Section 1.1-1.2

Elementary Statistics

Statistics

the science of collecting, organizing, summarizing, and analyzing information to draw conclusions or answer questions. Also provides a measure of confidence in any conclusions.

Variable

a characteristic or attribute of the individuals within the population that can assume different values (they can be numerical or non-numerical)

Data

values that the variable can assume. key aspects are that they vary

Population

entire group of individuals to be studied

Individual

a person or object that is a member of the population being studied

Sample

a subset of the population that is being studied

Parameter

numerical summary of a population

Statistic

a numerical summary based on a sample

Descriptive statistics

consist of organizing and summarizing data. describes data through numerical summaries, tables, and graphs

Inferential statistics

uses methods that take results from a sample, extends them to the population, and measures the reliability of the result

Qualitative variables

allow for classification of individuals based on some attribute or characteristic represented by non-numerical values

Quantitative variables

variables that provide numerical measures of individuals. can be added or subtracted and provide meaningful results

Discrete variable

a quantitative variable that has either a finite number of possible values or a countable number of possible values. cannot take on every possible value between any two possible values

Continuous variable

a quantitative variable that has an infinite number of possible values it can take on and can be measured to any desired level of accuracy

nominal level of measurement

(for qualitative variables) if the values of the variable name, label, or categorize. does not allow for the values of the variable to be arranged in a ranked or specific order

ordinal level of measurement

(for qualitative variables) the naming scheme allows for the values of the variable to be arranged in a ranked or specific order

Interval level of measurement

(for quantitative variables) properties of the ordinal level of measurement and the differences in the values have meaning. a value of zero does not mean the absence of the quantity

Ratio level of measurement

(for quantitative variables) has the properties of the interval level of measurement and the ratios of the values of the variable have meaning. a value of zero means the absence of the quantity

Confounding

occurs when the effects of two or more explanatory variables are not separated.

lurking variable

an explanatory variable that was no considered in a study, but that affects the value of the response variable in the study. typically related to any explanatory variables considered in the study

confounding variable

an explanatory variable that was considered in a study whose effect cannot be distinguished from a second explanatory variable in the study.

cross-sectional studies

Type of observational studies that collect information about individuals at a specific point in time, or over a very short period of time.

case-control studies

Type of observational study that are retrospective, meaning that they require individuals to look back in time or require the researcher to look at existing records. Individuals who have certain characteristics are matched with those that do not.

cohort studies

Type of observational study that first identifies a group of individuals to participate in the study, then they are observed over a long period of time. These studies are prospective