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Based on $k(\geqq 2)$ independent samples, a class of aligned rank order tests for the hypothesis of homogeneity of intercepts of the $k$ (simple) regression lines is considered here. The alignment procedure is similar to the one in Sen [Ann. Math. Statist. (1969) 19 1668-1683], and the theory is developed with the aid of the fundamental results of Jureckova [Ann. Math. Statist. (1969) 19 1889-1900] on the asymptotic linearity of rank statistics in regression parameters. Local asymptotic optimality of the proposed tests is also studied.

Problems in making inferences from a sample to a population and from one cohort to other cohorts are discussed. It is concluded that in most cases a longitudinal design using repeated measures is preferable to an independent samples design. Special attention is given to the often occurring large drop-out, and a simple regression analytical approach for estimating the mean of the drop-out group is indicated.

This study was designed to answer these questions: Can useful computer programs be developed? If such programs can be developed, how much storage is needed and what is the cost per student? Two Fortran programs were developed that created and analyzed data. The two types of analyses were correlational analysis and a t-test of differences between means for independent samples. Each program generated and solved thirty problems. A sample problem and the associated statistical analysis were presented in tabular form for each program. The computed values of r (and t) for each student were reported. These techniques could be used for other types of problems without exceeding the storage of many computers. The cost was substantial.

The following tentative conclusions are drawn from the results of cross spectrum analysis applied to the hemispheric 500-mb zonal index at latitudes of 25° N, 40° N, and 60° N. 1 Most of the variations of the indices at 40° N and 60° N are produced by oscillations with periods of the order of 25 days. This result is obtained from two independent samples of data, each at least 2 1/2 years in length. At latitude 25° N, longer periods seem to be predominant. High-frequency fluctuations with periods of the order of five days may also be important, but have been filtered out by the analysis. 2 The indices at latitudes 60° N and 40° N are correlated negatively. Most of this correlation is again contributed by oscillations with a period of the order of 25 days. The correlation between latitudes 25° N and 40° N is also negative, but so small as to be hardly significant. Again, both sets of observations agree fairly well in furnishing these results. 3 There is an indication of a slight lag of the long-period variation of index at latitude 40° N behind that at 60° N.DOI: 10.1111/j.2153-3490.1957.tb01873.x

A solution for the problem of obtaining a distribution-free one-sided confidence interval for $p = \Pr \{Y < X\}$ has been proposed in [1]. At present a numerical procedure is given for computing the sample sizes needed for such a confidence interval with given width and confidence level.

This study was designed to provide longitudinal data about the change and/or the stability of college-bound students' educational and vocational goals and plans as well as their background characteristics. Data from three studies were contrasted and compared. Included in these studies were: (a) a 2-year follow-up of 4,009 junior college students: (b) a 4-year follow-up of 5,623 4-year college and university students; and (c) a comparison of the responses of two independent samples (32,351 and 50,205) of high school seniors. Considerable differences in stability among characteristics were found; however, the changes seem to be orderly and according to logical expectations. The utility of the findings regarding changes and stability in these characteristics for those who work with college populations are discussed, and possible applications are suggested.

SUMMARY Approximations are found for the distribution of the standard criterion used to compare two observed proportions, when the reference set is generated by independent samples from binomial populations with the same parameter. The results are applied to study the overall performance of the continuity correction in 2 x 2 tables. Previous tentative conclusions are confirmed, to the effect that the correction is not appropriate for the reference set stated.

Summary.-Through use of correlational and multiple.regressioa techniques comparable predictive validities and regression weights of SIX tests in the Career Test Battery of the Los Angeles County Civil Service Commission arere obtained for two independent samples of 228 and 223 rypisr-clerks relative to a criterion concerning appraisal for promotability to a higher level position. Standardized tests of factored mental abilities are frequently used in selecting employees of high potential performance. The Career Test Battery of the Civil Service Commission of Los Angeles County has been used in employment processes for this purpose. The factorial content of the rests in this battery has been described in the recent paper by Michael, Stewart, and Rainwater (1959). The Office Series, which has been administered for most office and clerical positions, consists of six test units (with alternate form reliabilities between .70 and 35) that may be designated as follows: Wo~d Meaning (V for Verbal), Rearoning ( R ) , Speed of Perception ( P) , Numerical Facility (N ) , Space Relations (S), and Lmguuge Usage (L). The units P, N, and S are highly speeded tests. This study was planned to evaluate not only the individual test units, but also certain combinations of units in an attempt to predict which employees would more likely be successful in their ultimate performance in higher level positions.

