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When the life history functions B (E) and P (E)-fecundity and postbreeding survival-are subject to environmentally induced fluctuations, one of two patterns is selected for: If the functions are concave (iteroparity in constant environments), the optimal population is monomorphic. Variation in B (E) selects for reduced effort in all individuals; variation in P (E) for increased breeding. If functions are convex (semelparity in constant environments) and fecundity is the parameter at issue, the optimal population can be polymorphic, with only a fraction of the population reproducing annually. Increasing the severity of fluctuations reduces the optimal value of this proportion, even if the average rate of reproductive success is not changed.

In many practical problems in industry, it is desired to use the results of a previous sample to predict the results of a future sample. For example, data on warranty costs on large motors over the past three years are to be used for planning purposes t..

It has been suggested that the primary purpose for criterion-referenced testing in objective-based instructional programs is to classify examinees into mastery states or categories on the objectives included in the test. We have proposed that the reliability of the criterion-referenced test scores be defined in terms of the consistency of the decision-making process across repeated administrations of the test. Specifically, reliability is defined as a measure of agreement over and above that which can be expected by chance between the decisions made about examinee mastery states in repeated test administrations for each objective measured by the criterion-referenced test.

If the cell frequencies (i.e., the n's) in a factorial ANOVA are not equal to one another, the researcher must determine whether or not the condition of proportionality is satisfied. Although the authors of several texts demonstrate how to test for proportionality, their discussions (a) give the impression that every cell must be tested and (b) are restricted to the case of a simple two-factor ANOVA. The present authors point out that only some of the cells need to be tested, and two rules are provided which will allow the researcher to determine how many and which cells should be tested. More importantly, the authors demonstrate how to test for proportionality in a three-way ANOVA, with comments offered concerning how the test can be generalized to higher-order factorial designs.

Pigeons pecked a key and rats pressed a lever for food reinforcement under large values of the differential-reinforcement-of-low-rate schedule. Each subject was tested under 10 different schedule values ranging from 1 to 45 min and was exposed to each schedule value at least twice. The mean interresponse time and mean interreinforcement time increased with the schedule value according to power functions. Response-probability functions were computed for schedule values below 20 min and showed an increase in response probability as a function of time since the last response in most cases. Mean responses per reinforcer increased as a function of schedule value for the rats, but decreased as a function of schedule value for the pigeons. The proportion of responses with interresponse times shorter than 1 sec were an increasing function of schedule value for the pigeons, but did not vary as a function of schedule value for the rats.

Twenty-nine normal young men were administered the Halstead Battery and two additional tests commonly employed by neuropsychologists and were re-examined by the same instruments 20 weeks later. The results indicate that for our sample of normal Ss the classification of an individual as “normal” by t

The purpose of this study was to determine if the changes in operant responding observed after shifts in reinforcement magnitude are due to antecedent reinforcement conditions, or the absolute reinforcement magnitude in effect at any given time. All animals in both experiments were responding on a multiple VI 20 second-extinction schedule of reinforcement. In one experiment, the animals were trained on 0.04 ml dippers, and were subsequently switched to both large and smaller dipper sizes. In the second experiment, three groups of rats were trained on 0.01, 0.04 and 0.10 ml dippers; each group was run exclusively on its designated dipper size. Data from both experiments were computer processed to yield a detailed description of response pattern. Rate of response, during both schedule components, depended on reinforcement magnitude only in the first experiment. Pausing behavior, both after reinforcement and during response runs, was inversely correlated with reinforcement magnitude in both experiments. It was concluded that pausing is a function of absolute dipper size, but response rate is a function of prior reinforcement conditions.

A Markov Renewal Process (M.R.P.) is a process similar to a Markov chain, except that the time required to move from one state to another is not fixed, but is a random variable whose distribution may depend on the two states between which the transition is made. For an M.R.P. ofm (

