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Structural safety assessments are implemented based on measured data, but the limited number of sensors restricts the comprehensive acquisition of response information in large complex structures. A concurrent multi-scale model utilises global and local simulation characteristics to expand the insufficient measured data. Thus, good global and local simulation capability is necessary for structural health monitoring-oriented multi-scale model, and the updating of this monitoring model needs to consider the multi-type responses that are obtained from different structural scales. However, the existing methods usually integrate multi-type responses into a single-objective function, which cannot ensure the acquisition of the optimal parameters. Moreover, in common parameter screening method, the perturbation and threshold are set artificially, which causes a strong subjectivity, and the common polynomial response surface fits poorly for highly non-linear problem. Therefore, an updating method of the structural multi-scale monitoring model based on multi-objective optimisation is proposed. For the proposed method, a variance analysis based on the orthogonal experimental design is used to screen the unique significant influence parameters. The Kriging spatial interpolation technique is used to establish the approximate surrogate model between the response and its corresponding influence parameters. Simultaneously, the responses obtained from the global and local structural scales are used to define the sub-objectives of the multi-objective function vector in order to avoid the introduction of weight coefficients. Then, the multi-objective optimisation algorithm NSGA-II is used to obtain the optimal parameter values and realise the comprehensive updating of the initial multi-scale monitoring model. Finally, based on the health monitoring system of the large shell structure of the Zhuhai Opera House, the initial multi-scale monitoring model is updated using the proposed method. The structural dynamic characteristics and local stress obtained from the initial model, updated model and the real structure are compared to validate the effectiveness of the proposed method.

In this issue, the article entitled, "Theory of Mind and Cognitive Function in Adults with Alstrom or Usher Syndrome," by Henricson, Frolander, Moller, and Lyxell reports the statistical results of Kruskal-Wallis tests using the H statistic and Mann-Whitney tests using the U statistic. These statistical tests are the nonparametric analog or match to parametric tests. The Kruskal-Wallis test is similar to the Analysis of Variance (or ANOVA) and the Mann-Whitney test is similar to the t-test. The reason why an experimenter uses Kruskal-Wallis and Mann-Whitney U tests instead of ANOVA and t-tests is decided by what kind of data they are examining. To give a bit of background: A parametric test is a statistical test that is generally used when the data conforms to certain assumptions. One of the most important of these assumptions is that the data are distributed "normally." If data are distributed normally, when the scores are plotted around the mean or average, they form a bell shape in which most of the scores are located around the mean and progressively fewer scores appear above or below the mean. If there are only two groups of data that are being compared to each other, and the data are normally distributed (as well as conforming with some other assumptions that I will not go into right now), a t-test can be used to compare those two means to each other to see if they are statistically significantly different. If there are three or more groups being compared to each other, then instead of a t-test, an ANOVA should be used. The t-test is really just a special case of the ANOVA in which the calculations are made easier because of the fact that only two groups are being compared. If the data are not normally distributed, the mathematics for the /-test and ANOVA often do not work out properly. A result can still be generated, but it might very well not truly reflect what is going on in the data. In this case, a statistical test that does not require the data to be normally distributed needs to be used. This test is the nonparametric alternative. If there are two groups being compared, a researcher can choose to use the Mann-Whitney U test. It is much like the parametric /-test, but it is based on medians instead of means. Because of its basis in medians, the mathematics behind the Mann-Whitney U test are different; the test also has the benefit of not requiring the data to be distributed along a bell curve. Similarly, if more than two groups are being compared and the data do not fit the assumptions for a parametric test, a Kruskal-Wallis test can be used, since it is also based on medians instead of means. "What's with all the letters?" a person may ask. The fact that the ANOVA gives an F statistic, the /-test a "/" statistic, the Mann-Whitney a "U" statistic, and the Kruskal-Wallis test an "H" statistic was essentially decided by the folks who developed these measures so that the test results could be talked about without having to repeat the tests' long names over and over. Treat the cryptic symbols simply as shorthand for referring to the test results. …

