Statistics Master Doc

Sampling Bias

When some members of a population are systematically more likely to be selected in a sample than others.

Undercoverage

A situation where part of the population has a reduced chance of being included in a sample.

Stratified Random Sample

A sampling method that divides the population into homogeneous groups and selects a few individuals from each group.

Systematic Sample

A sampling method that selects individuals at fixed intervals.

Voluntary Response Sample

A sample where individuals choose to participate after being invited.

Simple Random Sample (SRS)

A sampling method where every individual has an equal chance of being selected.

Convenience Sample

A sampling method that uses individuals who are easy to reach.

Cluster Sample

A sampling method that divides the population into groups and selects random clusters to collect data from all members.

Non-response Bias

Bias that occurs when individuals chosen for a sample don’t respond.

Undercoverage Bias

Bias that occurs when segments of the target population are excluded or less represented.

Voluntary Response Bias

Bias that occurs when the sampling is composed of volunteers.

Confusing Wording Bias

Bias that occurs when survey questions are confusing or leading.

Self-reported Response Bias

Bias that occurs when individuals inaccurately report their own traits.

Observational Study

A study in which data is collected without imposing any treatments.

Retrospective Study

A study that examines existing data on individuals.

Prospective Study

A study that follows individuals to gather future data over time.

Experimental Study

A study in which treatment is imposed on subjects to observe effects.

Explanatory Variable

The variable that is purposely manipulated in an experiment.

Response Variable

The measured outcome of an experiment that is compared between treatment groups.

Confounding Variable

A variable that potentially affects the results of a study but is not accounted for.

Comparison (Experimental Design Principle)

A principle that involves comparing different treatment groups.

Random Assignment (Experimental Design Principle)

Assigning experimental units to treatments randomly to reduce confounding.

Replication (Experimental Design Principle)

Having many experimental units in each treatment group to ensure reliability.

Control (Experimental Design Principle)

Controlling for confounding variables by making conditions identical except for the explanatory variable.

Completely Randomized Design

An experimental design where experimental units are assigned to treatments completely at random.

Randomized Complete Block Design

An experimental design where units are blocked by a similar trait before random assignment to treatment.

Matched Pairs Design

An experimental design where participants are paired based on similar characteristics for controlled comparison.

Placebo Effect

The phenomenon where participants experience beneficial effects from an inactive treatment.

Single Blind Study

A study where either the subject or the researcher is unaware of who receives the active treatment.

Double-blind Study

A study where both the subject and the researchers are unaware of who receives the treatment or placebo.

Generalization

Applying study results to a larger population based on the sample’s findings.

Statistical Significance

Results are statistically significant when they are unlikely to have occurred by chance alone.

Experimental Units

The object to which a treatment is randomly assigned.

Explanatory Variable

The variable that is purposely manipulated in an experiment, also known as the factor.

Treatments

The different levels of the explanatory variable in the experiment.

Response Variable

The measured outcome of an experiment that is compared between treatment groups.

Confounding Variable

A variable that potentially affects the results of a study but is not accounted for.

Marginal Distributions

The breakdown of one variable located in the margins of a table.

Conditional Distributions

Distribution of one variable under a specific condition of another variable.

Dot Plots

Graphical representation used for small data sets to display individual data points.

Histograms

Graphs that summarize discrete or continuous data measured on an interval scale, visualizing the data distribution.

Stem-and-Leaf Plots (Stemplots)

A method for displaying quantitative data where each number is split into a 'stem' and a 'leaf'.

Measures of Center

Statistical metrics including mean, median, and mode that summarize the central tendency of data.

Mean

The average of a data set, calculated as the sum of all values divided by the total frequency.

Median

The middle value of ordered data, less affected by outliers than the mean.

Interquartile Range (IQR)

The difference between the first (Q1) and third quartiles (Q3), measuring the spread of the middle 50% of data.

Standard Deviation

A measure of data spread that quantifies how much each data point differs from the mean.

Box Plots

Visual representations of the five-number summary (minimum, Q1, median, Q3, maximum) of a data set.

Outliers

Data points that lie beyond 1.5 times the interquartile range above Q3 or below Q1.

Statistic

A numerical value that describes a characteristic of a sample.

Parameter

A numerical value that describes a characteristic of a population.

Bimodal Distribution

A distribution with two distinct peaks.

Unimodal Distribution

A distribution with one peak.

Skewed Distribution

A distribution where one tail is longer than the other, indicating asymmetry.

Symmetric Distribution

A distribution where the left and right sides are mirror images of each other.