# Statistics: Introduction

## 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.