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Subjects were intructed to select one rod to lie halfway in length between two given rods. These bisection instructions imply an additive model in the subjective metric. However, the data were inherently nonadditive; the length of the bisector could be an increasing or a decreasing function of the length of one given rod, depending on the length of the other given rod. A convexity analysis and a nonmetric analysis both showed that no monotone transformation could make the data additive. The bisection problem is used to contrast the axiomatic and functional approaches to measurement theory.

Wood‐mining Chironomidae in Oregon were studied using sound wood submerged for 5–6 years as standard substrates. The dominant species were the orthocladiine midges Orthocladius lignicola Kieffer and Chaetocladius ligni Cranston and Oliver. Larvae were much more abundant in alder than in conifer wood. Using a combination of multiple washings and rearing, the population density of xylophagous midges in alder posts was estimated as 618 ± 173/m2 of wood surface. This was over 25% of the total wood‐associated invertebrates at the site, indicating that a significant component of the fauna is missed if the subsurface Chironomidae are not collected.

The guiding idea of functional measurement is that measurement theory and substantive theory form an organic unity. Psychological scales are inherent in the statement of quantitative psychological laws, and these laws themselves form the base and frame for psychological measurement. Valid scales thus depend on empirically valid laws. But establishing empirical validity of any law requires appropriate data analysis. Several statistical problems are discussed with respect to simple algebraic laws. To illustrate the necessity for proper tests of goodness of fit for algebraic models, five sets of experimental data are reanalyzed. In each case, the factorial plot and the analysis of variance showed that the data were nonadditive. Nevertheless, an additive model was fit to the data. The correlations between the data and the predictions from the additive model were extremely high, ranging from .964 to .9997. The corresponding observed-predicted scatterplots also gave little sign of the deviations from additivity. These correlation-scatterplot analyses conceal and obscure what the factorial plot and the analysis of variance reveal and make clear. Other topics discussed are accepting and rejecting the null hypothesis, the use of nonmetric smoothing for parameter estimation, and problems of stimulus-response-model generality. An extension of functional measurement is suggested for a practicable error theory for nonmetric analysis.

Three algebraic models for inequity were shown to be simply testable in terms of their additivity structure. The model from integration theory correctly represented the sequence of comparisons, first between persons, then between input and outcome. Also, it gave a good though not perfect account of the additivity structure.

In a loudness bisection task, subjects varied one sound to lie halfway between two given sounds in terms of loudness. The two given sounds were varied from 30 to 90 dB in a 4 by 9 factorial design. Functional measurement methods based on monotone analysis provided good support for the bisection model, and yielded a loudness scale with an exponent of about .3, except for a falloff at lower intensities. Two other tasks, judging average loudness and difference in loudness of the two given sounds, yielded mixed results. In Experiment 2, in particular, the differencing judgments were not additive, even under monotone transformation. These analyses also indicated that previous applications of monotone analysis have typically lacked adequate power to allow any conclusion about the operative model. Overall, the present bisection scale agrees with Garner’s lambda scale, and the present theoretical approach agrees with that of Garner in its emphasis on algebraic models as a foundation for psychological measurement.

Functional measurement methodology was applied to test theMotive×Expectancy×Value (MEV) model of human motivation. Subjects judged the value of hypothetical “games of chance” in which hunger, chance of winning a sandwich, and sandwich preference were varied along with similar information concerning a drink. Graphical tests showed excellent agreement between the data and the theoretical properties of parallelism and linear fan shape. Exact statistical tests of goodness of fit confirmed these graphical tests. Despite the complexity of the task, which required integration of six pieces of information, subjects' judgments obeyed a simple cognitive algebra. Applications of functional measurement were suggested for approach-avoidance conflict, level of aspiration, work motivation, and achievement motivation. These methods can provide exact tests of the behavior models in terms of the subjective values at the level of the individual. They thus provide a unified nomothetic-ideographic approach to motivation theory.

