A frequency table is a tabular method used to display the distribution of a variable. It organizes data by listing the possible values of the variable in one column and the frequency—the number of times each score occurs—in a second column. For numerical data, the values are typically ordered from highest at the top to lowest at the bottom, and only the range of scores actually present in the dataset is included. This format allows researchers to quickly observe important features of the distribution, such as the range of scores, the most and least common values, and any extreme outliers.

Frequency Table

An outlier is an extreme score that falls significantly above or below the rest of the scores within a distribution. While these extreme values can represent genuine cases on the variable being measured—such as a single clinically depressed individual in an otherwise happy sample—they can also result from equipment malfunctions, participant misunderstandings, or researcher errors.

Outlier

A unimodal distribution is a specific shape of a distribution that features exactly one distinct peak. In a histogram, this appears as a single prominent high point from which the tails taper off.

Unimodal Distribution

A skewed distribution is an asymmetrical shape of a data distribution where scores cluster heavily toward one end of the scale, creating a prominent peak, while a relatively long tail trails off toward the opposite end.

Skewed Distribution

A variable's distribution can be illustrated using both quantitative and categorical variables. For instance, in a sample of 100 students, the distribution for the quantitative variable 'number of siblings' might show that 10 students have no siblings, 30 have one, and 40 have two. Similarly, the distribution for the categorical variable 'sex' in the same sample might indicate that 44 students have a score of 'male' and 56 have a score of 'female'.

Examples of a Variable Distribution

The shape of a quantitative variable's distribution describes the visual pattern formed when its scores are plotted, such as in a histogram. A distribution's shape is characterized by the number of distinct peaks it contains—such as being unimodal or bimodal—and whether its tails fall symmetrically or are skewed to one side.

Distribution Shape

The percentile rank of an individual score describes its relative location within a distribution. It is defined as the percentage of all scores in the distribution that are strictly lower than that specific score. This measure provides a standardized way to compare an individual's performance against the rest of the group and is frequently used to report results on standardized tests of ability or achievement.

Percentile Rank

Measures of central tendency are descriptive statistics used to describe the typical, average, or center scores within a distribution. Common examples of these measures include the mean, median, and mode.

Measures of Central Tendency

Measures of dispersion are descriptive statistics that describe how spread apart or dispersed the scores in a distribution are. Common examples of these measures include the range, standard deviation, and variance.

Measures of Dispersion

What does the distribution of a variable describe in a dataset?

The distribution of a variable describes how individual scores or values are spread across the different levels or categories of that specific variable within a dataset.

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A variable is any quantity, quality, or characteristic that can change or vary across different individuals, situations, or over time. In psychological research, some variables are straightforward and simple to measure, such as age or height, while others are more complex and require careful operational definition to be studied empirically.

Variable

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A constant is a property or quantity that does not vary across individuals or situations, such as the speed of light. Because constants do not change, they are not the focus of psychological research questions, which instead seek to understand phenomena that vary.

Constant

A quantitative variable is a type of variable that represents a measurable quantity, typically assessed by assigning a numerical value to each individual. Common examples in psychological research include a person's height, level of talkativeness, number of siblings, or score on a depression scale.

Quantitative Variable

A categorical variable is a type of variable that represents a characteristic or quality, typically assessed by assigning a descriptive category label to each individual rather than a number. Examples include a person's chosen major, nationality, occupation, or whether they are receiving psychotherapy.

Categorical Variable

An abstract construct, also referred to as an intangible variable, is a psychological characteristic or internal state that cannot be directly observed, such as self-esteem, mood, or a behavioral intention. Because psychological research relies on empirical data, researchers must develop specific methods to transform these intangible concepts into quantifiable variables so they can be measured and studied.

Abstract Construct

In experimental research, an independent variable is the presumed cause in a cause-and-effect relationship. It is the specific factor that a researcher systematically manipulates or varies to observe its impact on another variable. While experiments require manipulation, in some non-experimental or factorial designs, an independent variable may simply be measured.

Independent Variable

A dependent variable is the factor in an experiment that represents the presumed effect within a causal relationship. It is the variable that researchers measure to evaluate if it changes as a direct result of the manipulation of the independent variable.

Dependent Variable

In research, a population is the entire group of individuals that the researchers seek to draw conclusions about based on their findings from the sample. 

Population

In research, a population is the entire, often very large, group of individuals that researchers are interested in studying and drawing conclusions about. Depending on the researcher's goals, a population could be as broad as all human beings or as specific as all American teenagers, children with autism, or professional athletes.

To illustrate how quantities and qualities can vary across individuals or situations, consider the students enrolled in a university course. The physical height of these students serves as a clear example of a variable because it differs from one individual to another. Similarly, their chosen major is also a variable, provided that the class consists of students who have declared different fields of study. These illustrations demonstrate how commonly variations occur in the world.

Example of a Variable: Height and Chosen Major

Non-experimental research is a broad category of research methodologies defined by the lack of manipulation of an independent variable. Instead of controlling factors, researchers simply measure variables as they naturally occur in real-world or laboratory settings. Although experimental research can provide strong evidence that changes in an independent variable cause differences in a dependent variable, non-experimental research generally cannot. Despite this inability to draw causal conclusions, non-experimental research is still considered extremely important and is utilized in cases where experimental research cannot be carried out.

Non-Experimental Research

Variable Distribution

In psychology, a construct is a complex variable that defies direct observation or straightforward measurement—such as an attitude, ability, personality trait, or emotional state. These variables cannot be seen directly because they represent broad behavioral tendencies rather than isolated actions, and they involve hidden internal processes like specific feelings, thoughts, and nervous system activities. Ultimately, a construct acts as a theoretical summary that encapsulates these intricate sets of internal and external processes.

Psychological Construct

Measurement is the process of systematically assigning scores to individuals or objects so that these scores accurately represent a specific characteristic of interest. Crucially, this broad concept does not limit measurement to the use of specific physical instruments or tools; rather, it requires any methodical procedure that yields a representative score.

Measurement

An operational definition defines a psychological variable in terms of the exact procedures used to measure or observe it. Because most variables are abstract constructs that cannot be directly observed (e.g., stress), researchers must transform these conceptual definitions into concrete, quantifiable forms. For instance, stress could be operationally defined as a score on a standardized questionnaire, the concentration of cortisol in saliva, or the number of recent stressful life events experienced.

Operational Definition

A participant variable, also known as an individual difference, is a type of extraneous variable derived from the pre-existing characteristics of the individuals involved in an experiment. Examples of these variables include demographic factors such as gender, as well as personal attributes or habits like diet and writing ability. Because these individual differences are likely to have their own independent effect on the dependent variable, they must be controlled to prevent them from obscuring the effect of the experimental manipulation.

Participant Variable

Psychological measurement is the systematic empirical process of quantifying abstract variables and constructs—such as moods, self-esteem, or behavioral intentions—to facilitate scientific analysis. By utilizing standardized tools and methodologies, researchers can translate intangible psychological characteristics into objective, numerical data that can be rigorously evaluated and studied.

Psychological Measurement

The distribution of a variable describes how scores or values are spread out across the different levels or categories of that specific variable.

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