Plan for Today: Chapter 1: Where Do Data Come From? Chapter 2: Samples, Good and Bad Chapter 3: What Do Samples Tell US? Chapter 4: Sample Surveys in the Real World

The Purpose of Statistics: Statistics is the study of the collection, organization, analysis, and interpretation of data.

An Simple Example: One day, you woke up after a nice nap. And suddenly this crazy idea flashed across your mind: you want to find the average age of all Purdue students. Population: the entire group of individuals about which you want information. It is determined by your research topic. Individuals: the minimum subjects in your study - students - all students at Purdue

An Simple Example: You have two choices: 1) Interview every single student at Purdue and calculate the average age. 2) Randomly choose 500 students and calculate their ages. - It’s a Census. - It’s time-consuming. Sample: part of the population where we obtain information and draw conclusion. - the 500 students you chose

Population VS Sample: -It changes from time to time. Population: all Purdue students. Sample: 500 students you randomly chose -It’s fixed once you decided your research topic. BIG question: can a sample represent the population reasonable well?

How the Data Were Produced: Observational study observes individuals but does not attempt to influence them. Census attempts to include the entire population Experiment impose some treatment on individuals.

Bad Sample Biased sampling method: The design of a statistical study is biased if it systematically favors certain outcomes. Convenience sampling: selection of whichever individuals are easiest to reach is. e.g.: Our age study Voluntary response sample: subjects choose themselves as part of the sample by responding to a general appeal. e.g.: write-in or call-in polls

Good Sample Simple random sample (SRS): every set of n individuals has a equal chance to be selected.

From Sample to Population: A parameter is a number that describes the population. It’s fixed. And in practice we don’t know the actual value. parameter Population A statistic is a number that describe a sample. The value is known when we have taken a sample. It chances from sample to sample. statistic Sample Generated Draw conclusion

Two Types of Error in Estimation: Bias is consistent, repeated deviation of the sample statistic from the population parameter in the same direction. Variability describes how spread out the values of the sample statistic are.

Managing Bias and Variability: To reduce bias, use random sampling. To reduce the variability of an SRS, use a larger sample.

Margin of Error: MoE is a way to describe the variability in sample survey. For percentage-type data, an approximation of MoE is n is the sample size.

Margin of Error: If we took many samples using the same method, 95% of the times the population proportion will be captured by

How Sample Surveys Go Wrong In statistics, sampling error or estimation error is the error caused by observing a sample instead of the whole population. The likely size of the sampling error can generally be controlled by taking a large enough random sample from the population, although the cost of doing this may be prohibitive. e.g.: undercoverage

How Sample Surveys Go Wrong non-sampling error is a catch-all term for the deviations from the true value that are not a function of the sample chosen. It includes various systematic errors and any random errors that are not due to sampling. Non-sampling errors are much harder to quantify than sampling errors. e.g.: response error and typo