Advanced Stats

Population

A group of individuals that share (a) certain trait(s) who we are looking to examine.

Sample

A subset of a population that we have access to; represent the characteristics of the entire population.

Census

Data collected on the entire population, about every individual.

Observational Study

Investigators examine data for a sample of individuals (retrospective) or follow a sample of individuals into the future collecting data (prospective) in order to investigate a topic of interest about the population, without influencing or imposing.

Sample Survey

Type of observational study that collects data from a sample in an attempt to learn about the population from which the sample was taken. Cannot prove causal relationships.

Experiment

Deliberately imposing the treatment. Controlled, systematic procedure where researchers manipulate one or more variables (independent variables) to observe and measure the effects on another variable (dependent variable). Can prove causation.

Convenience Sampling

A non-probability sampling method where participants are selected based on their easy accessibility and proximity to the researcher, often leading to potential biases in the sample.

Voluntary Response Sample

A non-probability sampling method where participants self-select to be included in a survey or study, which can result in biases due to the nature of who chooses to respond.

Simple Random Sample (SRS)

A sampling method where each individual in the population has an equal chance of being selected, ensuring that the sample is representative and free from bias.

Stratified Random Sampling

A method where the population is divided into subgroups, or strata, and samples are randomly selected from each stratum, ensuring representation from all segments of the population.

Cluster Sampling

A sampling method where the population is divided into clusters, usually geographically, and entire clusters are randomly selected to form the sample, allowing for efficient data collection.

Systematic random sampling

A sampling method where individuals are selected at regular intervals from a randomly ordered list of the population, ensuring an organized and representative sample.

With vs Without Replacement

In sampling, "with replacement" allows selected individuals to be returned to the population for potential re-selection, while "without replacement" means once an individual is selected, it cannot be chosen again, affecting the sample size and probability.

Biased Samples

Samples that are systematically not representative of the desired population; occurs when certain responses are artificially favored over others.

Voluntary Response Bias

A type of bias that occurs when individuals select themselves to participate in a survey or study, often leading to overrepresentation of those with strong opinions or interests.

Undercoverage

Occurs when some groups in the population are left out of the process of choosing a sample (ex. Latin American immigrants on US Census, fearful of government invasion)

Non-response

Occurs when individuals selected for a survey fail to participate, potentially leading to biased results.

Response bias

Untruthful answers, caused by the respondent (“Do you drink alcohol?) or the interviewer (race).

Ignorance

Lack of knowledge or information on a subject, which can affect responses in surveys or studies (Princeton’s non-existent business program)

Lack of memory

When a respondent cannot recall information accurately, leading to incomplete or incorrect survey responses.

Timing

The specific moment or duration during which data is collected, which can influence the outcomes and accuracy of survey results (ex. Football during Superbowl)

Phrasing

The way questions are structured or worded in surveys, which can impact respondents' understanding and their answers.

Sampling error

The error that occurs when a sample does not accurately represent the population from which it was drawn, often due to the size or selection method of the sample.

Non-sampling error

The error that arises from issues other than sampling errors, such as measurement errors, data processing errors, or non-response bias, which can lead to inaccuracies in survey results.

Experimental Units

The subjects or objects upon which an experiment is conducted, which receive the treatment being tested.

Subjects

The individuals or entities that participate in an experiment or study, receiving treatments or interventions to assess the effects of those treatments.

Treatment

The specific intervention or condition applied to experimental units in order to observe its effects during a study.

Explanatory variable

Independent variable that is manipulated or controlled in an experiment to observe its effect on a response variable.

Response variable

The dependent variable measured in an experiment to assess the impact of the explanatory variable.

Factor

An explanatory variable that is manipulated in an experiment, often consisting of different levels or values, to determine its effect on the response variable.

Level

Specific value or category of a factor in an experiment that is tested to assess its effect on the response variable.

4 Critical Elements of Experimental Design

Comparison (two or more treatments studied), Randomization (in selection or distribution), Control (have a control group that does not receive the treatment), and Replication (use enough subjects to be statistically valid so it could be repeated)

Placebo

A treatment that has no therapeutic effect, used in experiments as a control measure to compare against actual treatments and assess their efficacy.

Placebo Effect

The phenomenon where a patient experiences a perceived effect on their condition due to believing they are receiving treatment, despite having received a placebo.

Blinding

A methodology in experiments where participants or researchers are unaware of which treatments participants are receiving, to prevent bias in the results.

Double Blind

A study design in which neither the participants nor the researchers know who is receiving the treatment or the placebo, minimizing bias.

Confounding variables

Factors not being studied or controlled that can influence the outcomes of an experiment, leading to incorrect conclusions about the relationship between variables.

Completely randomized design

The experimental units are assigned to the treatments completely by chance.

Confounding vs lurking variables

Lurking variables drive each of the two variables under investigation, causing a spurious association between them; the two variables in the study would logically have no correlation. Confounding variables are somehow related to the factor under investigating, leaving us unable to tell which of the two variables caused the observed response; it would ideally be controlled for.

Completely Randomized Design

Experimental units are assigned to the treatments completely by chance.

Matched Pair Design

A type of experimental design that pairs individuals or units based on a certain characteristic, with each pair receiving different treatments to compare outcomes.

Block Designs

An experimental design that divides subjects into homogeneous groups, or blocks, before random assignment to treatments to reduce variability.

Random Selection Scope of Inference

Allows for generalization of results to the entire population.

Random Assignment Scope of Inference

Allows for causal inferences from the experimental results.