Sampling and Data - Elementary Statistics

Vocabulary flashcards covering fundamental definitions in elementary statistics, including sampling techniques, data types, levels of measurement, errors, and experimental design.

Statistics

The science of planning studies and experiments, obtaining data, then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on the data.

Population

The complete collection of all individuals or items being studied, such as every single college student in the United States.

Census

A collection of all data from every single member of the population.

Sample

A subcollection of individuals or items selected from a population.

Sample Size

The total number of individuals or items surveyed or observed in a sample.

Random Sample

A sample selected in such a way that any individual in the population is just as likely to be chosen as any other individual.

Simple Random Sample

A sample selected in such a way that every possible group of $n$ individuals is just as likely to be chosen as any other group of $n$ individuals.

Systematic Sampling

A sampling method in which every $k^{\text{th}}$ individual or item in an ordered population is selected.

Convenience Sampling

A non-scientific sampling technique where data is collected from whatever subjects are easiest to access.

Stratified Sampling

A sampling method where the population is subdivided into groups (strata) and quotas are set to ensure each group has proportionate representation in the sample.

Cluster Sampling

A sampling method where the population is divided into sectors or clusters, a few sectors are randomly selected, and all members from those chosen sectors are sampled.

Voluntary Response Bias

Bias that occurs when respondents themselves decide whether to participate in a survey, often overrepresenting individuals with strong views.

Probability

A measure of the chance of an outcome occurring, represented as a value between $0$ and $1$ inclusive.

Parameter

A numerical measurement describing a characteristic of an entire population.

Statistic

A numerical measurement describing a characteristic of a sample.

Quantitative Data

Data consisting of numbers representing counts or measurements.

Categorical Data

Data consisting of names, labels, or categories that are not numerical counts or measurements (also called qualitative data).

Discrete Data

Quantitative data resulting from a counting process.

Continuous Data

Quantitative data resulting from a measuring process.

Nominal Level of Measurement

A measurement level for categorical data consisting of names, labels, or categories without any natural ordering.

Ordinal Level of Measurement

A measurement level for data that can be arranged in a specific ranking or order, but differences between data values cannot be meaningfully determined.

Interval Level of Measurement

A measurement level where data can be ordered and differences between values are meaningful, but there is no natural zero starting point and ratio comparisons are not meaningful.

Ratio Level of Measurement

A measurement level with a natural zero starting point where both differences and ratios between values are meaningful.

Sampling Error

An error arising from the sampling process itself, caused by flawed sample design or random chance resulting in an unrepresentative sample.

Nonsampling Error

An error caused by human mistakes or faulty equipment during data collection or processing, such as typing errors or inaccurate measuring tools.

Frequency Distribution Table

A table showing the number of observations or values falling into each defined category or class interval.

Class Width

The difference between two consecutive lower class boundaries in a frequency distribution table.

Relative Frequency Distribution

A distribution table where raw frequencies are replaced by proportions or percentages of the total sample size.

Cumulative Frequency

The sum of frequencies for a particular class and all classes below it.

Explanatory Variable

The variable in an experiment that is manipulated or evaluated to measure its potential causal effect on an outcome.

Response Variable

The variable in an experiment that measures the outcome or effect resulting from changes in the explanatory variable.

Control Group

The group of subjects in an experiment that does not receive the active treatment being tested.

Treatment Group

The group of subjects in an experiment that receives the specific treatment being tested.

Placebo

An inactive dummy treatment, such as a sugar pill, given to subjects in a control group to control for psychological effects.

Lurking Variable

A variable that was not intentionally included or controlled in a study, yet influences the relationship between the variables being examined.

Blinding

A technique in experimental design where subjects do not know whether they are receiving the active treatment or a placebo.

Double-Blind Experiment

An experimental procedure in which neither the subjects nor the individuals administering the treatment know who receives the placebo versus the active treatment.