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Unit 3: Theory and Variables

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Theory and Variables

This unit focuses on theory and variables. Because researchers usually speak of "variables" and "designs" in the same sentence, this unit also conatains a very brief overview of research designs. This unit contains three topics:


In A Midsummer's Night Dream Shakespeare wrote that one goal of poets was "to give to airy nothingness a local habitation and a name." Although the context suggests the passage refers to the emotional tenor and tumultuous interaction between individuals, the passage is, nonetheless, an apt characterization of (a) theory, and (b) the goal held by empirical researchers who attempt to establish publicly verifiable methods for observing the intangible.

Theory consists of generalized, abstracted terms that name an interrelated set of ideas (the "airy nothingness") and also describes the way in which those ideas are connected to corporality (giving a "local habitation and a name").

Mullins (1971) offers a similar though less poetic definition: "A theory uses concepts and variables . . . to span the gap between what we know as ideas and what we perceive as experience" (p. 7). Theory is a set of interrelated conceptions or ideas that describe a phenomena. Theories often contain statements of interrelated, lawlike generalizations. Because such statements describe a phenomena, they must be related to observational statements (i.e., variables) through correspondence rules. That is, theory should specify the way in which each variable corresponds to a particular concept.

Attempts to span the gap between ideas and sensory experience -- by using publicly verifiable methods -- underlies social science research. Words such as intelligence, learning, motivation, personality, stimulation, expectancy, attitude, self-esteem, achievement, performance, language acquisition, love, hate, emotion, faith, belief, and anxiety are clearly ideas, and represent some of the phenomena of interest to social scientists. But these words existed in everyday language long before the practice of social science began and were used in everyday conversation to refer to a variety of informally observed behaviors and unobservable entities. Novelists and poets and playwrights developed their artistic works by describing how such ideas play out in the lives of characters in a particular time and place. Even elaborate, scholarly explanations for phenomena, such as Freud's theory of personality, included such terms, but did not include replicable methods of observation that would enable others to make reach similar inferences.

All of us carry around certain meanings associated with each of these words. If each of us were to write a paragraph that contains our definition of words such as "intelligence" or "learning" or "love," we would likely see considerable variety among those definitions. When empirically-oriented social scientists use such words, careful conceptual and operational definitions are required, for the denotation of these words in an empirical research report likely differs from both the denotation and connotation of the same words as they are encountered in everyday conversation.

Academic psychology -- which was the first social science to investigate empirically phenomena such as intelligence and learning -- sought to emulate the empirical, experimental procedures and methatheoretical practices used by the natural sciences in the 1800's. Thus, rather than sitting in an overstuffed chair and cogitating grand theories, psychologists explored empirical relationships and attempted to derive empirical generalizations. If you examine psychology journals in nearly every area of specialization (e.g., learning, developmental, social, personality) you will likely see much more scholarly activity focused on the investigation of empirical relationships between variables rather than focused on the testing of existing theories or on theory development.

Psychologists tended not to view theory as a set of principles for practice nor as a collection of ideas that give an account of intrinsic or philosophic values -- two other traditional ways of viewing theory. Instead, the only view of theory to gain widespread acceptance among experimentally oriented psychologists was theory as a set of interrelated, lawlike generalizations that gives an acount of a phenomenon, and is anchored to the empirical data base. Bolles (1967) provides a brief description of theory from the perspective of an experimental psychologist. Turner (1968) elaborates this perspective. The following diagram from Bolles illustrates these relationships.

[Note: This diagram may not appear when you print this page. It is included in the Bolles chapter under Suggested Readings.]

Link to Bolles diagram

Theories have a formal structure and an empirical base. The formal structure includes abstract terms, known as concepts or constructs, and a set of relational rules (syntax) tying the terms together and interrelating them in some way. Further, the abstract terms (the airy nothingness) must be related in some way to empirical observations (the local habitation). These correspondence rules that relate the abstract terms to the empirical observations are known as the semantics of the theory.

Psychologists are often more interested in the empirical base of a theory than in its formal structure. Their focus is usually on establishing strong definitions that link the formal structure to the empirical data language. For example, suppose an investigator is interested in "creativity," which might be described as an individual's ability to generate ideas or solutions that are novel and appropriate. How might the abstract, theoretical term, "creativity," be linked to empirical observations? How might you rate individuals as relatively more or less creative? Torrance (1974) developed a paper based instrument that purports to measure creativity. In a research paper you might see a sentence like: "Creativity was defined as the individual's score on the Torrance Test of Creative Thinking."

