Identify biased samples

Learning Objectives Define population, sample, and sampling bias. Differentiate between a representative (unbiased) sample and a biased sample. Identify common types of sampling bias, including convenience, voluntary response, and undercoverage. Analyze a given sampling method to determine if it is likely to produce a biased sample. Explain how a specific bias could skew the results of a survey or study. Propose an unbiased sampling method for a given research question. Evaluate the validity of a statistical claim based on the sampling method used. A new app claims 90% of users love their new update after polling the first 100 people who downloaded it. 🤔 Do you trust this number? This tutorial will teach you how to spot a biased sample, which is a sample that doesn'...

TermDefinitionExample PopulationThe entire group of individuals, items, or data about which we want to draw conclusions.If we want to know the average height of students at a specific high school, the population is ALL students enrolled at that high school. SampleA subset of the population that is selected for study. We use data from the sample to make inferences about the entire population.Instead of measuring all 1,500 students at the high school, we select and measure 100 students. This group of 100 is the sample. Biased SampleA sample in which some members of the population are more likely to be included than others, leading to a systematic over- or under-representation of certain characteristics.To find the average height of all students, we only sample the members of the varsity bas...

Principle of a Simple Random Sample (SRS) For a population of size N, the probability of selecting any individual is P(selection) = 1/N. Every possible sample of size n has an equal chance of being selected. This is the gold standard for unbiased sampling. If a sampling method does not give every individual an equal chance of being selected, it is likely biased. Use this principle as a benchmark to evaluate other methods. Conceptual Definition of Bias Bias = E[\hat{\theta}] - \theta This formalizes the concept of bias. Here, \theta (theta) is the true population parameter (e.g., the true average height), and E[\hat{\theta}] (E of theta-hat) is the expected value, or long-run average, of the sample statistic from a particular sampling method. If the sampling method is unbiase...