The method of investigating interactions in two-way tables by the regression analysis introduced by Yates and Cochran (1938) has been applied to data from competition diallel experiments with plant species reported by Williams (1962) and Norrington-Davies (1968). Arithmetic and logarithmic scales were used in both experiments and the relative advantages of these are briefly discussed. Significantly high proportions of the interactions between species (row) and associates (column) effects were explained as differences between the linear regressions of individual performance on the associate values. Consequently the performance of the species in competition could largely be specified by three parameters. These were the species mean (ν), the regression coefficient (b) and the mean effect of associates (a), which respectively measured the general vigour of the species, its sensitivity to competition and its aggressiveness. These parameters jointly provided estimates of what we have termed the general competitive abilities of the species. Specific competitive abilities of particular mixtures are detected as significant deviations from the regression lines. The parameters were used to derive formulae which provide descriptive and predictive measurements of the competitive advantage of species in particular combinations, and of the mixture performances relative to the performance of other mixtures or monocultures. The types of competition phenomena which could derive from a situation involving only general competitive abilities were shown to vary greatly and depended on the correlations between the three parameters in the experimental material. The possible types of interactions between associated genotypes (competition, co-operation, antagonism, etc.) can be defined in terms of the general competitive ability parameters, or recognised as specific competitive abilities. It is thus suggested that the regression technique forms a useful approach to the discovery and classification of these effects among competing species. The second experiment (Norrington-Davies, 1968) involved competition between grass species under four different treatments. Common regression lines constructed over all treatments indicated that response to competitive stress was to some extent similar to the response to other kinds of environmental stress. This raised the concept that some aspects of general competitive abilities could be determined from general response to limitation in environmental factors. The plant breeding implications of this are briefly discussed, particularly the possibility of predicting performance under competition from performance as spaced plants.

The use of statistical successive analysis at the first stage of checking measuring devices (when the readings of these are subject to random scatter) enables us to monitor the quality of the manufactured product (by reference to the value of c) and estimate the state of production (by reference to the value ofa).

It is demonstrated that contours which vary in extent across space according to the Mach pattern include an increment in apparent extent and a decrement in apparent extent at a position corresponding to the position of Mach bands, i.e., at the inflection points of the pattern. It is also shown that increasing the slope of the gradient of the Mach pattern has an effect upon extent comparable to the effect upon Mach bands. These data are interpreted as supporting the position that lateral inhibitory interaction is involved in the perception of extent. A modification of the Hartline and Ratliff (1956) model for lateral inhibitory interaction is applied, and discrepancies between predictions generated from the model and obtained data provide the basis for recommended changes in the model.

On a criterion of minimum asymptotic coefficient bias, it has been shown recently [McCallum (1972), Wickens (1972)] that faced with a choice of using or discarding a (perhaps poor) proxy for an otherwise relevant independent variable which appears in a multiple regression model, one should always use the proxy. In this paper the analysis is expanded to consider variance in addition to bias in the criterion function. Our major finding is that although inclusion of the proxy is not a superior strategy unequivocally, it is recommended over a broad range of empirical situations.

A Factor Analysis of the Coleman report data on Equality of Educational opportunity is performed. The results of this analysis are used to suggest hypotheses about the nature of interactions affecting educational production functions. These hypotheses are then used as an aid in the specification of a simultaneous equation regression model of the educational process. Finally, a set of TSLS estimates of the parameters of this regression model is presented.

A linear model with measurement error in the independent variables is considered. An errors-in-variables procedure is presented that provides estimators of the coefficients and their variances. If the dependent variable has multiple measures, the total variance of the dependent variable can be decomposed into measurement error, variance of true values explained by the true values of the independent variables and variance of true values not explained by the model. An application to the measurement of role performance is presented.

Composite complete-incomplete (C-I) block designs are formed by combining complete blocks of size t units with balanced incomplete blocks of k units (1 ≤ k < t) resulting in blocks of size t+k units. In sensory experiments, composite C-I block designs have been shown to be more efficient than the standard complete block designs. Replication of the blocks in these C-I block designs permits accurate interpretation of panelist X treatment interaction effects. Also, the formulae for calculating estimates of the treatments, panelists, and interaction effects are simpler in form with the replicated C-I designs than the corresponding formulae with the unreplicated C-I block designs. The analysis of an experiment involving the rating of flavor of three strawberry preserves using a replicated C-I block design is presented.

