Glossary
Bias
A systematic deviation of a sample statistic from the true population parameter, causing the distribution of estimates to be consistently shifted in one direction.
Example:
If a survey only contacts people during working hours, it might introduce bias by underrepresenting those who work during the day, leading to an inaccurate estimate of public opinion.
Minimum variability
A characteristic of a sampling distribution where the sample statistics are very close to each other, indicating high consistency across samples.
Example:
When a pollster increases their sample size from 100 to 1000, the results from repeated polls will show minimum variability, clustering tightly around the true population percentage.
Nonresponse bias
A type of bias that occurs when a significant portion of the selected sample does not respond to a survey, and those who do respond differ systematically from those who don't.
Example:
A survey about online privacy might suffer from nonresponse bias if people highly concerned about privacy are less likely to complete the survey.
Population mean
The true average value of a quantitative variable for an entire population, which is typically unknown and estimated by sample statistics.
Example:
The actual average height of all adult males in a country is the population mean, which we try to estimate using sample data.
Population proportion
The true proportion of individuals in an entire population that possess a certain characteristic, typically unknown and estimated by sample statistics.
Example:
The actual percentage of all registered voters in a state who support a particular candidate is the population proportion.
Random assignment
The process of assigning experimental units to treatment groups by chance, aiming to create groups that are roughly equivalent before treatment application.
Example:
In a medical trial, patients are given random assignment to either the new drug group or the placebo group to ensure any observed differences are due to the drug, not pre-existing conditions.
Random sampling method
A procedure for selecting a sample from a population where each member has a known, non-zero chance of being selected, ensuring representativeness and allowing for inference.
Example:
Using a computer program to randomly select 100 student IDs from a school's database for a survey is an example of a random sampling method.
Sample mean
The average value of a quantitative variable calculated from a specific sample, used to estimate the population mean.
Example:
After surveying 50 randomly selected students, the calculated average GPA of 3.2 is the sample mean.
Sample proportion
The proportion of individuals in a sample that possess a certain characteristic, used to estimate the population proportion.
Example:
If 30 out of 100 surveyed students say they prefer online classes, then 0.30 is the sample proportion of students who prefer online classes.
Sampling variability
The natural tendency of sample statistics to differ from one another due to random chance, even when drawn from the same population.
Example:
If you take multiple random samples of students' heights from the same school, you'll find slightly different average heights for each sample due to sampling variability.
Skewness
A measure of the asymmetry of a probability distribution, indicating if one side has more values than the other.
Example:
A distribution of housing prices in a wealthy neighborhood might show skewness to the right, with a few very expensive homes pulling the mean higher than the median.
Unbiased estimator
An estimator whose sampling distribution mean equals the true population parameter, meaning it does not consistently over or underestimate the parameter.
Example:
If a survey's average sample proportion of people who prefer coffee consistently matches the true proportion of coffee lovers in the city, then the sample proportion is an unbiased estimator.
Variability
The spread or dispersion of a sampling distribution, indicating how much sample statistics differ from one another.
Example:
If a machine fills bags of chips, high variability in the bag weights means some bags are much lighter and some much heavier than the target weight.