The technique of stepwise multiple regression is applied to 45 days of data in establishing functional relations between the heights of the 500-mb. surface and TIROS IV long-wave radiation data during the period March to June, 1962. Twenty-six points were selected for height specification in the general area.of the eastern Pacific and the North American Continent. Sixty points were selected as a source of radiation “predictors” in a larger area that not only encompasses most of the 26 height points but extends farther westward across the Pacific. Sample charts show the correlation fields that result when the height values at each point are correlated with the radiation data at each of 60 poipts. The screening process that selects the best predictors is arbitrarily stopped at preset numbers of predictors. The resulting regression equations are evaluated on both dependent and independent samples. Even though the independent results are not outstanding for this particular sample, the method itself appears to offer promise for height and height contour specification over areas where direct measurements of heights are sparse or missing entirely.

Given independent samples from three multivariate populations with cumulative distribution functions F(1)(x), F(2)(x), and F(0)(x) = θF(1)(x) + (1 − θ)F(2)(x), where 0 ≤ θ ≤ 1 is unknown, the three-action problem involving decision as to whether the value of θ is high, low, or intermediate, is considered. A class of consistent procedures based on the relative spacing of three sample averages of linearly compounded rank scores is formulated. The asymptotic operating characteristics of the procedures when F(1) and F(2) come close together are studied and the best choice of the compounding coefficients in terms of these considered. The consequence of using estimates of the best coefficients on the asymptotic operating characteristics is also examined.

A technique has been developed for the simultaneous determination of carbon and hydrogen in at least four independent samples. A largediameter furnace and small combustion tubes make it possible to position at least four combustion tubes in the furnace at one time. An operator can analyze eight samples in one hour (7 1/2 minutes per analysis). The low cost of the apparatus and the relatively small amount of bench space needed make this technique especially advantageous for low-budget industrial, governmental, and academic laboratories.

Earlier findings suggested that the Wechsler Object Assembly (OA) subtest scores were significantly lower in adults and children who had major concerns about bodily intactness. Subsequent research with children has yielded equivocal results about the relationship between OA and bodily concerns. The present paper presents several additional attempts to test the previous observation of a relationship between OA and bodily concerns in adults. In three independent samples, adults with a Wechsler profile in which OA was the first or second lowest subtest had a significantly greater number and percentage of Rorschach responses which indicate bodily concern than Ss in which OA was the first or second highest subtest. Also, based on a brief one-line description of presenting symptoms in the appendix to the Rapaport volumes, the Wechsler scores of 5s with reports of bodily concern were compared with the rest of the patients. Of all the Wechsler subtests, only the Digit Span and OA tended to have a significantly lower rank for the patients with bodily concerns.

Let (xi, yi), i = 0, 1, 2, …, v, v ≥ 1 be independent samples from bivariate normal distributions with zero means, variances σ2 x , σ y 2, and covariances, σ x σ v ρ i , |ρ i| ≤1. Let xi , i=v + 1, ≤, v+n, yi, i = v+1, …, v+m, be independent samples from N (0, σ x ), N(0, σ y ) respectively and independent of (xi, yi ), i = 0, 1, 2, …, v. Let , and let . We show that

Consider two independent samples (called x's and y's) of mutually independent observations from populations with c.d.f.'s F(x) and G(x) respectively. Let υ be the number of x's which are smaller than the median of the y-sample and let u be the number of y's which are less than the median of the x-sample. If the x-sample is regarded as the control group, then the control median test proposed by Kimball et al. [9], rejects the hypothesis that F(x) ≡ G(x) if u is small. The present paper discusses a symmetrized version of this test, the first median test, which is based on u if the median of the x-sample precedes the median of the y-sample and on υ, otherwise. The asymptotic distribution theory of both tests is developed. The tests are useful in analyzing life trial data because they permit the experimeter to reach a decision early. In the life trial situation it is important to minimize the expected number of observations required to reach a decision. It is shown that in large samples, when curtailed sampli...

