Statistics: Introduction

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Definitions

Statistics

Collection of methods for planning experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions.

Variable

Characteristic or attribute that can assume different values

Random Variable

A variable whose values are determined by chance.

Population

All subjects possessing a common characteristic that is being studied.

Sample

A subgroup or subset of the population.

Parameter

Characteristic or measure obtained from a population.

Statistic (not to be confused with Statistics)

Characteristic or measure obtained from a sample.

Descriptive Statistics

Collection, organization, summarization, and presentation of data.

Inferential Statistics

Generalizing from samples to populations using probabilities. Performing hypothesis testing, determining relationships between variables, and making predictions.

Qualitative Variables

Variables which assume non-numerical values.

Quantitative Variables

Variables which assume numerical values.

Discrete Variables

Variables which assume a finite or countable number of possible values. Usually obtained by counting.

Continuous Variables

Variables which assume an infinite number of possible values. Usually obtained by measurement.

Nominal Level

Level of measurement which classifies data into mutually exclusive, all inclusive categories in which no order or ranking can be imposed on the data.

Ordinal Level

Level of measurement which classifies data into categories that can be ranked. Differences between the ranks do not exist.

Interval Level

Level of measurement which classifies data that can be ranked and differences are meaningful. However, there is no meaningful zero, so ratios are meaningless.

Ratio Level

Level of measurement which classifies data that can be ranked, differences are meaningful, and there is a true zero. True ratios exist between the different units of measure.

Random Sampling

Sampling in which the data is collected using chance methods or random numbers.

Systematic Sampling

Sampling in which data is obtained by selecting every kth object.

Convenience Sampling

Sampling in which data is which is readily available is used.

Stratified Sampling

Sampling in which the population is divided into groups (called strata) according to some characteristic. Each of these strata is then sampled using one of the other sampling techniques.

Cluster Sampling

Sampling in which the population is divided into groups (usually geographically). Some of these groups are randomly selected, and then all of the elements in those groups are selected.