In most papers on parameter estimation schemes the order of the process under study is assumed to be known a priori. In many practical situations, however, this information is lacking. Consequently simple methods for the determination of the order are necessary. In this paper a description is given of five tests based on respectively: (1) the behaviour of the error function, (2) the whiteness of the residuals (correlation function), (3) the statistical independency of loss functions, (4) the behaviour of the determinant, and (5) the pole-zero cancellation effect. Some of these methods, the pole-zero cancellation, test of whiteness, and F-test are used as known, but the others are revised in such a way that a better discrimination of the order is obtained. The methods based on the behaviour of the error function and the behaviour of the determinant respectively are extended in such a way that the orders of both process- and noise dynamics are estimated separately. An extensive set of simulations of the Astrom-process is presented in order to elucidate the comparison of the different methods. It turns out that an acceptable determination of the order is possible even with a signal-to-noise ratio at the process output of - 15dB.

A general method is developed for obtaining confidence limits on the mean of X + Y where X and Y are two independent random variables whose individual distributions and percentiles are in standard statistical tables. The procedure uses this information to obtain approximations for the percentiles of the sum or approximate confidence limits on the mean of the sum. The method is applied to two problems: approximating the percentiles of the noncentral t distribution, and determining confidence limits for variance components in a one-way classification. Numerical examples compare it to other approximations.

In repeated sampling from an infinite population consisting of unequal proportions ofN types, the distribution of the waiting time till the attainment of somen(≤N) different types has been obtained.

This article briefly reviews graphical, maximum likelihood, and linear estimation methods for analyzing censored life data to estimate relationships between stress and product life. Each method is illustrated by an example dealing with accelerated life test data on motor insulation. The advantages and disadvantages of the methods are compared to guide the choice of a method for a given application.

While various experimental methods may show the number of butterflies in a given area, this, of itself, is no pointer either to general scarcity or to the reverse. Even less can it be taken as being the result of a particular set of outside influences. However, low levels in certain (otherwise plentiful) species may be taken as indicating unsuitable management trends.

where P( t ) is the total population at time t and 5 is the growth modulus. This law is clearly inapplicable to situations in which the population competes for resources (e.g., space and food), for in these situations 5 should depend on the size of the population: the larger the population, the slower should be its rate of growth. To overcome this deficiency in the Malthusian law, VERHULST [1845, 1847] assumed that f i= (6o-co0 P ) P (5o, COo=constant). (1.2)

A cross-validation approach to the a priori determination of sample size requirements and the a posteriori estimates of the validity of a derived regression equation is developed for regression models, where sampling from multivariate normal populations is discussed in particular. Tables of sample size estimates are presented for the random model and their applications illustrated. An algorithm is given to obtain tables for the fixed model directly from those for the random case.

Indeterminacy becomes intelligible in terms of an event-probability distribution where there is no predefinable event alternative which can be assigned any significant probability of occurence—or where the array of significantly probable alternatives is simply too large to be manageable within traditional analytical boundaries. In simplest terms, this suggests that the real future state will be some as yet undefined event, or some alternative for which we have not been able to prepare a contingency response. When faced with indeterminacy, the traditional response has been to drop the mantle of science and turn back to the realm of rhetoric or, more seriously, to cease the attempt to understand society and simply inaugurate an effort to change it. At any rate, it is at the point of phenomenal indeterminacy that the interests of the long-range forecaster and systems analyst intersect. For both, the distant future and the inherently complex, protean and equifinal systemshare the property of indeterminacy, and neither the long-range forecaster nor the complex-systems analyst is able to rely entirely on statistical extrapolation or, indeed, on any of the instruments derived from inductive (ampliative) inference. Instead, the approach of both begins to take on a deducive flavor, with the scientific aspect of the effort maintained largely through the offices of our ability to employ subjective probabilities in much the same way that the inductivist employs objective probabilities. Here, then, we want to explore some of the operational implications of subjective probabilities within the domain of phenomenal indeterminacy, and the role of deductive instruments within the arsenal of the long-range forecaster and complex-systems analyst.

