Statistical Inference: Population, Sampling, and Confidence Intervals

Vocabulary flashcards covering key terms from the lecture notes on population, sampling, and confidence intervals.

Population

The entire group of interest from which a sample is drawn; the set the study aims to represent.

Sample

A subset of the population that researchers actually study; usually a smaller number of individuals.

Parameter

A characteristic of the population, such as the population mean (μ).

Population parameter

The true, but unknown, value of a population characteristic (the 'true' value).

Statistic

A numerical characteristic calculated from data in a sample (e.g., sample mean x̄).

Sample statistic

A numerical descriptor calculated from a sample used to estimate a population parameter (e.g., x̄).

Statistical inference

Generalizing from a sample to a population with a stated degree of certainty.

Confidence interval

A range computed from sample statistics that is expected to contain the population parameter with a stated confidence level (e.g., 95%).

Confidence level

The probability that the confidence interval contains the population parameter across repeated samples (commonly 95%).

End points of a confidence interval

Lower end = x̄ − z × SE; Upper end = x̄ + z × SE (e.g., using 1.96 for 95% CI).

Population mean

The average value of a measurement across the entire population (μ).

Sample mean

The average value of a measurement in a sample (x̄).

Measurement

The process of quantifying a variable in a study.

Independent variable

The variable believed to influence or cause changes in another variable; the predictor.

Dependent variable

The outcome variable measured to assess the effect of the independent variable.

Data collection

The process of gathering observations or responses for analysis.

Representative sample

A sample that closely reflects the characteristics of the population.

Large sample size

A larger number of observations helps sample means better approximate the population mean.

Sampling error

The difference between a sample statistic and the population parameter due to sampling variability.

Measurement error

Error arising from the measurement process or instrument.

Respondent error

Errors arising from respondents providing inaccurate or incomplete information.

Researcher error

Errors arising from the research process, data handling, or interpretation.

Pearson's correlation coefficient (r)

A measure of linear association between two variables, ranging from -1 to 1.

Correlation strength

Common interpretations: r ≥ 0.5 indicates moderate; r ≥ 0.7 indicates strong correlation.

Relationship between variables

An association or linkage between two variables, often assessed via correlation.

Hypothesis / research question

A testable statement about a population or about relationships between variables that guides data collection.

Random sample

A sample selected so that every member of the population has an equal chance of selection.