Association values, in terms of percentage of S s who responded “Yes,” for selected trigrams were obtained from children in grades 4–6 and from a residential school for the deaf. Correlations of from .83 to .87 were obtained between the values from children and the corresponding adult values from Archer for CVC trigrams, and of .88 between values from Witmer and from the children for a sample of 25 CCC trigrams. Reliability measures from the children were good. Values obtained from deaf children correlated .90 with those obtained from grades 4–5. Independent samples of normal children correlated .93 and .97 with each other, and a test-retest reliability group had an r of .99.

A study of comparison in performance in selected motor skills between elementary school children taught by the specialist in physical education and those taught by the classroom teacher was made. Five tests of motor skills related to running, jumping, and ball handling were administered to approximately 200 grade 6 boys and girls from eight different schools who were taught physical education by the specialist, and to 200 grade 6 boys and girls from nine additional schools who were taught physical education by the classroom teacher. Mean scores for each test were compared separately for boys and girls using the t test of significance for two independent samples. Significant differences in favor of the group taught by the specialist were found on all five tests for girls and in three of the five tests for boys.

We propose a method of deconvolution based upon the sampling theorem. Interlaced samples are used to find the sampled values at the zeros of the transfer function. The space–bandwidth product is used to determine how many independent samples are required to find the required object g(x). The technique eliminates so-called invisible solutions, and gives a unique solution in the absence of noise.

Summary Correlates of two related MMPI code types (2-8, 8-2) were obtained by comparing descriptors for these profiles with all other profiles in two large independent samples of white psychiatric inpatients. Replicated findings for 2-8/8-2s as well as for 8-2s alone included more frequent ratings for suicidal thoughts, voice is soft, and withdrawal; and higher mean scores on reduced speech. A finding unique to the 2-8/8-2s was greater frequency of depressed mood. Unique for the 8-2s were more frequent ratings for auditory hallucinations, delusions of persecution, and blocking. Only somatic delusions replicated for the 2-8s. Findings for male vs. female, highly elevated vs. less highly elevated, and 8-2-7 vs. 8-2 analyses disclosed no correlates unique to any of these subtypes.

Interest in impression formation as a function of adjectival descriptions and in interpersonal attraction as a function of attitude statements has led to two separate bodies of research and theory which are conceptually similar. It was proposed that the positive and negative descriptive adjectives used in investigations of impression formation would influence attraction responses in the same linear fashion as had been established for similar and dissimilar attitudes. It was also hypothesized that the motivational context of the stimuli would be positively related to the steepness of the linear function. With two independent samples of subjects ( N = 63 and 90), three sets of adjectives of differential favorableness were presented at three levels of personal relevance. Analysis of variance indicated strong support for the first hypothesis ( p p p

A logistic model developed by Birnbaum was tested in two ways. First, plots of proportions of subjects in different score categories were examined for consistency with the assumption of a logistic trace line, and especially for departures from the logistic which seemed due to guessing in multiple choice items. The results showed that guessing seemed to have little effect. Second, an attempt was made to predict the obtained score distributions of samples of subjects on six tests from item parameters estimated on independent samples. The fits were good in all cases, despite considerable differences between the tests, and some extremely odd distributions.

An experimenter has a sample for estimating the variance σ3 2. Suppose he has two other independent samples which are suspected to have come from the same population with variance σ3 2. Whether to pool the three samples to estimate σ3 2 depends on the outcome of two preliminary tests. This article discusses a sometimes pool estimate of σ3 2 and compares this with the usual estimate of σ3 2, obtained from the first sample only, as regards bias and mean square error.

A factorial study is reported of a 70-item matrix containing extraversion-introversion, neuroticism, and lie scale items; the correlations were obtained from a sample of 300 men and women, and questionnaire responses were also available from another similar sample of identical size for the purpose of confirming certain findings. The questions to be answered related (1) to the unitary nature of extraversion, and (2) to the independence of extraversion from adjustment. A third problem raised was the possibility that there might be two identifiable components of extraversion, sociability and impulsiveness; the study was designed to investigate the existence and relationship of these two traits. The results showed (1) that extraversion may be regarded as a unitary factor, depending somewhat on the definition of the term ‘unitary’ (a) that extraversion and adjustment are essentially independent; and (3) that sociability and impulsiveness do emerge as separate traits, correlating about 0–5 with each other in two independent samples. It was also found (4) that sociability has a slightly positive correlation with adjustment, whilst impulsiveness has a slight negative correlation.