It is important to note that a distinction is usually made between terms that are not directly observable (such as creativity) and those that are directly observable (performance on an instrument that is said to measure creativity). Terms referring to phenomena that are not directly observable are known as (theoretical) constructs and must be interrelated syntactically. Further, constructs must be tied semantically to empirical terms, which in turn are known as empirical constructs.

The collection of empirical constructs is known as the data language. This language describes the way in which observations are made and operations are performed. In psychology the primary function of the data language is the description of behavior and the context in which that behavior occurs.

Traditionally, psychologists have rejected the rationalistic position that maintains the language of human experience is the only valid language for the study of humans. Natural languages are considered so ambiguous that assertions contained in them are not testable. Consequently, psychologists prefer to reduce, through operational definitions, the data language to the physical-thing language, which is the language of common perceptual experience. In those instances where such direct linkages are not possible (e.g., latent variables), psychologists attempt to interconnnect terms by means of several functional properties; that is, the term is tied in several differing ways to empirical constructs.

A distinction is usually made between theories that describe and those that explain, with the latter receiving more attention. The broader the range of phenomena the theory encompasses, the more explanatory power the theory is said to possess.

Theoretical accounts often include a model and it is not uncommon to see theories referred to as models. Theories are called models if they are (a) stated in terms of mathematical concepts, (b) taken as simplications of the facts or the intrinsic values under investigation, (c) radical departures from previous theory, or (d) not fully established as theory.

Models used in the educational and pscyhological literature are often what Black (1962) describes as analogue models and mathematical models. An analogue model focuses on the similarity of structure or pattern of relationships. For example, some cognitive psychologists have used the procedures involved in looking up the call number of a library book, searching the stackes, and checking the book out as a model for memory retrieval. Another common model is the use of computer data processing as a model for human information reception and storage. These are examples of analogue models. Mathematical models also exist. Atkinson's theory of motivation and the Estes-Burke learning theory are two examples. The idea behind mathematical modeling is that the mathematical relations partially explain the relations or operations of, say, motivation or learning.

In Y520 we do not focus on theory explication or extension. Instead, our goal is usually to identify:

  • whether the theory is one of description, explanation, or of causation;
  • the conceptual constructs and the relations between constructs; and
  • the operational definitons for each conceptual construct.

What are the parallels between types of theories and types of research designs? Theories may be classified as descriptive, explanatory, or causative (or predictive). Research designs can also be classified as descriptive, correlational, and experimental.

The number of books and articles concerning theory analysis and extension that you could read is quite large and includes standards such as Black (1962), Mullins (1971) and Turner (1967). The two books that I have found most useful are Fawcett & Downs (1986, 1992) and Britt (1997). The two editions of Fawcett & Downs are quite different and the first edition may be the more useful.


Black, M. (1962). Models and metaphors. Cornell, NY: Cornell University Press.

Bolles, Robert C. (1967). Theory of Motivation. New York: Harper & Row.

Britt, David W. (1997). A conceptual introduction to modeling: Qualitative and quatitative perspectives, Mahwah, NJ: Erlbaum.

Fawcett, Jacqueline, & Downs, Florence (1986). The relationship of theory and research. Norwalk, CT: Appleton Century Crofts.

Fawcett, Jacqueline, & Downs, Florence (1992). The relationship of theory and research, Second Edition. Philadelphia, PA: F. A. Davis Company.

Torrance, E. P. (1974). The Torrance tests of creative thinking: Technical norms manual. Bensenville, IL: Scholastic Testing Services.

Turner, M. B. (1967). Psychology and the philosophy of science. New York: Appleton Centrury Crofts.

Variables and Hypotheses

In Unit 2 we discussed the research hypothesis. In this section the focus will be on variables. Variables may be thought of as an attribute at we wish to investigate. Demographic variables related to schools include enrollment, percent of students receiving free or reduced lunch, Census Bureau classification (e.g., rural, urban, suburban, etc.), expenditure per pupil, assessed valuation per pupil, percent passing proficency test, percent suspensions, and so forth. Individual variables might include age, gender, level of anxiety, level of performance, and so forth.

An adjective, such as "independent" or "dependent" often precedes the word "variable." Unfortunately, the careless use of the adjectives that qualify type-of-variable has created some problems (see Mueller in the readings section). If we are reading an article in which the investigators state they are conducting an experiment, then quite justifably they speak of "independent" and "dependent" variables. The dependent variable in an experiment is the outcome. If an experimenter wants to measure the effect of type of keyboard (qwerty versus dvorak) on typing speed, then number of words is the dependent variable. If the interest is in typing accuracy, then number of errors is the dependent variable. The independent variable is the one variable that is varied by the experimenter. In this example it is the type of keyboard used.

