Sampling Methods and Data Analysis PDF

SAMPLING ○ Simple Random Sampling (SRS) ○ Stratified Random Sampling DESCRIPTIVE VS INFERENTIAL STATISTICS ○ Systematic Sampling...

SAMPLING ○ Simple Random Sampling (SRS) ○ Stratified Random Sampling DESCRIPTIVE VS INFERENTIAL STATISTICS ○ Systematic Sampling ○ Cluster Sampling Descriptive Statistics The methods that primarily help summarize and present data. SIMPLE RANDOM SAMPLING (SRS) Inferential Statistics ○ every member of the population has an equal chance Methods that use data collected from a small group to reach of being included in the sample. conclusions about a larger group. ○ Selection may be with replacement or without replacement ○ This sampling method requires a listing of the Population elements of the population called the sampling frame. Selection may be with replacement (selected totality of the observations of interest individual is returned to frame for possible reselection) group of objects, events, or individuals or without replacement (selected individual isn't from which a conclusion will be drawn returned to the frame). ○ Samples may be obtained from the table of random Sample numbers or computer random number generators. a subset of the population a portion of the population selected for study Census complete enumeration tool where information or data is obtained from the entire population Survey data are obtained from a sample WHY DO SAMPLING? ○ Cost ○ Timeliness ○ Detailed Information PROBABILITY SAMPLING - sampling methods where every member of the population to have a known, nonzero chance of being selected into the sample - Done to ensure that the segment or sample taken is representative of the entire population STRATIFIED SAMPLING - Also called random sampling ○ an extension of simple random sampling which allows for different homogeneous groups, called strata, in the population to be represented in the sample. ○ To obtain a stratified sample, the population is divided into two or more strata based on common characteristics. A SRS is then used to select from each strata, with sample sizes proportional to strata sizes. Samples from the strata are then combined into one. TYPES OF PROBABILITY SAMPLING  ○ Simple to use. ○ May not be a good representation of the population's underlying characteristics. Stratified sample: ○ Ensures representation of individuals across the entire population. Cluster sample: ○ More cost effective. ○ Less efficient (need larger sample to acquire the same level of precision). SYSTEMATIC SAMPLING NON-PROBABILITY SAMPLING ○ elements are selected from the population at a uniform interval that is measured in time, order, or ○ Haphazard or accidental sampling space. ○ Convenience sampling ○ First, a decision on a desired sample size n. The ○ Volunteer sampling population of N units is then divided into groups of k ○ Purposive Sampling units: k=N/n. Then, one unit is randomly selected from ○ Quota sampling the first group, with every kth unit thereafter also ○ Snowball sampling selected. EVALUATING SURVEY WORTHINESS ○  hat is the purpose of the survey? W ○ Is the survey based on a probability sample? ○ Coverage error - appropriate frame? ○ Nonresponse error - follow up. ○ Measurement error - good questions elicit good responses. CLUSTER SAMPLING ○ Sampling error - always exists. ○ Population is divided into several "clusters," each TYPES OF SURVEY ERRORS representative of the population. ○ A simple random sample of clusters is selected. Coverage error or selection bias: ○ All items in the selected clusters can be used, or items can be chosen from a cluster using another - Exists if some groups are excluded from the frame probability sampling technique. and have no chance of being selected. ○ A common application of cluster sampling involves election exit polls, where certain election districts are Nonresponse error or bias: selected and sampled. ○ People who do not respond may be different from those who do respond. Sampling error: ○ Variation from sample to sample will always exist. Measurement error: ○ Due to weaknesses in question design and / or respondent error. TYPES OF SURVEY ERRORS COMPARING PROBABILITY SAMPLING METHODS Coverage error - Excluded from frame Simple random sample and Systematic sample: Nonresponse error  - Follow up on nonresponses Sampling error - Random differences from sample to sample Measurement error - Bad or leading question ETHICAL ISSUES ABOUT SURVEYS ○  overage error and nonresponse error can be C leveraged by survey designers to purposely bias survey results. ○ Sampling error can be an ethical issue if the findings are purposely not reported with the associated margin of error. ○ Measurement error can be an ethical issue: ○ Survey sponsor chooses leading questions. ○ Interviewer purposely leads respondents in a particular direction. ○ Respondent(s) willfully provide false information. Developing a Sampling Distribution Assume there is a population... (A tennis team consists of four members 68, 72, 76, and 80 kilograms.) Population size N=4. Variable of interest is, X, weight of the individual. Values of X: 68, 72, 76, & 80 (kilograms). What is the mean and variance, and standard deviation of the population? 68, 72, 76, 80 µ = 68 + 72 + 76 + 80/4 = 74 2 2 2 2 2 δ = (68 − 74) + (72 − 74) + (76 − 74) + (80 − 74) /4 = 20 δ = 4. 47 Variance= 5486-74^2= 10 µ 68 70 72 74 76 78 80 P(x) 1/16 2/16 3/16 4/16 3/16 2/16 1/16 P(X=74)= 4/16 P(X