Summary.-This comment shows that Braun and Farrell's (1974) reply to Schwab (1970) was deficient because it inappropriately generalized from an independent samples design to a repeated-measures design. It further corrects several erroneous ~oterpretations made by Braun and Farrell of the Schwab study. Finally, it suggests some new directions for test-faking research. It is well known (Campbell & Stanley, 1963) that repeated-measures designs are subject to potential order effects. Counterbalancing order of ueatments or utilization of control groups are routine procedures for counreracting this effect. A review by Schwab (1970) showed that Braun had conducted 10 repeatedmeasures studies on the ability to fake various personality inventories, including the Gordon Personal Inventory and Profile, which failed ro employ these elementary safeguards. Specifically, Braun consistently measured fakability by examining difference scores obtained when student Ss were instructed to answer the inventory items honestly on a first administration, followed by insuuctions to fake on a second administration. Since there is substantial evidence showing that Ss tend to increase their scores after repeated administrations of personality inventories (Windle, 1954), Schwab (1970) hypothesized that the procedure employed by Braun would tend to overstate the fakability of any inventory so tested. To test his hypothesis Schwab administered the Gordon inventory and the profile to student Ss, counterbalancing instructions to fake and to take the inventories honestly. A significant faking effect was found on 6 of the 8 scales tested in the honesr-fake condition but on only 3 of the 8 scales tested in the fake-honest condition. The observed faking effect was greater in the former condirion (Braun's) than in the latter condition on all 8 scales. While the magnitude of the differences between the two treatment conditions was not significant for any scale, the fact that all 8 differences were larger in the honest-fake treatment is significantly greater (sign

The performance of random reference correlators is examined in terms of sample rate and signal-to-noise ratio. A method to improve the performance is suggested that requires three-level quantization. Comparisons are made using weakly correlated jointly Gaussian processes as inputs to the correlator and independent samples in each channel.

It is shown in the classification problem, when independent samples are taken from uniform distributions, that for small sample sizes the probability of misclassification when using the nearest-neighbor rule is "close" to its asymptotic value. It is also shown that when using this rule the probability of classification in many cases is close to its Bayes optimum even for small sample sizes. Moreover, if one is restricted to a small sample size from one population, it is shown that it is not necessary to "make up" this deficiency by taking a large sample from the other population; best results may be obtained when both sample sizes are small.

JOHN TUKEY'S quick test of location (19) has been described as the simplest and quickest signif icance test for comparing independent samples that has been devised to date (11). Indeed it is, and Tu key's marvelous contribution of an authentic "prac tical power" technique has not received the attention it deserves. Thorough examination of 19 books fea turing titles with the words "statistics", "statisti cal analysis" or the like, all published since 1959 when Tukey's test was published, failed to yield one which even made mention of it. An excellent devel opment of Tukey's test by Neave (14) and a review by Rosenbaum (15) are two notable acknowledge ments in the recent literature. Used with Link's slick test of the ratio of sample ranges, a shortcut F-test (13), and particularly when n is equal to or greater than six, Tukey's "compact" has been found sufficient for most 2k cases. Experience with it demonstrates the "prac tical power" as Tukey has expressed it, and seldom does one find the classic t-test superior in testing H0.

Let $X_1 \leqq X_2 \leqq\cdots \leqq X_m$ and $Y_1 \leqq Y_2 \leqq \cdots \leqq Y_n$ be independent samples of i.i.d. random variables from continuous distributions $F$ and $G$, respectively, and suppose $F(x) = \lbrack G(x)\rbrack^k$ or $F(x) = 1 - \lbrack 1 - G(x)\rbrack^k, k > 0.$ Let $R_i$ and $S_j$ denote the ranks of $X_i$ and $Y_j$, respectively, in the ordered combined sample. We express $P(R_i \leqq b_i$, all $i$) as the determinant of a simple $m \times m$ matrix. We also show that for increasing sequences $\{a_i\}$ and $\{b_i\}, P(a_i \leqq R_i \leqq b_i$, all $i\mid F, G) = P(\alpha_j \leqq S_j \leqq \beta_j$, all $j\mid F, G)$, where $\{\alpha_j\} = \{b_i\}^c$ and $\{\beta_j\} = \{a_i\}^c$ and complementation is with respect to the set $\{i\mid 1 \leqq i \leqq m + n\}$, for any pair of continuous distributions $F$ and $G$.

