Surveys, Experiments, and Simulations Unit 3 Part 1 Surveys

Why Survey? We need information to guide decisions. Conducting a census is either too hard or impossible. The Purpose of Surveys Population (parameter) Sample (statistic) Mean μ x̄ Standard Deviation σ s Parameters are often impossible to know, so we conduct good surveys to find statistics.

Observational Studies: Sample Size < Population Size Prohibitively difficult to conduct Powerful because they report parameters μ (mu): “true mean” or population mean σ (sigma): “true standard deviation” or population standard deviation Types of Surveys Census: Sample Size = Population Size Easier to conduct Weaker because they report statistics (x-bar): “estimated mean” or sample mean s: “estimated standard deviation” or sample standard deviation

Statistics have been shown to be very good predictors of parameters under certain conditions Having a good idea of where a parameter is, if imprecise, is still useful! The Power of Statistics If we can’t know the truth, what’s the point? When are Statistics good predictors of Parameters? No Bias Large Sample Size If both of these conditions are met, the statistics generated by an observation study can be considered useful.

Certain outcomes are systemically favored. Example, if I ask volunteers to come up to a platform to be measured for height at lunch, taller people might be more inclined to participate for various reasons. Our observed statistics will not match the population’s parameters. Bias What does bias mean? Result of Biased Survey Design: Taller individuals were more represented X-bar > mu s < sigma

Make sure everybody from the population of interest has an equal chance to be part of the observational study. Bias How do you reduce bias? Types of Bias: Convenience Sample (Leads to under coverage bias) Voluntary Response (Leads to non response bias) Leading Questions (Essentially the survey conductor is lying) Bad Design: Under Coverage Bias (Having a lower or no chance of being selected) Non Response Bias (Refusing to participate) Response Bias (Lying)

Make sure everybody from the population of interest has an equal chance to be part of the observational study. Bias How do you reduce bias? Good Design: Simple Random Sample (SRS) Stratified Random Sample Multistage Sampling Design Cluster Sample

The “Rule of Thumb” in Statistics is 15+ individuals. This might seem low but even with that few participants, a statistics can be surprisingly accurate! Sample Size How big should a sample be? Is bigger always better? No. Simply because a large sample cannot compensate for bad design. Having a balance of good design and sample size to produce accurate statistics is the goal of this process.