Suppose that a high school English teacher wished to investigate the effect of constructivist techniques on student performance, and divided a class into two groups to study Macbeth. One class, known as the comparison group, was taught in the traditional manner by using lecture and discussion without cooperative groups. The experimental group, based on constructivist teachniques, was further divided into groups of three to five students and used film, CD-Rom, websites, books, and small group discussion. In this example the independent variable is type of instruction and the dependent variable is student performance on the final exam (This example is from the December 2000 issue of Phi Delta Kappan, page 329).

D'Amato (1970) discusses the use of variables in considerable detail (see the readings section), and careful study of D'Amato will reward you with a thorough understanding of variables and and introduction to research designs. In education research the dependent variable is often amount, type, or rate of learning. One independent variable might be type of instruction.

An important but somewhat subtle distinction D'Amato makes is between direct manipulation of variables (as in an experiment), in contrast to achieving variation in the variable of interest by a selection procedure. The latter occurs when a variable, say intelligence, cannot be manipulated directly and so the experimenter gives a test, and on the basis of test scores ranks individuals according to level of intelligence. One drawback is that the selection procedure introduces another source of error. For this reason, as D'Amato explains, direct manipulation of variables is always preferable when possible.

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Research Designs

Research designs can be classified as:

  • Description (includes all qualitative studies)
  • Correlation or relational
  • Experimental
  • Quasi-experimental (ex post facto and causal-comparative)

D'Amato discusses the first three designs in some detail. Why is it important to be able to identify the design used in a study? The type of design limits the strength of the claim that can be made concerning causation:

  • Description. Authors are justified in describing a phenomena. They may note certain variables that occur earlier in time appear to be (i.e., might be) related to variables that occur later, but this design does not justify causal statements.
  • Correlation. Authors are justified in stating that a relationship may exist between certain predictor and criterion variables, but the design and results from a single study do not justify stating that a causal relationship exists.
  • Experimental. If the study is conducted in such a way that threats to internal and external validity are minimized, then the experimenter is justified in stating that the independent variable is causally related to the dependent variable.
  • Quasi-experimental designs. This type of design is the most controversial. In some instances it is reasonable to infer causality. However, more often than not, investigators who use this design are not justified in making causal statements -- nonetheless, causal statements appear with amazing frequency.

When evaluating research articles, keep in mind Mueller's three questions:

  1. What do the authors want us to believe?
  2. What data address these (often causal) arguments/inferences/suggestions?
  3. Based on these data, how strong is the case for a causal argument?

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Lecture slides

Reserved for Lecture Slides

  Review of concepts from Units 1 & 2

  Theory [to be added]

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Instructor notes

    Press the button for notes. No instructor notes this time

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Fraenkel & Wallen, Chapters 4

Fraenkel & Wallen, Chapter 22

  D'Amato, M. R. (1970). Experimentation in psychological research. In Experimental psychology: Methodology, psychophysics, and learning. New York: McGraw-Hill.

  Mueller, Daniel J. (2000). "Independent" variables.

  Fawcett, J., & Downs, F. (1986). Excerpt from The Relationship of Theory and Research.

  Glossary of variable types, for use throughout semester.

  Trochim, Bill. (2000). "Variables."


  Bolles, Robert C. (1967). Theory of Motivation. New York: Harper and Row.

  Trochim, Bill (2000). Types of research questions/designs.

  MacCorquodale, Kenneth, and Meehl, Paul E. (1948). On a distinction between hypothetical constructs and intervening variables. Psychological Review, 55, 95-107.

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Learning Activities

The learning activity for this unit is optional but provides a good self test of your understanding of the different research designs. Below is a research topic. Write a few sentences addressing each point and post your response on SSF.

Research Topic: The relationship between alcohol consumption and academic performance.

  1. Design a correlational study to investigate the relationship between these two variables. What is your hypothesis? How will you operationally define and measure the two variables?
  2. How will you obtain a random sample of participants?
  3. Assume that your study produces a correlation of r=.56 between the two variables. What are at least three possible causal explanations for this relationship? (r=.56 means there is a moderate relationship between the variables).
  4. Now design an experimental study to investigate these variables. What is your hypothesis? What type of hypotheses does the experimental method allow you to test that the correlational method does not?
  5. What is your independent variable? What is your dependent variable?
  6. How will you make sure that the study has high internal validity? Will you use random assignment to conditions?
  7. Do any ethical concerns about the treatment of participants emerge from your experimental design?

If you have difficulty, re-read Shulman's discussion of the different designs for studying reading:

  Shulman, Lee S. (1997). "Disciplines of inquiry in education: An overview." In Richard M. Jaeger (Ed.). Complementary methods for researchers in education. Washington, D.C.: American Education Research Association, 3-19.

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Web resources

None listed for this unit.

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Last Updated: 01/01/30