Drug combination is a critically important therapeutic approach for complex diseases such as cancer and HIV due to its potential for efficacy at lower, less toxic doses and the need to move new therapies rapidly into clinical trials. One of the key issues is to identify which combinations are additive, synergistic, or antagonistic. While the value of multidrug combinations has been well recognized in the cancer research community, to our best knowledge, all existing experimental studies rely on fixing the dose of one drug to reduce the dimensionality, e.g. looking at pairwise two-drug combinations, a suboptimal design. Hence, there is an urgent need to develop experimental design and analysis methods for studying multidrug combinations directly. Because the complexity of the problem increases exponentially with the number of constituent drugs, there has been little progress in the development of methods for the design and analysis of high-dimensional drug combinations. In fact, contrary to common mathematical reasoning, the case of three-drug combinations is fundamentally more difficult than two-drug combinations. Apparently, finding doses of the combination, number of combinations, and replicates needed to detect departures from additivity depends on dose–response shapes of individual constituent drugs. Thus, different classes of drugs of different dose–response shapes need to be treated as a separate case. Our application and case studies develop dose finding and sample size method for detecting departures from additivity with several common (linear and log-linear) classes of single dose–response curves. Furthermore, utilizing the geometric features of the interaction index, we propose a nonparametric model to estimate the interaction index surface by B-spine approximation and derive its asymptotic properties. Utilizing the method, we designed and analyzed a combination study of three anticancer drugs, PD184, HA14-1, and CEP3891 inhibiting myeloma H929 cell line. To our best knowledge, this is the first ever three drug combinations study performed based on the original 4D dose–response surface formed by dose ranges of three drugs.

The PARSCALE G2 statistic is arguably the most popular item fit statistic in operational testing. For long tests, the Type I error rates of the statistic have often been found to be satisfactory. However, the Type I error rates of the statistic have only been studied for sample sizes of up to several thousands. The authors examined the Type I error rates of the PARSCALE G2 statistic in a simulation study using sample sizes much larger than those considered in the literature. For any fixed test length, the Type I error rate of the PARSCALE G2 statistic is found to increase to 1 as the sample size increases. The findings contradict the claim in the PARSCALE software manual that the PARSCALE G2 statistic leads to a large-sample test and also contradict the common belief that the statistic has reasonable Type I error rates for long tests. Thus, this simulation study conveys the important practical message that the use of the PARSCALE G2 statistic cannot always be recommended even for long tests. The Type I error rates of the item fit statistics of Orlando and Thissen were found to be close to the nominal level for all simulation conditions considered here.

This article presents a simple, computer-assisted method of determining the extent to which increases in reliability increase the power of the F test of equality of means. The method uses a derived formula that relates the changes in the reliability coefficient to changes in the noncentrality of the relevant F distribution. A readily available computer applet translates the noncentrality parameter into the power value of the F test.

When the categories of the independent variable in an analysis of variance are quantitative, it is more informative to evaluate the trends in the treatment means than to simply compare differences among the treatment means. A permutation alternative to the conventional F test is shown to possess significant advantages when analyzing trend among quantitative treatments in a one-way analysis of variance. An example with and without an extreme data point illustrates the effectiveness of the permutation alternative for the analysis of trend when homogeneity of variance is compromised.

This paper deals with a novel patronage ramp-up analysis model. The ramp-up effect represents the delay in ridership take-up during the first periods of new transport services or facilities. This influence is known as one of the external errors of transport demand forecasts, which degrades the reliability of demand studies and economic appraisal for transport schemes. Traditionally, professional judgment and regression analyses have been used to investigate this effect, but the existing methodologies suffer from the inherent limitations of being biased and arbitrary. In this paper, a heuristic F-test is suggested as an alternative framework. The model proposed is tested with road and rail schemes of South Korea. The case studies illustrate the ability of the model to find the ramp-up parameters involving the duration and the ratio of this effect. Subsequently, a numerical example of cost-benefit analysis including ridership ramp-up is provided. The experiment shows that incorporating the ramp-up effect could provide help for more cautious decision making during the appraisal. A summary and future directions of the study are also provided.

The Skillings-Mack statistic (Skillings and Mack, 1981, Technometrics 23: 171–177) is a general Friedman-type statistic that can be used in almost any block design with an arbitrary missing-data structure. The missing data can be either missing by design, for example, an incomplete block design, or missing completely at random. The Skillings–Mack test is equivalent to the Friedman test when there are no missing data in a balanced complete block design, and the Skillings–Mack test is equivalent to the test suggested in Durbin (1951, British Journal of Psychology, Statistical Section 4: 85–90) for a balanced incomplete block design. The Friedman test was implemented in Stata by Goldstein (1991, Stata Technical Bulletin 3: 26–27) and further developed in Goldstein (2005, Stata Journal 5: 285). This article introduces the skilmack command, which performs the Skillings–Mack test. The skilmack command is also useful when there are many ties or equal ranks (N.B. the Friedman statistic compared with the x2 distribution will give a conservative result), as well as for small samples; appropriate results can be obtained by simulating the distribution of the test statistic under the null hypothesis.

