Random Sampling Methods Simple Random Sampling Stratified Sampling Cluster Sampling Systematic Sampling Biased Sampling
4	Devising a Study
5	Population The entire group of interest May consist of people, objects, observations, scores, etc. May be of any size The target population is a realistic population that is being studied and which has the characteristic(s) to be studied.
6	Conducting the Study
7	Sample A subgroup of a population being studied Is assumed to have the same characteristic(s) being studied as the population Consists of a collection of elements (units) that actually can be measured, or a collection of measurements that actually can be obtained
8	Populations vs. Samples
9	Bias
10	What is Bias?
11	Selecting a Sample
12	Unbiased Sampling
13	Random Sampling Methods Simple Random Sampling Stratified Sampling Cluster Sampling Systematic Sampling
14	Simple Random Sampling Every member of the target population has the same chance of being selected. Selection is of individual members. Steps: 1. Obtain a list of all members (units) 2. Use physical methods, tables of random digits, or computerized methods of random selection Example: Place a population of 20 names in a hat and select 5 randomly. (Physical mixing and selection are applicable to small populations. Tables and computer selection are more appropriate for large populations and for selecting large samples.) Q: Why was investigating class notes via responders to an advertisement a bad way to sample?
15	Stratified Sampling Process of selecting a random sample from meaningful subgroups (strata) in a population The characteristic(s) studied is/are represented in the strata in the same proportion as in the whole population Selection is of individuals within the strata or of whole strata (if that is manageable) Steps: 1. Divide the population into strata 2. Take a simple random sample of units from each stratum Example: Stratify the population of the U.S. into regions (South, Midwest, etc.) with respect to a relevant characteristic, such as political party affiliation or property values, in order to observe regional differences.
16	Cluster Sampling Process of selecting a random sample from convenient subgroups (clusters) of a population Clusters, not individual members, are selected Steps: 1. The population is divided into clusters 2. The clusters are then randomly chosen Example: From the entire population of fifth graders in Lee County, define the clusters as classes. Randomly select two fifth grade classes from each school, and study/survey the students of the selected classes. Q: In investigating class notes, why was selecting one class a bad method of sampling?
17	Systematic Sampling Process of selecting a random sample from a listing of the population Units are selected from the list by taking every k^th entry Steps: 1. Divide a list of the population into as many sequential segments as will be needed 2. Randomly choose a starting point k, then choose the k^th unit in each segment Example: Suppose we want a sample of 100 people from a population of 5000. We could randomly list all 5000 names (perhaps by computer), then select the 17^th name from each group of 50.
18	Biased Sampling Bias occurs when sampling is not random. Convenience (accidental or haphazard) sampling: uses whomever happens to be available (the most convenient group) does not give each member of the population an equal chance of being selected Volunteer sampling: results reflect the opinions of only those who decide to respond probably acquires the input only of those who have a strong or extreme opinion
19	Example of Sampling