5-1Chapter 5MeasurementOperational DefinitionsNumbers and PrecisionScales of MeasurementNominal ScaleOrdinal ScaleInterval ScaleRatio ScaleValidity of MeasurementContent ValidityFace ValidityConcurrent ValidityPredictive ValidityConstruct ValidityThinking Critically About Everyday InformationReliability of MeasurementTest–Retest ReliabilityAlternate Form ReliabilitySplit-Half ReliabilityFactors That Affect ReliabilityCase AnalysisGeneral SummaryDetailed SummaryKey TermsReview Questions/Exercises

5-2Operational DefinitionsAn essential component of an operational definition is measurement. A simple and accurate definition ofmeasurement is the assignment of numbers to a variable in which we are interested. These numbers willprovide the raw material for our statistical analysis.Measurement is so common and taken for granted that we seldom ask why we measure things orworry about the different forms that measurement may take. It is often not sufficient to describe a runneras “fast,” a basketball player as “tall,” a wrestler as “strong,” or a baseball hitter as “good.” If coachesrecruited potential team members on the basis of these imprecise words, they would have difficultyholding down a job. Coaches want to know how fast the runner runs the 100-yard dash or the mile. Theywant to know exactly how tall the basketball player is, the strength of the wrestler, the batting average ofthe hitter. Measurement is a way of refining our ordinary observations so that we can assign numericalvalues to our observations. It allows us to go beyond simply describing the presence or absence of anevent or thing to specifying how much, how long, or how intense it is. With measurement, ourobservations become more accurate and more reliable.Precision is important in all areas of our lives, especially in the sciences and technologies, and welook for ways of increasing it. Here is an interesting classroom demonstration of the precision of numbersversus the precision of words Ask the class members to write down on a piece of paper what number theword “several” represents to them. Gather the responses and then plot them on the board. You will besurprised at the wide range of numbers represented by the word (it usually ranges from 2 to 7).How often have you been in an argument with a friend, only to find out after much debate that you areusing key words in different ways? The argument is one of semantics rather than of issues. You definedthe word one way, and your friend defined it a different way. This experience is more common amonglaypersons than among scientists, but it still occurs. Before the merits of an issue or a position can bediscussed, there must be agreement about the meaning of the important terms. The same is true in science.If we are to avoid confusion and misinterpretation, we must be able to communicate unambiguously themeaning of such terms as intelligence, anxiety, altruism, hostility, love, alienation, aggression, guilt,reinforcement, frustration, memory, and information. These terms have all been used scientifically, invery precise ways. Each of these terms could be given a dictionary definition, usually referred to as aliterary or conceptual definition. But dictionary definitions are not sufficiently precise for many scientificterms because they are too general and often too ambiguous. When a word is to be used scientifically ortechnically, its precise meaning must be conveyed—it must be clear and unambiguous. We achieve thisclarity of meaning by operationally defining the term. To state the operations for a term means to makethe term observable by pointing to how it is measured. An operational definition, then, makes theconcept observable by stating what the scientist does to measure it.

5-3For example, anxiety could be defined in dictionary terms as “a state of being uneasy, apprehensive,or worried.” An operational definition of the term could include observable measures such as sweatingpalms (observable as sweat gland activity), increased heart rate (observable with heartbeat recording),dilated pupils, and other observable physiological changes. It could also be a self-rating scale or a paperand-pencil questionnaire. We could in each case specify the precise amounts of each measure necessaryfor our operational definition of anxiety.As another example, consider the hypothesis that we proposed in the last chapter. We hypothesizedthat the effect of TV violence on older children’s aggressive behavior at school will be less if thecharacters are not human. Although this appears to be a clear statement, more specific operationaldefinitions would be necessary before any research could be undertaken to test the hypothesis. Theresearcher must make several decisions. What is violence on TV? Certainly, one character killing anothercharacter would be considered violence. What about a shove or push? What about a verbal assault? Whatabout when Wile E. Coyote falls off the cliff and is hit in the head with a rock? What constitutes acharacter that is not human? We could probably agree that Wiley Coyote fits this category. What about acomputer-animated person? How will aggressive behavior at school be defined? Of course, getting into afight would be aggressive behavior. What about profanity directed toward another student or teacher?What about little Johnny chasing Mary on the playground? Notice that there are no correct answers tothese questions. However, the researcher must decide what is going to be meant by each of the variablesin a particular study and be able to communicate those operational definitions to those who will beconsumers of the research findings.Table 5.1 contains both dictionary definitions and operational definitions of some common terms.Note that in each case, the operational definition refers to events that are observable or events that caneasily be made observable. Note further that the definition is very specific rather than general.