SUMMARY The accuracies of several normalizing transformations of a t distribution with v degrees of freedom are examined for large and small values of v. Expansions of the inverse transformations in terms of powers of v-' are produced and the first few terms compared with Fisher's general expansion. For small values of v the transformations are used to determine approximate percentage points of t which are then compared with the exact percentage points. The problem of transforming a Student's t variable with v degrees of freedom to a standard normal variable has received attention for a variety of reasons. Quenouille (1953, p. 235) was concerned with the combination of results from a series of experiments and suggested analysing the treatment effects using an inverse sinh transformation. This transformation is related to Fisher's normalizing transformation of the product moment correlation coefficient and is fairly good provided v is not too small. Anscombe (1950) proposed a modified form of this transformation which is suitable for smaller values of v. Chu (1956) examined the proportional errors in using the normal cumulative distribution function as an approximation to the cumulative distribution function of t and considered a square root of a logarithmic transformation. Modified versions of this were proposed by Wallace (1959) who constructed bounds on the deviation from the exact normal deviates. Moran (1966) used an empirical approach to develop a simple transformation of a particular percentage point of the t distribution and showed that the approximation is very good even for quite small values of v. Scott & Smith (1970) used the general expansion of the percentage points of the t distribution in terms of the corresponding normal percentage points, given by Fisher (1926), to develop a simple transformation similar in form to Moran's but suitable for any percentage point of t. In the following sections the accuracies of these transformations are compared for a selection of percentage points for large and small values of v.

Nearly 7,000 first lactations of daughters of 90 sires 187 progeny test herds were used to compare estimators of sire merit. The standard model among the several contains fixed effects of herd-year-seasons and sire groups and random effects of error and sires within groups. The estimate of merit for a sire is the sum of the appropriate group and sire within group estimates from a generalized least squares solution. This approach accounts for sires of hedmates, considers the number of daughters and herdmates in each herd-year-season, and simultaneously regresses sire constants toward appropriate group means. Three definitions of groups, as well as a model not including groups, were compared with the conclusion that virtually any grouping is preferable to ignoring groups for sires in general. Two herdmate comparisons, Predicted Difference, and regressed-mean weighted difference were compared, and evaluations by the latter approach were more like those from standard method. Both herdmate comparisons ignore the merit of sires of herdmates. Neither this omission nor ignoring environmental correlation seriously altered evaluations of the majority of sires.

After rats were trained to lever press, response elimination began with factorial combinations of fixed vs variable and adjusting vs constant omission training schedules. A time interval scheduling reinforcement remained the same in a constant schedule, and its length was increased as response rate declined in the adjusting schedule. A variable time (VT) response-independent reinforcement schedule followed response elimination to test the durability of response cessation. Experiment I included groups whose reinforcement was yoked to that received by the omission schedule groups. Rate of response elimination was faster with an adjusting than a constant schedule, and slightly faster with a variable than a fixed schedule. There were no significant differences in rate of response elimination between omission schedule and yoked groups. Shorter delay of reinforcement tended to increase rate of response elimination. In the subsequent VT durability test all groups displayed near-zero response rates. In Experiment II adjusting fixed and variable omission schedules, including yoked groups, were compared with fixed time (FT) and VT reinforcement schedules. Response elimination was slower in the FT and VT groups, and they responded more in a subsequent VT durability test. It was concluded that differential reinforcement of other behavior fails to account for these omission training effects, and suggestions were made for an analysis based on the correlation between response and reinforcement rate.

The primary concern of this paper is the establishment of a forecasting procedure for largest earthquake magnitudes of the next n years. It is shown that the use of the third-type asymptotic distribution of the largest values as an approximation to the exact distribution provides for an expression for the expected value and the mode of the largest earthquake magnitude in the next n years. An example of the application of this procedure is given and the results are compared with actual observations.

Many questions in the social sciences reduce to a comparison of mean values across groups in a classical analysis of variance F test. Often the original data my come from a set of items in a questionnaire or personality inventory. When this occurs, some sort of data reduction, combining of items, or scaling procedure is first performed before the hypothesis of no difference in mean values across groups can be made. In many cases, this problem causes undue concern t0 a researcher because the effect of the scoring procedure on the distribution of F is not clear. To help solve this problem, this study was undertaken to investigate whether the method used to calculate scores has any effect on the magnitude of the F ratio in an analysis of variance, for, if it were shown that no statistical difference existd, then a researcher would have some justification for showing the procedure having minimal messes. On the other hand, if statistical differences were b arise because of the kind d scaling procedure employed, then a researcher would have to be more cautious in his choice. For this empirical investigation, Guttman, Saaotor, and simple sum scores were generated using item responses from a large pool of high school seniors. No difference in scoring method was detected when the F ratios resulting from each of the three scoring methods were analyzed. This suggests that, for chin analyses, a simple sum score may be as effective as mres derived by more complicated methods.

