stats 161 lecture 1 and 2

Population

Population is the entire group we are interested in studying.

Sample

A sample is a subset of the population used to gain information about the whole.

Census

A census is a survey or study of every member of the population.

Parameter

A parameter is a numerical summary of a population.

Statistic

A statistic is a numerical summary of a sample.

Variable

A variable is a characteristic, number, or quantity that can be measured or counted and can vary across individuals.

Quantitative Variable

Quantitative variables represent measurable quantities.

Discrete Variable

Discrete variables are countable values (e.g., number of children).

Continuous Variable

Continuous variables can take any value within a range (e.g., height, weight).

Qualitative Variable

Qualitative (categorical) variables represent categories or groups.

Nominal Variable

Nominal variables are categories with no inherent order.

Ordinal Variable

Ordinal variables are categories with a meaningful order but differences between levels are not measurable or equal.

Interval Variable

Interval variables can be ordered, differences are meaningful, but have no natural zero.

Ratio Variable

Ratio variables have all properties of interval variables plus a natural zero; ratios are meaningful.

Identifier Variable

Identifier variables are used only to identify individuals and are not analyzed.

Bias

Bias is the tendency for a sample to differ from the population in some systematic way.

Selection Bias (Undercoverage)

Selection bias occurs when some portion of the population is not sampled or underrepresented.

Response Bias

Response bias occurs when survey design influences the responses.

Voluntary Response Bias

Voluntary response bias occurs when individuals can choose whether to participate.

Non-response Bias

Non-response bias occurs when a large proportion of those sampled fail to respond.

Observational Study

An observational study is one where the researcher observes and records information without applying any treatment.

Experiment

An experiment involves intervention by the researcher, applying a treatment or manipulation to study its effects.

Random Sampling

Random sampling is the process of selecting individuals so that each member of the population has an equal chance of being included.

Convenience Sampling

Convenience sampling involves selecting a sample that is easiest to access or collect.

Simple Random Sample (SRS)

In an SRS, each member of the population has an equal chance of being selected.

Stratified Random Sampling

Stratified random sampling divides the population into subgroups (strata) and randomly samples from each subgroup.

Systematic Random Sampling

Systematic random sampling selects every k-th individual from a population list.

Cluster Random Sampling

Cluster random sampling divides the population into clusters, randomly selects clusters, and includes all individuals in those clusters.

Five W's of Statistical Research

The Five W's are Who, When, Where, Why, and What, used to establish the context of a study.