Subjects rated their preference between pairs of sandwiches, drinks, or sandwich-drink combinations. Use of factorial designs allowed simple tests of a subtractive model for preference. The results gave considerable support to the model, although some discrepancies were obtained. These seemed to stem partly from idiosyncratic discrepancies in a few subjects, partly from certain number preferences by the subjects as a group. In addition, two methods of estimating the scale values of the preference alternatives were compared. Model-based estimates appeared to be superior to independent ratings of the single alternatives. Finally, it was noted that the results tended to validate the use of rating scales to measure preference and, more generally, to support a functional theory of measurement.

Ss judged average heaviness of two unseen lifted weights on a 20-step rating scale. They also rated heaviness of a single visible object of variable size and weight. The data for each task obeyed the parallelism prediction of the linear integration model. This within-task consistency validates jointly the model and the response scale. Functional measurement procedure yielded independent scales of subjective heaviness from each task. These were linearly related, a criterion of external consistency. The plot of subjective heaviness against objective weight was slightly negatively accelerated. These results disagree with those that have been obtained with magnitude estimation. Since the rating data satisfy both internal and external consistency, they constitute the true measure of sensation. Magnitude estimation, in contrast, must be biased and invalid.

Summary In two experiments, S s were read sets of 6 or 8 personality adjectives, and asked to rate their liking of the person so described. In some conditions, S was also requested to recall the adjectives just read. The personality impression data showed a primacy (first impression) effect when recall was not required. Introduction of recall reduced the primacy and, in one condition, caused a recency effect. These results were interpreted as indicating that the primacy was primarily caused by decreased attention to the later adjectives, and that the use of concomitant recall destroyed this primacy by causing S to attend to the later adjectives more completely. The serial recall curves showed a small to moderate primacy component, and a very strong recency component. Further detailed analyses of the recall data were also given. Two implications were drawn from the data. First, it was concluded that the impression memory is distinct from the verbal memory for the adjectives. This conclusion was based on contrasts between the observed impression effects and those that would be expected if the impression depended on the verbal memory. Three objections to this conclusion, based on the possibility that recall probability was an inappropriate index of verbal-memory strength, were also discussed. Second, it was tentatively suggested that a linear model, together with the attention decrement notion, gave the best account of the data. It was finally noted that the linear model also provides a representation of the impression memory that is in harmony with the first conclusion.

Subjects estimated average value of angle pairs using magnitude estimations or graphic ratings. These numerical response data follow a simple averaging model. Functional scaling yields a linear relation between subjective and objective angle. The numerical data are then reduced to rank orders, and J. B. Kruskal's monotone analysis of variance (MONANOVA) procedure is applied. This allows a reconstruction of the original metric information from the strictly ordinal information, illustrating the power of MONANOVA in scaling. Limitations of MONANOVA in testing the underlying model are discussed.

The averaging hypothesis of information integration was tested in two experimental tasks. Both supported the averaging hypothesis and infirmed the adding hypothesis. In Experiment I, Ss judged the likableness of persons described by personality-trait adjectives, then rated the importance of one or all of the individual traits. These importance ratings suggested that differential weighted averaging could account for a certain nonadditivity that has obtained with negative traits. In Experiment II, Ss chose which of two personality descriptions would be more likable. This critical test supported the averaging model, which predicted that adding moderately favorable to highly favorable information would produce a less favorable response.

A first-order linear model for responses measured on a continuous scale is considered. Expressions are derived for stimulus dependencies, autocorrelations, and variances, thus giving a unified treatment of previous work. The stimulus dependencies are shown to remain essentially unchanged for certain cases of nonconstant parameters. The analysis of continuous contingent schedules is illustrated. A higher-order linear model is also discussed briefly. It is shown that the stimulus dependencies can provide parameter-free tests of the whole class of models under consideration. Relations of these models to autoregressive models, and to discreteresponse, linear operator models are pointed out.

Adjective-noun combinations in person perception are analyzed from an integration-theoretical view, with special reference to judgments of likableness, occupational proficiency, and social value. Different theoretical considerations are shown to apply to these three judgment dimensions, but all can be conceptualized in terms of the valuation and integration operations of integration theory. Experimental support for this conceptual analysis is given for likableness and occupational proficiency. Advantages of the integration-theoretical analysis over congruity formulations are pointed out.