In coding verbal behavior there is always a certain amount of disagreement among coders regarding the most appropriate category for particular segments of behavior. Unlike the scoring procedures for many category systems, the Uncertainty Reduction Index weights S’s response in proportion to the degree of uncertainty exhibited by all Ss responding to a given segment of verbal behavior. A comparison is made between Ss’ responses when scoring transcripts of verbal behavior with the Flanders’ system and the Uncertainty Reduction Index. The Uncertainty Reduction Index appears to have certain advantages when applied in the circumstances outlined in this paper.

Seventeen albino rats were trained to perform two sound‐localization tasks with single and paired sound sources. The conditioned suppression of a licking response was used as a behavioral measure. All animals were first trained to detect a change from a series of single clicks on the left to a series on the right. They were then given further training with paired clicks separated by a small time interval; the discrimination was between left‐right pairs and right‐left pairs. The intervals used were 0.5, 1.0 2.0, 4.0, 8.0, 16.0, 20.0, and 32.0 msec. Five animals were given further tests with smaller values using the method of constant stimuli. Additional values tested were 31, 62, 125, and 250 μsec. Transition from single clicks to paired clicks was good for values between 0.5 and 4.0 msec. An ability to discriminate paired clicks was easily demonstrated for values between 0.25 and 16.0 msec. The upper limit for discrimination was somewhere between 20.0 and 32.0 msec. The lower limit for discrimination was between 31 and 62μsec. These results were discussed in relation to the precedence effect in human hearing.

The performance of a random reference correlator (RRC) in terms of its precision is studied. It is shown that the precision depends almost entirely on a certain "peak factor". Processes with high peak factors must be clipped, which creates a compromise between the resulting bias and the optimization of precision. In this case a clipping factor has been defined. It is shown that, for clipping level values between 1 and 1.5 times the rms value, the distortion is reasonably acceptable and the variance of the estimate is of the same order of magnitude as that of direct estimators. A prototype, built with high-speed TTL logic circuits, allows incremental delays of 20 ns to be obtained.

Single unit activity was recorded from the area principalis of the dorsolateral prefrontal cortex during DA in 3 monkeys in order to analyze further the nature of observed differential changes in relation to the different positions of the choice keys (directional selectivity). Out of 354 related units obtained from 170 penetrations, 182 showed directional selectivity. A total of 111 directionally selective units were investigated in sufficient detail to determine whether the observed directional selectivity was related to the absolute or to the relative position of the choice keys. Twenty of these 111 units showed directional selectivity during the delay period and all of these units showed clear dependence on the relations between choice keys. For the remaining units, whose directional selectivity became apparent only after the choice keys were illuminated, dependence on relative factors was less marked. All units showed some dependence on the location of the choice keys, independent of the relations between choice keys.

A statistical model is developed that describes the population of women who are given a cytologic screening test for cervical cancer. The model is used to determine false positive and false negative rates as a function of (a) the proportion of "positive" cells in women free from cancer and in those with cancer, (b) the number of cells examined and (c) the minimal number of positive cells for a diagnosis of cancer. The model allows estimation of the minimal number of cells that must be examined in order to reduce both the false positive and the false negative rates below some predetermined levels. An expected cost equation is derived which combines the costs of examining each cell with the costs for false positives and false negatives. It is shown how cancer detection can be optimized through the use of this cost equation. The method determines both the maximal permissible cost for examining each cell and the optimal number of cells to examine in order to reduce the over-all expected cost below some predetermined level.

Pigeons were trained on a variable-interval 66-sec schedule of reinforcement that was segmented into either fixed- or variable-interval 10-sec components. Three-second access to food followed some components according to the overall VI 66-sec schedule, but 3-sec periods of nonreinforcement followed the other components. With both FI 10-sec and VI 10-sec segments, overall response rates were generally higher when the completion of unreinforced segments was signaled by a red key (never paired with food) than when it was unsignaled. Response rates during the red-key periods dropped to zero. Brief presentations of the red key engendered the distinctive (FI or VI) patterns of responding which would be expected if each segment were followed by food. These data demonstrate behavioral control by brief stimuli which are not paired with primary reinforcement and show that such control may develop even when the sequences of behavior required to produce food or brief stimuli are variable in duration.