Let us consider a sample of n ordered observations *(x < x2 < < x") drawn from a population with variance o2. Let w = (xn xl)/o. Let us consider the joint sampling distribution of w, and w2 for two samples, not necessarily the same size, drawn from populations with the same variance. If the two samples were drawn independently, then the joint sampling distributions of w, and w2 may be written as the product of the sampling distributions of w, and w2 . If we make the change of variable r = W11W2, W2 = w, and if w is integrated over its range of definition, the cumulative distribution of the ratio of two ranges remains. This may be written as

Objectives The best umbilical cord care after birth is a controversial issue. Aim of this research was to compare the effect of topical application of human milk and chlorhexidin on cord separation time in newborns. Methods One hundred seventy four neonates attending from hospitals affiliated to Kashan University of Medical Sciences were included. Newborns from birth were randomized to two groups. In group mother's milk, mother will rub her own milk to cord stump two times a day. chlorhexidin (group 2) were applied to the umbilical stump every 12 hours. The time to umbilical cord separation and any discomfort such as infection, hemorrhage, and discharge and odor were documented. Data was analyzed by SPSS software. Independent Samples t-Test, χ(2), Fisher were used in this study. Results Results showed a significant statistical difference between cord separation time in two groups and the mean cord separation time in the human milk group (7.15±2.15days) was shorter than the chlorhexidin group (13.28±6.79 days). In addition, a significant correlation was found between Signs of infection (discharge, redness, swelling and odor) in both groups. Conclusions Topical application of breast milk on umbilical cord care leads to quick cord separation time and can be used as easy, cheep, non injury methods for umbilical cord care.

1. 1. Using the “Silent Interview Technique” (S.I.T.) a measure of interview behaviour was obtained from a sample of 59 patients. 2. 2. Each patient filled in the Cornell Medical Index (CMI) and was given a score for the somatic (A-L) and psychological (M-R) parts of the questionnaire. On the basis of these scores the 59 patients were divided into 4 independent samples. These were (a) low somatic (A-L) and low psychiatric (M-R); (b) low somatic and high psychiatric; (c) high somatic and high psychiatric; (d) high somatic and low psychiatric. 3. 3. The high somatic low psychiatric sample spoke for significantly longer with the SIT than the high psychiatric low physical sample (p 4. 4. These results are discussed with regard to the possible explanations for them and also their clinical implications.

(mf) OTS. A method is presented for obtaining the variance of averages over nonindependent samples from a stationary time series. The problem is stated, a derivation of a solution is presented, and general applications of the method are discussed. Specific applications are included as illustrations. These include the derivation of the law of large numbers and the large sample solution for a low-frequency concentrated straight-line spectrum. Observations are included concerning spectra whose variances are concentrated at high frequencies. (C.H.)

The ratio of the diameter of the optic cup to that of the optic disc was studied in three independent samples of first degree relatives, one of which included those of glaucoma patients. The frequency distribution of this ratio did not differ for the three samples and was not influenced by age or sex. The three studies showed independently that in the individual subject, the ratio was similar for the two eyes and varied directly and significantly with that of his parents and with that of his siblings. It is proposed that this ratio is genetically determined and controlled by multifactorial inheritance.

In recent years, there has been increasing interest in acoustic techniques for estimating fish abundance. A lower bound on the variance of the abundance estimates is derived in this paper. The analysis assumes that the fish are Poisson-distributed in volume and that the estimate is obtained using independent samples from the received acoustic signal. It is shown that the variance of the estimate obtained from an echo counter satisfies the bound in low fish densities and that the variance of the estimate obtained from an echo integrator satisfies the bound in high fish densities.

Walk's A Scale has been reported to be associated positively and significantly with attitude measures of authoritarianism. The present writer, using two independent samples, found the Walk A Scale to have virtually no internal consistency. With 128 male university students, the application of the K-R 20 produced an r of .08. With 88 male college and female nursing students, use of the Tryon's Variance Form gave an r of .10. Moreover, computation of an inter-item correlational matrix for the 8 Walk A Scale items on the second sample produced consistently low, predominantly non-significant, and in one-third of the cases negative coefficients. Since these results indicate that Walk's A Scale it not homogeneous in a statistical sense, the scale should not be considered as a pure measure of “intolerance of ambiguity.”

