CHAPTER 1: Introduction to Design CHAPTER 2: Principles of Estimation and Inference: Means and Variance CHAPTER 3: Design and Analysis of Single-Factor Experiments: Completely Randomized Design CHAPTER 4: Single-Factor Experiments Having Repeated Measures on the Same Element CHAPTER 5: Design and Analysis of Factorial Experiments: Completely-Randomized Design CHAPTER 6: Factorial Experiments: Computational Procedures and Numerical Example CHAPTER 7: Multifactor Experiments Having Repeated Measures on the Same Element CHAPTER 8: Factorial Experiments in which Some of the Interactions are Confounded CHAPTER 9: Latin Squares and Related Designs CHAPTER 10: Analysis of Covariance

Statistical Principles in Experimental Design

Reliability coefficients often take the form of intraclass correlation coefficients. In this article, guidelines are given for choosing among six different forms of the intraclass correlation for reliability studies in which n target are rated by k judges. Relevant to the choice of the coefficient are the appropriate statistical model for the reliability and the application to be made of the reliability results. Confidence intervals for each of the forms are reviewed.

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Intraclass correlations: uses in assessing rater reliability.

Regression methods were used to select and score 12 items from the Medical Outcomes Study 36-Item Short-Form Health Survey (SF-36) to reproduce the Physical Component Summary and Mental Component Summary scales in the general US population (n=2,333). The resulting 12-item short-form (SF-12) achieved multiple R squares of 0.911 and 0.918 in predictions of the SF-36 Physical Component Summary and SF-36 Mental Component Summary scores, respectively. Scoring algorithms from the general population used to score 12-item versions of the two components (Physical Components Summary and Mental Component Summary) achieved R squares of 0.905 with the SF-36 Physical Component Summary and 0.938 with SF-36 Mental Component Summary when cross-validated in the Medical Outcomes Study. Test-retest (2-week)correlations of 0.89 and 0.76 were observed for the 12-item Physical Component Summary and the 12-item Mental Component Summary, respectively, in the general US population (n=232). Twenty cross-sectional and longitudinal tests of empirical validity previously published for the 36-item short-form scales and summary measures were replicated for the 12-item Physical Component Summary and the 12-item Mental Component Summary, including comparisons between patient groups known to differ or to change in terms of the presence and seriousness of physical and mental conditions, acute symptoms, age and aging, self-reported 1-year changes in health, and recovery for depression. In 14 validity tests involving physical criteria, relative validity estimates for the 12-item Physical Component Summary ranged from 0.43 to 0.93 (median=0.67) in comparison with the best 36-item short-form scale. Relative validity estimates for the 12-item Mental Component Summary in 6 tests involving mental criteria ranged from 0.60 to 107 (median=0.97) in relation to the best 36-item short-form scale. Average scores for the 2 summary measures, and those for most scales in the 8-scale profile based on the 12-item short-form, closely mirrored those for the 36-item short-form, although standard errors were nearly always larger for the 12-item short-form.

A 12-Item Short-Form Health Survey: Construction of Scales and Preliminary Tests of Reliability and Validity

In the early 1980s, a strategy for graphical representation of multivariate (multi-species) abundance data was introduced into marine ecology by, among others, Field, et al. (1982). A decade on, it is instructive to: (i) identify which elements of this often-quoted strategy have proved most useful in practical assessment of community change resulting from pollution impact; and (ii) ask to what extent evolution of techniques in the intervening years has added self-consistency and comprehensiveness to the approach. The pivotal concept has proved to be that of a biologically-relevant definition of similarity of two samples, and its utilization mainly in simple rank form, for example ‘sample A is more similar to sample B than it is to sample C’. Statistical assumptions about the data are thus minimized and the resulting non-parametric techniques will be of very general applicability. From such a starting point, a unified framework needs to encompass: (i) the display of community patterns through clustering and ordination of samples; (ii) identification of species principally responsible for determining sample groupings; (iii) statistical tests for differences in space and time (multivariate analogues of analysis of variance, based on rank similarities); and (iv) the linking of community differences to patterns in the physical and chemical environment (the latter also dictated by rank similarities between samples). Techniques are described that bring such a framework into place, and areas in which problems remain are identified. Accumulated practical experience with these methods is discussed, in particular applications to marine benthos, and it is concluded that they have much to offer practitioners of environmental impact studies on communities.

Non-parametric multivariate analyses of changes in community structure

Metrics of visual form.

