Basics of Statistics

In this Article, review some of the fundamental research principles and terminology including the distinction between samples and populations, methods of sampling, types of variables, and the distinction between inferential and descriptive statistics.

Statistic: A characteristic, or value, derived from sample data.

Descriptive statistics: Statistics used to describe the characteristics of a distribution of scores.

Inferential statistics: Statistics, derived from sample data that are used to make inferences about the population from which the sample was drawn.

Parameter: A value, or values, derived from population data.

A population is an individual or group that represents all the members of a certain group or Category of interest. A sample is a subset drawn from the larger population.

Sample: A collection of cases selected from a larger population.

Random sample (or random sampling): Selecting cases from a population in a manner that ensures each member of the population has an equal chance of being selected into the sample.

Representative sampling: A method of selecting a sample in which members are purposely selected to create a sample that represents the population on some characteristic(s) of interest (e.g., when a sample is selected to have the same percentages of various ethnic groups as the larger population).

Random assignment: Assignment members of a sample to different groups (e.g., experimental and control) randomly, or without consideration of any of the characteristics of sample members.

Convenience sampling: Selecting a sample based on ease of access or availability.

Constant: A construct that has only one value (e.g., if every member of a sample was 10 years old, the “age” construct would be a constant).

Variable: Any construct with more than one value that is examined in research.

Qualitative (or categorical) variable: A variable that has discrete categories. If the categories are given numerical values, the values have meaning as nominal references but not as numerical values (e.g., in 1 = “male” and 2 = “female,” 1 is not more or less than 2).

Quantitative (or continuous) variable: A variable that has assigned values and the values are ordered and meaningful, such that 1 is less than 2, 2 is less than 3, and so on.

Dependent variable: The values of the dependent variable are hypothesized to depend on the values of the independent variable. For example, height depends, in part, on gender.

Independent variable: A variable on which the values of the dependent variable are hypothesized to depend. Independent variables are often, but not always, manipulated by the researcher.

Four different scales of measurement for variables: nominal, ordinal, interval, and ratio.

A nominally scaled variable is one in which the labels that are used to identify the different levels of the variable have no weight, or numeric value.

Ordinal variable: Variables measured with numerical values where the numbers are meaningful (e.g., 2 is larger than 1) but the distance between the numbers is not constant.

Interval or Ratio variable: Variables measured with numerical values with equal distance, or space, between each number.

Dichotomous variable: A variable that has only two discrete values (e.g., a pregnancy variable can have a value of 0 for “not pregnant” and 1 for “pregnant”).

Frequency: How often a score occurs in a distribution.

Generalize (or Generalizability): The ability to use the results of data collected from a sample to reach conclusions about the characteristics of the population, or any other cases not included in the sample.

Correlational research design: A style of research used to examine the associations among variables. Variables are not manipulated by the researcher in this type of research design.

Experimental research design: A type of research in which the experimenter, or researcher, manipulates certain aspects of the research. These usually include manipulations of the independent variable and assignment of cases to groups.

Distribution: Any collection of scores on a variable.

F distributions: A family of distributions associated with the F statistic, which is commonly used in analysis of variance (ANOVA).

Chi-square distributions: A family of distributions associated with the chi-square (χ2) statistic.

t distributions: A family of distributions associated with the t statistic, commonly used in the comparison of sample means and tests of statistical significance for correlation coefficients and regression slopes.