Publisher Summary This chapter discusses some of the problems inherent in the statistical analysis of cranio-facial variables in man during growth and development. The study of populations during growth and development is highly dependent upon variations due to the changing intercorrelations between the measurements representing the cranio-facial complex. Total size, growth rate, sexual dimorphism, and social and physical environment affect the ability of the researcher to examine meaningful biological differences within and between samples under study. Further, a relatively homogeneous subsample is the choice of selection over a much larger heterogeneous population, as exemplified in the classification of malocclusion. Where control and experimental samples are available, the application of several different statistical methods, such as illustrated by the covariance analysis and the multiple regression techniques, help to support any biologic implications from the statistical results. The sample size and the statistical method are as strong as the measurements or variables that are representative of a biologic model of cranio-facial growth and development, especially where a specific hypothesis is to be tested. The biologic associations assigned to weights of eigen vectors, elements of the factor analysis and to the ordering of variables in the so-called “stepwise” or multiple regression analysis should be verified by more than one investigator on independent samples.

A method is described for examining recovery kinetics in irradiated biological systems. Independent samples of animals are first subjected to different single whole-body doses of radiation; then, after some chosen tirae interval, all the samples are exposed to a constant daily dose of gamma radiation for the duration of life. The daily exposure level is chosen to cause a selected acute or subacute radiation syndrome, wherein death occurs between about 15 and a20 days from the start of exposure. The mean after-survival from the start of daily exposure is the endpoint statistic. The results of this method in studies in mice are compared with certain existing data, and some advantages and disadvantages of the method are discussed. (C.H.)

Ss estimated the number of black circles in three contextual conditions: OX (no white circles), 4X (four times as many white as black circles), and 16X (16 times as many white as black circles); they further estimated the number of black circles under two designs: independent and related samples. For independent samples, estimates were significantly greater for the 0X than for the 4X and 16X conditions, while the latter two did not differ. For the related sample, the 0X and 4X produced higher estimates than the 16X, while the former two did not differ.

The purpose of the microphone system is to provide an estimate of the space average sound pressure level with the minimum possible variance for measurement of a tone. The variance in the estimate for measurement of a tone in a given room is a function of the number of independent samples taken, and the effectiveness of the rotating diffuser at the frequency of interest. Theoretical considerations indicate that the number of independent samples produced by an array is equal to the number of microphones (separated by more than one‐half wavelength) which are used. For a microphone traverse, the number of half‐wavelengths along the traversing path gives approximately the number of independent samples. Thus, there is always a frequency above which a traverse should provide a lower variance in the estimate than a given array. Experience suggests, however, that the lowest frequency of interest determines the accuracy requirements for the microphone system, assuming a reasonably effective rotating diffuser. In th...

The previous studies in this series1,2utilized illness histories covering time periods of 6 months. For the present study, health records were obtained extending over time periods of 4 years (girls) and 5 years (boys). No subject duplication occurs in the 3 studies; independent samples of Iowa City white schoolchildren were drawn. Martens and Meredith1used 90 kindergarten children between ages 4.7 years and 6.4 years; Evans2used 93 nursery school children between ages 2.5 years and 5.5 years; and the present study involves 135 elementary school children between ages 5.0 years and 10.0 years. Martens and Meredith1investigated associations between amount of absence from school for illness during a 6-month period, beginning in the autumn (x-variable) and each of 25 selected measures of body size, body form, and growth velocity (y-variables). None of their correlation findings was of sufficient magnitude to be useful

A more detailed analysis of factors contributing to the overrepresentation of first-borns in college populations is afforded by comparisons of years of schooling between siblings. Analysis of educational differences within twochild families reveals that: (1) first-borns attain significantly more education than their last born siblings only when the firstand last-born are of the opposite sex and (2) there is an overrepresentation of the cross-sex twochild family in three independent samples. The widely reported overrepresentation of first-borns in college is thus a function of not only ordinal position, but also sex of the subject and sex of the sibling.

Performance in a two‐interval forced‐choice signal detection experiment employing simultaneous presentation of the observation intervals was compared with the performance obtained when the observation intervals occurred successively in time. In the simultaneous condition, two independent samples of random noise, one of which contained a sinusoidal signal, were introduced into the observer's earphones at the same time, one sample to each ear. The observer's task was to indicate into which of his ears the signal had been introduced. In the successive observation condition, the bursts of noise were separated by a short time interval and the observer was to indicate whether the first or the second burst contained the signal. Detection under the two methods of presentation varied for different subjects and signal parameters, but, in general, performance during simultaneous presentation was inferior to that obtained during successive presentation. Although a gain in detectability might have been expected to result from the opportunity for direct stimulus comparison provided by the simultaneous method, these data show that any such gain is more than offset by the introduction of factors detrimental to detection.