For more than a century, vibrational properties of molecules have been given prominent consideration by theorists attempting to account for olfactory sensations; but little data have been presented in support of the role that these properties play. Among the more recent theories is that of Dyson (1937 & 1938), who proposed that odor was due to molecular vibrations, producing a Raman shift frequency$ of 1,400 to 3,500 crn.-’ (these frequencies correspond with a wave length from 7.14 to 2.86 microns, respectively). Wright$ (1954) pointed out that this region mainly reflects chemical properties of the molecule, and indicated on the basis of quantum and thermodynamic arguments that the region below about 600 cm.-l (wave length beyond about 16 microns) should be examined for relationsh,ip to odor, especially since the properties of the molecule as a whole should also be reflected in this region. Previous evaluations and reviews of Wright’s proposal have frequently been unfavorable (Pfaffmann, 1956; Thompson, 1957; Lauffer, 1959). However, detailed examination of the theoretical and empirical arguments presented against the proposal indicates they all are of questionable pertinence. In particular, no data were found to counter those presented by Wright and Serenius (1954), who found a significant similarity among the low-frequency Raman spectra of a group of chemicals having the bitter almond odor. It was the purpose of this investigation to independently evaluate Wright’s (1954) proposal that a relationship may exist between odor and molecular vibration properties as measured by Raman spectra. The investigation was initiated with a survey of the psychological olfactory literature, and a survey of the available Raman spectral data. The psychological and Raman data were then cross compared to determine if Raman characteristics could be defined for given olfactory characteristics, and vice versa. TABLE 1 illustrates the nature of the relationships found. Odorous chemicals generally were found to have vibrations in the proposed region, while nonodorous molecules tended not to have vibrations in the region. The excitation probabilities relate to the theoretical basis for considering this region, with greater excitation probability being noted for the lower frequencies. In general, the literature evaluation provided support for Wright’s ( 1954) proposal of a relationship between odor and low-frequency molecular vibrations. One of the problems of the literature evaluation concerned the paraffin hydrocarbons for which it was found difficult to make any conclusion. Standard samples from the National Bureau of Standards were found to have very faint odors for the members around heptane, and it seems likely the odors present might have been due to the remaining impurities. Ignoring the “strong gasoline

Evaluation of far infrared relations to odor by a standards similarity method.

Eye movements of 13 Ss in response to a structured sample of 42 polygons were recorded, using the Brandt Eye Camera, to find out “how people look at nonrepresentational shapes.” The ultimate purpos...

Nonrepresentational shapes and eye movements

In spite of an almost complete lack of knowledge concerning the role of the various aspects of form in perceptual tasks, patterns have served as stimuli in a wide variety of psychological studies. In most studies, no basis has been available for preselecting stimuli with given characteristics, nor has it been possible to evaluate systematically the effect of specific properties of form upon performance. Although such research allows the results to be generalized to the perceptual performance of other Ss, it is not possible to make inferences from the data relative to a population of stimuli. Attneave and Arnoult (1956) have described a set of techniques by which it is possible to generate samples of stimuli from known populations the physical characteristics of which are partially known. Further, initial attempts have been made to systematically relate quantified stimulus characteristics to certain perceptual response variables. Although variously defined, figural complexity, for instance, has been found to be reliably related to correct recognition (Vanderplas & Garvin, 1959b; Deese, 1956), association value (Vanderplas & Garvin, 1959a), and response time (Edelman, Karas, & Cohen, 1961). Other studies indicate that complex figures are not only harder to reproduce from memory (Attneave, 1954; Deese, 1956), but are also harder to learn by name (French, 1954) and to match (Weinstein, 1955). In addition to figural complexity, it has been demonstrated that symmetry (Atcneave, 1957; Hitchcock, 1961), rotation (French, 1954; Hitchcock, 1961 ) , and compactness ( Attneave, 1957) are characteristics of form that may be reliably related to perceptual performance. Although mostly exploratory in nature, these studies demonsuate the validity of a strictly analytical approach to determining the object-properties associated with perceptual performance. However, most of these studies have been limited to assessing a single, crudely defined, stimulus dimension and have involved statistical designs inadequate to assess possible interaction between stimulus

Quantitative studies in form perception: an evaluation of the role of selected stimulus parameters in the visual discrimination performance of human subjects.

Kenneth M. Michels

Papers

Statistical Principles in Experimental Design

Metrics of visual form.

Evaluation of far infrared relations to odor by a standards similarity method.

Nonrepresentational shapes and eye movements

Quantitative studies in form perception: an evaluation of the role of selected stimulus parameters in the visual discrimination performance of human subjects.