Glossary
Bias
A systematic error in a sampling method or study design that causes the sample to not accurately represent the population, leading to inaccurate conclusions.
Example:
If a survey about internet usage is only conducted via landline phones, it would introduce bias by excluding people who only use cell phones or have no phone.
Cluster Sample
A sampling method where the population is divided into heterogeneous groups (clusters), a few clusters are randomly selected, and then all individuals within the chosen clusters are sampled.
Example:
To assess the effectiveness of a new teaching method across a large school district, randomly selecting 5 schools (clusters) and surveying every student in those 5 schools would be a Cluster Sample.
Inferences
Conclusions or generalizations made about a population based on data collected from a sample.
Example:
After surveying a sample of voters, a political analyst might make inferences about the likely outcome of an election.
Non-Biased Sampling Methods
Sampling techniques designed to ensure that every individual or group has an equal chance of being selected, minimizing systematic favoritism.
Example:
Using a random number generator to select participants for a study is an example of employing non-biased sampling methods.
Population
The entire group of individuals or instances about whom we want to gather information and draw conclusions.
Example:
If you're studying the average height of all high school students in your state, then all high school students in your state constitute the population.
Random Sampling Methods
Techniques that involve chance in the selection process to ensure that each member of the population has a known, non-zero probability of being chosen.
Example:
Drawing names from a hat or using a computer program to pick participants are common random sampling methods.
Representative Sample
A subset of a population that accurately reflects the characteristics of the larger group, allowing for valid generalizations.
Example:
To understand student opinions on cafeteria food, a representative sample would include students from all grade levels and dietary preferences.
Sampling Methods
Techniques used to select a subset of individuals from a larger population to gather data and make inferences about the entire group.
Example:
When a polling company decides how to select voters for a survey, they are choosing a specific sampling method.
Sampling with replacement
A sampling procedure where an individual selected for the sample is returned to the population and can be selected again.
Example:
If you roll a die multiple times, each roll is independent and the same number can appear again, which is analogous to sampling with replacement.
Sampling without replacement
A sampling procedure where once an individual is selected for the sample, they cannot be selected again.
Example:
When drawing winning lottery tickets, once a ticket is drawn, it's not put back in, illustrating sampling without replacement.
Simple Random Sample (SRS)
A sampling method where every individual and every possible group of individuals in the population has an equal chance of being selected.
Example:
To select 50 students for a survey from a list of 1000, assigning each student a number and using a random number generator to pick 50 unique numbers would create a Simple Random Sample (SRS).
Strata
Homogeneous subgroups within a population that share a common characteristic, used in stratified random sampling.
Example:
In a study of voter preferences, age groups (18-25, 26-40, 41-60, 60+) could serve as strata.
Stratified Random Sample
A sampling method where the population is divided into homogeneous subgroups (strata), and then a Simple Random Sample is taken from each stratum.
Example:
To survey opinions on a new school policy, dividing students into grade levels (freshmen, sophomores, etc.) and then randomly selecting a few students from each grade creates a Stratified Random Sample.
Systematic Random Sample
A sampling method where a random starting point is chosen from a list, and then every k-th individual is selected.
Example:
From a list of 500 employees, choosing a random starting point (e.g., the 7th employee) and then selecting every 10th employee after that would be a Systematic Random Sample.