SMC- Math 54 C- Perez- Ch. 1 Stats Definitions

nominal level of measurement

A variable is at the nominal level of measurement if the values of the variable name,

label, or categorize. In addition, the naming scheme does not allow for the values of

the variable to be arranged in a ranked or specific order.

ordinal level of measurement

A variable is at the ordinal level of measurement if it has the properties of the

nominal level of measurement, however the naming scheme allows for the values of

the variable to be arranged in a ranked or specific order.

interval level of measurement

A variable is at the interval level of measurement if it has the properties of the

ordinal level of measurement and the differences in the values of the variable have

meaning. A value of zero does not mean the absence of the quantity. Arithmetic

operations such as addition and subtraction can be performed on values of the

variable.

ratio level of measurement

A variable is at the ratio level of measurement if it 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. Arithmetic operations such as

multiplication and division can be performed on the values of the variable.

continuous variable

A continuous variable is a quantitative variable that has an infinite number of

possible values that are not countable. A continuous variable may take on every

possible value between any two values.

discrete variable

A discrete variable is a quantitative variable that has either a finite number of

possible values or a countable number of possible values. The term countable means

that the values result from counting, such as 0, 1, 2, 3, and so on. A discrete variable

cannot take on every possible value between any two possible values.

Quantitative variables

Quantitative variables provide numerical measures of individuals. The values of a

quantitative variable can be added or subtracted and provide meaningful results.

Qualitative, or categorical, variables

Qualitative, or categorical, variables allow for classification of individuals based on

some attribute or characteristic.

parameter

A parameter is a numerical summary of a population.

The entire group to be studied is called the population. An individual is a person or

object that is a member of the population being studied. A sample is a subset of the

population that is being studied.

statistic

A statistic is a numerical summary of a sample. Descriptive statistics consist of

organizing and summarizing data. Descriptive statistics describe data through

numerical summaries, tables, and graphs.

The entire group to be studied is called the population. An individual is a person or

object that is a member of the population being studied. A sample is a subset of the

population that is being studied.

Inferential statistics

Inferential statistics uses methods that take a result from a sample, extend it to the

population, and measure the reliability of the result.

Statistics

Statistics is the science of collecting, organizing, summarizing, and analyzing

information to draw conclusions or answer questions. In addition, statistics is about

providing a measure of confidence in any conclusions.

census

a list of all individuals in a population along with certain characteristics

of each individual.

confounding variable

an explanatory variable that was considered in a study

whose effect cannot be distinguished from a second explanatory variable in the study.

lurking variable

an explanatory variable that was not considered in a study,

but that affects the value of the response variable in the study. In addition, lurking

variables are typically related to explanatory variables considered in the study.

Confounding

in a study occurs when the effects of two or more explanatory

variables are not separated. Therefore, any relation that may exist between an

explanatory variable and the response variable may be due to some other variable

or variables not accounted for in the study.

designed experiment.

If a researcher assigns the individuals in a study to a certain group, intentionally

changes the value of an explanatory variable, and then records the value of the response variable for each group, the study is a

observational study

measures the value of the response variable without

attempting to influence the value of either the response or explanatory variables.

That is, in an observational study, the researcher observes the behavior of the

individuals without trying to influence the outcome of the study.

Random sampling

is the process of using chance to select individuals from a

population to be included in the sample.

simple random sample.

A sample of size n from a population of size N is obtained through simple random

sampling if every possible sample of size n has an equally likely chance of occurring.

The sample is then called a

stratified sample

A is obtained by separating the population into nonoverlapping

groups called strata and then obtaining a simple random sample from each stratum.

The individuals within each stratum should be homogeneous (or similar) in some way.

systematic sample

A is obtained by selecting every kth individual from the population.

The first individual selected corresponds to a random number between 1 and k.

cluster sample

A is obtained by selecting all individuals within a randomly selected

collection or group of individuals.

convenience sample

A is a sample in which the individuals are easily obtained and

not based on randomness.

bias

If the results of the sample are not representative of the population, then the sample

has .

Nonsampling errors

result from undercoverage, nonresponse bias, response bias,

or data-entry error. Such errors could also be present in a complete census of the

population.

Sampling error

results from using a sample to estimate information

about a population. This type of error occurs because a sample gives incomplete

information about a population.

experiment

An is a controlled study conducted to determine the effect varying

one or more explanatory variables or factors has on a response variable.

treatment

Any

combination of the values of the factors is called a .

single-blind

In experiments, the experimental unit (or subject) does not know

which treatment he or she is receiving.

double-blind experiments

In , neither the

experimental unit nor the researcher in contact with the experimental unit knows

which treatment the experimental unit is receiving.

completely randomized design

A completely randomized design is one in which each experimental unit is randomly

assigned to a treatment.

matched-pairs design

A is an experimental design in which the experimental units

are paired up. The pairs are selected so that they are related in some way (that

is, the same person before and after a treatment, twins, husband and wife, same

geographical location, and so on). There are only two levels of treatment in a

matched-pairs design.

blocking

Grouping together similar (homogeneous) experimental units and then randomly

assigning the experimental units within each group to a treatment is called .

block

Each group of homogeneous individuals is called a .

randomized block design

A is used when the experimental units are divided into

homogeneous groups called blocks. Within each block, the experimental units are

randomly assigned to treatments.