Glossary
Bias
A systematic error in a study's design or conduct that causes certain outcomes or responses to be favored over others, leading to inaccurate conclusions.
Example:
If a survey about healthy eating habits is only given to people at a gym, it might suffer from bias because gym-goers are likely more health-conscious than the general population.
Causation
A relationship where a change in one variable directly causes a change in another variable.
Example:
A well-designed experiment might show that increased study time directly leads to higher test scores, establishing causation.
Census
A study that attempts to collect data from every individual in the entire population.
Example:
The U.S. government conducts a census every ten years to count every person living in the country.
Cluster Sample
A sampling method where the population is divided into heterogeneous groups (clusters), and then a random sample of entire clusters is selected.
Example:
To survey opinions of residents in a large city, a researcher might randomly select a few city blocks (clusters) and then survey every household within those selected blocks, creating a cluster sample.
Comparison (in experimental design)
A key principle of experimental design that involves having at least two treatment groups, often including a control group, to assess the effect of the treatments.
Example:
To determine if a new teaching method is effective, a researcher must use comparison by having one group taught with the new method and another with the traditional method.
Completely Randomized Design
An experimental design where all experimental units are allocated at random among all the treatments.
Example:
If 100 volunteers are randomly assigned to one of two diet plans, with no other grouping, this is a completely randomized design.
Confounding Variables
Variables that are related to both the explanatory and response variables, making it difficult to determine if the explanatory variable alone is causing the observed effect.
Example:
In a study linking coffee consumption to heart disease, stress levels could be a confounding variable because stressed people might drink more coffee and also be more prone to heart disease.
Control (in experimental design)
The principle of keeping all other variables constant for all experimental units except for the explanatory variable, to minimize the influence of confounding factors.
Example:
In an experiment on plant growth, ensuring all plants receive the same amount of light and water, regardless of the fertilizer type, is an example of control.
Control Group
A group of experimental units that receives no treatment or a placebo, serving as a baseline for comparison to assess the effect of the active treatment.
Example:
In a drug trial, the group receiving a sugar pill instead of the actual medication is the control group, helping to isolate the drug's effect.
Experiment
A study in which researchers intentionally manipulate one or more variables (factors) to observe their effects on a response variable.
Example:
To test a new drug, researchers randomly assign patients to receive either the drug or a placebo, making it an experiment designed to establish causation.
Experimental Units
The individuals or objects to which treatments are applied in an experiment.
Example:
In a study testing a new fertilizer, the individual plants or plots of land receiving the fertilizer are the experimental units.
Explanatory Variables (Factors)
The variables that are manipulated or controlled by the experimenter to see if they cause a change in the response variable.
Example:
In an experiment testing different types of exercise on weight loss, the type of exercise (e.g., cardio, strength training, none) would be the explanatory variable.
Generalization
The ability to extend findings from a sample to the larger population from which the sample was drawn.
Example:
If a study on a randomly selected group of high school students finds that 70% prefer online learning, we might be able to generalize this finding to all high school students in the district.
Observational Study
A study where researchers observe individuals and measure variables of interest without attempting to influence the responses.
Example:
A study tracking the health outcomes of people who regularly consume organic food versus those who don't, without assigning diets, is an observational study.
Population
The entire group of individuals or objects about which we want to gather information and draw conclusions.
Example:
If a researcher wants to study the average height of all adult males in the United States, then all adult males in the U.S. constitute the population.
Prospective Study
An observational study that follows individuals forward in time, collecting data as events unfold.
Example:
A study that enrolls a group of newborns and tracks their development and health over the next 18 years to identify risk factors for certain diseases is a prospective study.
Random Assignment
The process of assigning experimental units to treatment groups using a chance process, which helps create roughly equivalent groups and reduces the impact of confounding variables.
Example:
Flipping a coin to decide whether a patient receives the new drug or a placebo ensures random assignment in a clinical trial.
Random Sampling
The process of selecting individuals from a population in a way that gives each member a known, non-zero chance of being selected, reducing bias and allowing for generalization.
Example:
Using a random number generator to pick student IDs for a survey ensures random sampling and helps the sample represent the entire student body.
Randomness
The characteristic of an event where outcomes are uncertain but follow a predictable pattern over many repetitions, essential for reliable statistical conclusions.
Example:
When flipping a fair coin, the outcome of any single flip is uncertain, but over many flips, the proportion of heads will approach 0.5, demonstrating randomness.
Replication (in experimental design)
The principle of applying each treatment to more than one experimental unit to reduce the impact of chance variation and increase the reliability of results.
Example:
Testing a new fertilizer on 50 plants rather than just one ensures replication, making the results more trustworthy.
Response Variable
The outcome variable that is measured in an experiment to see if it is affected by the explanatory variable.
Example:
If a study investigates the effect of sleep deprivation on reaction time, the measured reaction time would be the response variable.
Retrospective Study
An observational study that looks back in time to collect data on past events or exposures.
Example:
Researchers examining medical records from the last 20 years to see if there's a link between childhood vaccinations and later health issues are conducting a retrospective study.
Sample
A subset of the population that is actually examined to gather data and make inferences about the larger group.
Example:
To estimate the average GPA of all students at a large university, a researcher might select a sample of 200 students to collect data from.
Sample Survey
A type of observational study that collects data from a sample of a population to estimate population parameters.
Example:
A poll conducted by calling a random selection of registered voters to gauge their opinions on an upcoming election is a sample survey.
Sampling With Replacement
A sampling method where an individual selected for the sample is returned to the population and can be selected again.
Example:
Rolling a die multiple times, where each roll is independent and the same number can appear again, is analogous to sampling with replacement.
Sampling Without Replacement
A sampling method where once an individual is selected for the sample, they cannot be selected again.
Example:
Drawing names from a hat for a raffle where each drawn name is set aside is an example of sampling without replacement.
Simple Random Sample (SRS)
A sampling method where every possible group of individuals of the desired size has an equal chance of being selected from the population.
Example:
Putting all 1000 student names into a hat and drawing out 50 names without looking creates a Simple Random Sample (SRS) of students.
Stratified Random Sample
A sampling method where the population is first divided into homogeneous subgroups (strata), and then a simple random sample is taken from each stratum.
Example:
To survey student opinions, a school might divide students by grade level (freshman, sophomore, etc.) and then take an SRS from each grade, forming a stratified random sample.
Systematic Random Sample
A sampling method where individuals are selected from an ordered list at regular intervals, starting from a randomly chosen point.
Example:
Selecting every 10th customer entering a store, after randomly choosing the first customer between 1 and 10, is an example of a systematic random sample.