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Bias
Systematic tendency for a sampling method to overestimate or underestimate a true population value.
Population
The entire group a researcher wants to study.
Sample
The individuals actually selected and observed in a study.
Parameter
A numerical value describing an entire population.
Statistic
A numerical value calculated from a sample.
Representative Sample
A sample that reflects important characteristics of the target population.
Generalization
Using sample results to draw conclusions about a larger population.
Random Sampling
Selecting individuals by chance to reduce selection bias and support generalization.
Simple Random Sample (SRS)
A sample in which every possible sample of a given size has an equal chance of selection.
Undercoverage Bias
Occurs when some population members have little or no chance of being selected.
Voluntary Response Bias
Occurs when people choose to participate, often favoring those with strong opinions.
Nonresponse Bias
Occurs when selected individuals do not respond and responders differ meaningfully from nonresponders.
Response Bias
Occurs when responses are systematically inaccurate because of wording, interviewer influence, memory, or social pressure.
Wording Bias
Occurs when a question's phrasing nudges respondents toward a particular answer.
Convenience Sampling
Selecting individuals who are easiest to reach, potentially producing a biased sample.
Overestimation
When a method tends to produce a sample statistic higher than the true population parameter.
Underestimation
When a method tends to produce a sample statistic lower than the true population parameter.
Direction of Bias
The tendency of a method to push an estimate above or below the true population value.
Sampling Variability
Natural differences between sample statistics caused by chance selection.
Random Sampling vs. Bias
Random sampling reduces selection bias but does not guarantee a perfectly representative sample.
Large Sample Size
A larger sample can reduce random variability but does not automatically eliminate bias.
Stratified Random Sample
Divide the population into groups and randomly sample individuals within each group.
Cluster Sample
Randomly select entire groups and survey all individuals within the chosen groups.
Systematic Sample
Select individuals using a fixed interval, such as every 10th person.
Convenience Sample Example
Surveying students who happen to be in the cafeteria.
Voluntary Response Example
An online poll where anyone chooses whether to submit a vote.
Undercoverage Example
Surveying only club members to estimate the opinions of all students.
Nonresponse Example
Randomly selecting 100 people but receiving only 40 completed surveys.
Response Bias Example
People underreporting socially undesirable behavior in a survey.
Wording Bias Example
Asking, "Should the school waste money on unnecessary programs?"
Overestimation Example
Surveying enthusiastic fans to estimate the popularity of a product among everyone.
Underestimation Example
Respondents systematically reporting fewer hours spent on social media than they actually spend.
Generalization from a Random Sample
Results can generally be generalized to the population from which the sample was randomly selected, subject to study limitations.
Generalization from a Convenience Sample
Results cannot confidently be generalized to the entire target population because selection may be biased.
Random Sampling vs. Random Assignment
Random sampling supports generalization; random assignment supports cause-and-effect conclusions.
Can Random Sampling Still Be Biased?
Yes. Nonresponse, undercoverage, response bias, and chance variation can still affect results.
Does a Larger Sample Eliminate Bias?
No. Increasing sample size reduces random variability but does not necessarily correct systematic bias.
Identifying Overestimation or Underestimation
Determine who is overrepresented or underrepresented and how that affects the measured variable.
When Is Bias Direction Unknown?
When the scenario does not provide enough information to determine whether the estimate tends high or low.
Effect of Leading Questions
They can influence responses and cause response bias.
Effect of Excluding Low Values
If excluded individuals have lower values than the rest of the population, the sample average tends to be too high.
Effect of Excluding High Values
If excluded individuals have higher values than the rest of the population, the sample average tends to be too low.
Effect of Strong Opinions in a Poll
People with strong opinions may participate disproportionately, making results unrepresentative.