A collection of 220 paragraphs of graded value about U.S. presidents is given. The collection includes 16 paragraphs about each of nine presidents and 8 paragraphs about each of eight presidents. For each president, the paragraphs have one of four rough values for judgments of statesmanship, H, M+, M-, and L. These paragraphs have proved useful in experimental applications of integration theory to attitude change. Other advantages of U.S. history as a source of issues and material for research on attitudes are also pointed out.

Loudness judgments of stimulus sets composed of four bursts of noise were analyzed for two types of contextual effects: between-set and within-set. Experiment I demonstrated between-set effects for these four-component stimuli; they were shown to be similar to those found in previous work with single stimuli. Experiment 2 tested an averaging model for within-set contextual effects. The results were inconsistent with the model. One interpretation is that there are within-set effects and that these are caused by shifts in the effective range of stimuli. Alternative interpretations attribute the apparent contextual effects either to an averaging of physical values or to an inappropriate scale of judgment.

Inclusion of several variables in a design is often desirable, but each added variable doubles the number of significance tests in the routine analysis of variance. This note discusses a procedure of partial analysis in which interactions, primarily those involving minor variables, are omitted from the analysis when prior evidence indicates that they are probably negligible. The rationale of this procedure is given, and its use illustrated in a model experiment. Specific recommendations for handling systematic sources and error terms are given.

Two experiments studied the Ebbinghaus illusion as a function of four stimulus variables: the size of the context circles, the number of context circles, the distance between the context circles and the center circle, and the size of the center circle. The results provided a quantitative test of a judgmental model that considers the Ebbinghaus illusion to be comparative in nature. The context circles, then, serve as standards or yardsticks, and the center circle is judged partly relative to them. The model provided a reasonably good description of the magnitude of the illusion as a function of the several stimulus variables. The center circle in Fig. 1 appears larger when surrounded by small circles, smaller when surrounded by large circles. This figure, known as the Ebbinghaus illusion, or Titchener circles, has seen relatively little systematic study. The present article reports two parametric studies done within a judgmental theory of stimulus integration (Anderson, 1970a, 1970b; Massaro &

The 5s estimated the average of several lengths presented serially one at a time. In Exp. I, the judgment was made only at the end of the sequence. In Exp. II, 5 estimated a cumulative average as each new length was presented. The main phases of these experiments used sequences of six lengths. For the most part, each S's data could be described by a subjective averaging model as tested in single-5 analyses. There was a general recency effect, the later lengths in the sequence having greater influence. Recency was fairly uniform across .Ss with the end responding procedure of Exp. I, but large individual differences in the serial position curves appeared with the continuous responding procedure of Exp. II. In Exp. Ill, two hypotheses about the cause of recency were tested, but received little support. Functional measurement technique showed that subjective length differed from objective length, apparently by a constant error for each 5. It was noted that the present methods could be applied to psychophysical scaling of other stimulus dimensions. Suppose that you are shown several lines, one at a time, and asked to estimate their average length. Can your response be described as a mathematical average? If so, is it an arithmetic mean, geometric mean, weighted midpoint, or some other measure of central tendency? The present experiments were designed to consider this question. They test a subjective averaging model for length. Averaging model.—The basic assumption of the model is that the response (R) at Serial Position N is simply a weighted sum: Rff = L Wk.Sk[1]

In two experiments, No-Paragraph S s formed an impression of a person described by three trait-adjectives, rated the person on likableness, and then rated each component trait. Paragraph S s were treated identically after writing a paragraph describing the person in their own words. A strong positive context effect was obtained: component ratings were displaced toward the values of the other traits; quantitatively, this effect followed the parallelism prediction of information integration theory. Since this positive context effect was equal for Paragraph and No-Paragraph conditions, it was interpreted as a generalized halo effect, not as contextual change of meaning. A third experiment obtained greater context effect for larger sets of equal-valued traits, casting doubt on an assimilation of meaning explanation.