5-4The feature that determines whether a particular definition is more useful than another is whether it allowsus to discover meaningful laws about behavior. Some will, and some will not. Those definitions that arehelpful to our understanding of behavior will be retained; those that do not will be discarded. The firststep in the life of a concept is to define it in clearly unambiguous, observable terms. It then may or maynot be useful. If the concept of intelligence were defined as “the distance between the ears,” or “thecircumference of the head,” its meaning would be clear, but it is very doubtful that it would ever becomeuseful.Let’s look at one additional point before leaving the topic of definitions. An operational definition, orany other kind of definition, is not an explanation. When definitions are unintentionally used asexplanations, we label them as tautological or circular reasoning. Circular reasoning has little value. Adefinition doesn’t explain behavior or provide you with information that will, in and of itself, help inunderstanding behavior. It is a necessary step in discovering lawful relations, but it is only one side of atwo-sided law. To explain behavior, two independent (different) types of observation are necessary: one isobservations that relate to the independent variable (variable manipulated by the experimenter or“cause”), and the second is observations that relate to the dependent variable (behavior of participant or“effect”). When the relationship between the independent and dependent variables is predictable, we say

5-5that we have a lawful relationship. A circular argument uses only one side of the relationship—only oneof these observations. For example, suppose we observe two children fighting with each other (bodycontact with intent to harm). We may be tempted to say they are fighting because they are hostilechildren, because hostility leads to fighting. To this point, we have not explained anything. All we have isan operational definition of hostility as fighting behavior. Our argument would be a tautology (circular) ifwe said that the children are fighting because they are hostile and then said that we know that they arehostile because they are fighting. To avoid circularity and to explain the behavior, we would have todefine hostility and fighting independently and show that the operations for defining hostility do in factgive rise to fighting.Tautological reasoning occurs with a higher frequency than it should. For example, it is notuncommon to hear the statement “Individuals who commit suicide are mentally ill.” To the question“How do you know they are mentally ill?” the response is often “Because they committed suicide.”Another common tautology refers to musical ability. For example, it is said “Individuals who play thepiano well do so because they have musical ability.” To the question “How do you know they havemusical ability?” the response is “Because they play the piano well.” Another example is “Individualsdrink excessively because they are alcoholics. We know that they are alcoholics because they drinkexcessively.” We repeat, tautological arguments do not advance our knowledge. To avoid circularity inour last example, we would have to define what we mean by “drinks excessively” and then identify thefactors that give rise to drinking excessively—for example, genetics, specific early experiences, orstressful events. We then would have an explanation for the drinking.Numbers and PrecisionAs noted earlier, measurement scales are important because they allow us to transform or substituteprecise numbers for imprecise words. We are restricted in what we can do with words but less so withnumbers. Numbers permit us to perform certain activities and operations that words do not. In manyinstances, numbers permit us to add, multiply, divide, or subtract. They also permit the use of variousstatistical procedures. These statistics, in turn, result in greater precision and objectivity in describingbehavior or other phenomena. At a minimum, we know that the numbers 1, 2, 3, 4, and so on, whenapplied to the frequency of occurrence of any event, mean that 4 instances are more than 3, which in turnare more than 2, and so on. Contrast numbers with words such as frequently, often, or many times. Doesan event occurring frequently occur a greater or fewer number of times than an event occurring often? Itmay be true that a given individual uses the two terms frequently and often consistently across situations;another individual may also use the two terms consistently, but in reverse order. The result would be confusion.

5-6The use of numbers rather than words increases our precision in communicating in other ways also.Finer distinctions (discriminations) can often be achieved with numbers if the distinctions can be madereliably. Instead of saying a certain behavior was either present or absent, or occurred with high, medium,or low frequency, numbers permit us to say, more precisely, how frequently the behavior occurred. Wordsare often too few in number to allow us to express finer distinctions.Our number system is an abstract system of symbols that has little meaning in and of itself. Itbecomes meaningful when it becomes involved in measurement. As noted earlier, measurement is theprocess of assigning numbers to objects and events in accordance with a set of rules. To grasp the fullimpact of measurement, we need to understand the concept of a measurement scale. There are severaldifferent kinds of scales: nominal, ordinal, interval, and ratio. The distinction among scales becomes ofparticular importance when we conduct statistical analyses of data. Underlying statistical tests are variousassumptions, including those relating to the scale of measurement. In other words, the scale ofmeasurement for a variable can determine the most appropriate type of statistical analysis of the data.Scales of MeasurementNominal ScaleThere has been some disagreement among experts whether a nominal scale should even be described as ascale. Most would agree that it should. The fact is that we do name things, and this naming permits us todo other things as a result. The word nominal is derived from the Latin word for name. With a nominalscale, numbers are assigned to objects or events simply for identification purposes. For example,participants in various sports have numbers on their jerseys that quickly allow spectators, referees, andcommentators to identify them. This identification is the sole purpose of the numbers. Performingarithmetic operations on these numbers, such as addition, subtraction, multiplication, or division, wouldnot make any sense. The numbers do not indicate more or less of any quantity. A baseball player with thenumber 7 on his back does not necessarily have more of something than a player identified by the number1. Other examples include your social security number, your driver’s license number, or your credit cardnumber. Labeling or naming allows us to make qualitative distinctions or to categorize and then count thefrequency of persons, objects, or things in each category. This activity can be very useful. For example, inany given voting year, we could label or name individuals as Democrat or Republican, Liberal orConservative, and then count frequencies for the purpose of predicting voting outcomes. Other examplesof nominal scales used for identifying and categorizing are male–female, violent show–nonviolent show,and punishment–reward. As you will see later, a chi-square statistic is appropriate for data derived from acategorical (nominal) scale.

5-7Ordinal ScaleAn ordinal scale allows us to rank-order events. Original numbers are assigned to the order, such as first,second, third, and so on. For example, we might determine that runners in a race finished in a particularorder, and this order would provide us with useful information. We would know that the runner finishingfirst (assigned a value of 1) ran the distance faster than the runner finishing