Chapter 1: Introduction to Statistics

Statistics

a set of mathematical procedures for organizing, summarizing, and interpreting information.

Population

set of all the individuals of interest in a particular study.

Sample

set of individuals selected from a population, usually intended to represent the population in a research study

Variable

a characteristic or condition that changes or has different values for different individuals

Data (plural)

measurements or observations

Data set

a collection of measurements or observations.

Datum (singular)

single measurement or observation and is commonly called a score or raw score

Parameter

a value, usually a numerical value, that describes a population. A parameter is usually derived from measurements of the individuals in the population.

Statistic

a value, usually a numerical value, that describes a sample. A statistic is usually derived from measurements of the individuals in the sample.

Descriptive statistics

statistical procedures used to summarize, organize, and simplify data.

Inferential statistics

consist of techniques that allow us to study samples and then make generalizations about the populations from which they were selected.

Sampling error

naturally occurring discrepancy, or error, that exists between a sample statistic and the corresponding population parameter.

Correlational method

two different variables are observed to determine whether there is a relationship between them

Experimental method

one variable is manipulated while another variable is observed and measured. To establish a cause-and-effect relationship between the two variables, an experiment attempts to control all other variables to prevent them from influencing the results.

Independent variable

the variable that is manipulated by the researcher. In behavioral research, the independent variable usually consists of the two (or more) treatment conditions to which subjects are exposed. The independent variable consists of the antecedent conditions that were manipulated prior to observing the dependent variable.

Dependent variable

the one that is observed to assess the effect of the treatment.

Control condition

Individuals do not receive the experimental treatment; instead, they either receive no treatment or they receive a neutral placebo treatment. The purpose of a control condition is to provide a baseline for comparison with the experimental condition

Experimental condition

Individuals placed in this group do receive hte experimental treatment

Quasi-independent variable

in a nonexperimental study, the "independent variable" that is used to create the different groups of scores

Constructs

internal attributes or characteristics that cannot be directly observed but are useful for describing and explaining behavior.

Operational definition

identifies a measurement procedure (a set of operations) for measuring an external behavior and uses the resulting measurements as a definition and a measurement of a hypothetical construct. Note that an operational definition has two components. First, it describes a set of operations for measuring a construct. Second, it defines the construct in terms of the resulting measurements.

Discrete variable

consists of separate, indivisible categories. No values can exist between two neighboring categories.

Continuous variable

there are an infinite number of possible values that fall between any two observed values. A continuous variable is divisible into an infinite number of fractional parts

Real limits

the boundaries of intervals for scores that are represented on a continuous number line

Upper real limit

at the top of the interval

Lower real limit

at the bottom of the interval

Nominal scale

consists of a set of categories that have different names. Measurements on a nominal scale label and categorize observations but do not make any quantitative distinctions between observations.

Ordinal scale

consists of a set of categories that are organized in an ordered sequence. Measurements on an ordinal scale rank observations in terms of size or magnitude

Interval scale

consists of ordered categories that are all intervals of exactly the same size. Equal differences between numbers on scale reflect equal differences in magnitude. However, the zero point on an interval scale is arbitrary and does not indicate a zero amount of the variable being measured.

Ratio scale

an interval scale with the additional feature of an absolute zero point. With a ratio scale, ratios of numbers do reflect ratios of magnitude