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Topic 1 Collecting and Producing Data

Topic 1 Collecting and Producing Data. Basically, 3 parts to this topic. All three are important and fundamental to statistics Sampling methods Design of studies Simulations. What to take away from Chapter 1 of your textbook. Relevance of statistics in our daily lives Variability

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Topic 1 Collecting and Producing Data

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  1. Topic 1Collecting and Producing Data

  2. Basically, 3 parts to this topic • All three are important and fundamental to statistics • Sampling methods • Design of studies • Simulations

  3. What to take away from Chapter 1 of your textbook • Relevance of statistics in our daily lives • Variability • The Data Analysis Process • Types of Data • Frequency Distributions and Bar charts • Dotplots

  4. Sampling • Important concepts of WS Topic 12 • Why we sample • Difference between sample and population • Parameter and statistic • Bias – Types of bias • Sampling Methods • Concept of sampling variability • Effects of sample sixe on distribution of sample statistics • Effect of population size on distribution of sample statistics

  5. SummarizingWS Topic 12: Sampling In statistics, we often want to answer questions about a larger group We must get sound answers We need to produce data in a way that is designed to answer our questions

  6. Continuing … • We are usually interested in studying a large group referred to as the population. • Sampling involves studying a part in order to gain insight about the whole. • We sample because it’s not practical to take a census. • If we want to make valid conclusions about the population, we want our sample to be representative of the population we are studying.

  7. Sample Design • When we speak of selecting our sample we are talking about sample design – that is, how our sample is chosen from the population. • Poor sample designs produce misleading conclusions.

  8. Sample Design • Voluntary response sample • Convenience sample • Probability based sample • Only samples based on probability lead to representative samples. All other samples are generally not representative of target populations and are considered biased.

  9. Bias • Bias is the tendency for a sample to be different from the population is a systematic way. The design of a study is biased if it systematically favors certain outcomes.

  10. Types of Bias • Selection bias • Some part of the population is systematically excluded from the sample • How can this happen? • Convenience sample • Telephone survey • Shopping mall • Response bias • Wording of a question • Memory activity/Yates pg 282 • Measurement bias • Method of observation produces values that differ from the truth • Improperly calibrated scale • Non-response bias • Members of sample who choose not to respond • Yates pg 283

  11. Sample Design and Bias • Poorly designed samples will introduce bias and lead to misleading conclusions about the population you are studying. • How can we eliminate bias? • Increase sample size? No • Base your sample on probability? Yes The use of chance to select the sample is the essential principle of statistical sampling.

  12. Sample Design • The list of subjects from which you will choose your sample is called the sampling frame • Commonly used sample designs based on probability • Simple Random Sample (SRS) • Stratified Random Sample • Systematic Sample • Cluster Sample

  13. Simple Random Sample (SRS) • Conceptually, probably the easiest way to sample. • Sample of size n, where every sample has an equal likelihood of being selected. • Assign numbers to each member of your sampling frame, randomly pick n numbers corresponding to your sampling frame • Use of random number table and generating random numbers on the TI-83

  14. Stratified Random Sample • Divide population into strata and then choose simple random samples within each strata • Used when it might be useful to obtain more information relating to characteristics of the population and allows for more accurate inferences about the population

  15. Things to Keep Mind … • What is the population we are interested in? • and what questions are we interested in answering • What sample design will best serve our needs? • We want to eliminate bias • Bias by sample design • Bias not by sample design

  16. Part I • Population vs sample • Parameter vs statistic • Sample Designs • Probability based and not • Probability based sample designs • How to use TI83 and random number table • Effects of sample size and population size on statistics • Bias • Types • Sources • Vocabulary • Sampling frame, census, sample design, bias, sampling variability, SRS

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