This study was directed to answering the question, “Can the items in a test which is slightly speeded be rearranged in such a way as to discourage cooperation among test takers in a group setting, without affecting the item and score properties of the test?” The literature on the rearrangement problem consists of studies in which the test was either highly speeded or completely unspeeded, or in which rearrangements were extreme. Only moderate rearrangements were used in the present study. Two types of items were used. One group contained 40 items typical of those in the Verbal section of the CEEB Scholastic Aptitude Test (SAT) and one contained 25 items typical of the Mathematics section of the SAT. Four different arrangements of each type of test were administered to spaced samples of a college applicant group in March 1965. Five thousand cases were drawn from each of the eight groups for analysis of total score effects, and independent samples of 495 cases were drawn for item analysis. Results indicated no significant alteration of the item statistics or of the tests' correlations with other tests, but analysis of the regression of the experimental Verbal tests on a longer Verbal test revealed significant differences in intercepts; i.e., some of the Verbal arrangements were slightly more difficult than others. No such difference was found for the Mathematics tests. A possible explanation for these results is that in some of the Verbal arrangements relatively easy items occurred last and were not reached by some students. Thus dropout may have affected test scores differentially. It was concluded that for tests of this type and degree of speededness, an a priori assumption of equivalence among different arrangements might well be false. It was recommended, therefore, that if different arrangements are used in operational administrations of the SAT, separate equating statistics be computed for each arrangement.

When computing θ = arctan (Y/X) from k independent samples of each of the random variables X and Y, the variance of θ, σθ2, may be reduced by averaging in either of two ways: (1) averaging X and Y individually, then computing θ from the resulting averages; (2) averaging the individual values of θ obtained from each pair of values of X and Y. Theoretically, if X and Y are normally distributed and minimum σθ2 is desired, Method (1) is best if S/N ratio >0 dB and method (2) is best if S/N ratio

Methodologies were proposed for combining background and aptitude and/or achievement information in an approach to the classification problem using the concept of under- and overachievement. The methodologies were applied to independent samples from four high school curricula. The results suggest that when past achievement and/or aptitudes were held constant (1) groups characterized by overachievement in all four curricula had similar backgrounds as defined by their level and pattern of responses to five biographical variables, (2) groups characterized by underachievement in the four curricula appeared to have similar response patterns but had more variation with respect to level and (3) underachieving groups regardless of curricular choice reported that they spent more time on extracurricular technological projects than did overachieving groups. To a somewhat lesser extent underachievers tended to have fathers who discouraged their going on to college and they (the underachievers) also tended to spend more time on extracurricular reading.

There are several circumstances in which we may wish to test the homogeneity of the two sets of marginal probabilities in a two-way classification. For example, a sample from a bivariate distribution (say height of father, height of son) may be classified into a two-way table with identical (height) groupings in each margin. Or a similar classification may be possible for a non-measurable variable (say strength of right hand - strength of left hand). Again, in surveys of the same sample (a 'panel') on two different occasions, the interrelation of the results on the two occasions may be displayed in a two-way table, with one margin corresponding to each occasion. In all these cases, the question may arise: are the two sets of marginal probabilities identical? If the variable is measurable, we may test the difference between the means of the two marginal distributions by a large-sample standard-error test. However, we may be interested in the overall distributions, rather than only in their means. For the more stringent hypothesis of homogeneity, a test exists if we have two completely independent samples. when an ordinary x2 test of homogeneity may be applied (Cramer, 1946, p. 445). This test does not meet the essentially bivariate situations described above, where non-independence of the marginal distributions is a fundamental feature of the problem. When the classification is a double dichotomy, the problem of testing marginal homogeneity is simple, and its solution is a special case of the large-sample solution of the more general 2K classification problem given by Cochran (1950). Bowker (1948) gave a largesample test for complete symmetry in a two-way classification, a more restrictive hypothesis which is concerned with the entire set of probabilities in the classification, and not only with the marginal probabilities as we are here. In the present paper, a large-sample test for marginal homogeneity is derived and illustrated.