This study proposes an approach for determining appropriate sample size for Welch's F test when unequal variances are expected. Given a certain maximum deviation in population means and using the quantile of F and t distributions, there is no need to specify a noncentrality parameter and it is easy to estimate the approximate sample size needed for heterogeneous one-way ANOVA. The theoretical results are validated by a comparison to the results from a Monte Carlo simulation. Simulation results for the empirical power indicate that the sample size needed by the proposed formulas can almost always achieve the desired power level when Welch's F test is applied to data that are conditionally nonnormal and heterogeneous. Two illustrative examples of the use of the proposed procedure are given to calculate balanced and optimal sample sizes, respectively. Moreover, three sample size tables for two-, four-, and six-group problems are provided, respectively, for practitioners.

Users of rwg may find situations where they want to compare the levels of within-group agreement across two or more groups. F tests are presented that compare two values of rwg, rwg(J), or r*wg(J), and recommendations are made for comparing pairwise group values for three or more groups with a control for alpha inflation. More robust and flexible methods based on O'Brien's test are then recommended when sufficient raw data are available. The meaning of findings that agreement statistics are either the same or different across groups is discussed in light of simultaneous comparisons of mean differences. Examples are shown to demonstrate the robust methods using employee responses to questions regarding climate perceptions of organizational support for employee development activities. Other scenarios where the F test may prove useful are discussed, and directions for future research are provided.

This article proposes alternative expressions for the two most prevailing definitions of suppression without resorting to the standardized regression modeling. The formulation provides a simple basis for the examination of their relationship. For the two-predictor regression, the author demonstrates that the previous results in the literature are incomplete and oversimplified. The proposed approach also allows a natural extension for multiple regression with more than two predictor variables. It is shown that the conditions under which both types of suppression can occur are not fully congruent with the significance of the partial F test. This implies that all the standard variable selection techniques—backward elimination, forward selection, and stepwise regression procedures—can fail to detect suppression situations. This also explains the controversial findings in the redundancy or importance of correlated variables in applied settings. Furthermore, informative visual representations of various aspects of these phenomena are provided.

A commonly used method for comparing groups of individuals is the analysis of variance (ANOVA) F test. When the assumptions underlying the derivation of this test are true, its power, meaning its probability of detecting true differences among the groups, competes well with all other methods that might be used. But when these assumptions are false, its power can be relatively low. Many new statistical methods have been proposed—ones that are aimed at achieving about the same amount of power when the assumptions of the F test are true but which have the potential of high power in situations where the F test performs poorly. A brief summary of some relevant issues and recent developments is provided. Some related issues are discussed and implications for future research are described.

The current article proposes a bootstrap- F method and a bootstrap- T2 method for use in a one-way repeated measure ANOVA design. Using a Monte Carlo approach in which sample size, nonsphericity, and nonnormality are systematically manipulated, the Type I error rate of the two bootstrap methods are compared to that of the traditional F test, the Geisser-Greenhouse adjusted F test, the Box adjusted F test, the Huynh-Feldt adjusted F test, the β-trimmed mean method using β =.1and β = .2, and the one-sample multivariate T2 test. Results show the bootstrap- F method controls Type I error better than all other methods considered when normality and sphericity assumptions are violated simultaneously.

Researchers who examine multiple outcome variables sometimes invoke a multivariate analysis of variance approach known as the “protected F test” to control for experimentwise Type I error rate. Unfortunately, this procedure affords protection against experimentwise Type I error only in rare instances. The purpose of the present paper is to present the case against the protected F test and to discuss alternative methods of controlling for Type I error, including the Bonferroni adjustment and descriptive discriminant analysis. The latter approach is briefly elaborated as a truly multivariate solution for multivariate phenomena. The author cites multiple examples of proper and improper use of multivariate analysis of variance in research on child development.

This article gives equations for computing confidence interval estimates and conducting F tests for intraclass correlation coefficients (ICCs) defined using three-way random effects models for crossed and nested designs. The estimates and tests employ mean squares from analyses of variance. The equations are generalized so that data from an initial pilot study (G study) can be used to prophesy the confidence limits for ICCs in data with more or fewer factor levels. Equations also are included for determining the optimal number of factor levels to use in a design that will offer confidence of 1-[.alpha] that the population ICC is equal to or exceeds a fixed lower limit.

Tests of mean equality proposed by Alexander and Govern, Box, Brown and Forsythe, James, and Welch, as well as the analysis of variance F test, were compared for their ability to limit the number of Type I errors and to detect true treatment group differences in one-way, completely randomized designs in which the underlying distributions were nonnormal, variances were nonhomogeneous, and groups sizes were unequal. These tests were compared when the usual method of least squares was applied to estimate group means and variances and when Yuen's trimmed means and Winsorized variances were adopted. Based on the variables examined in this investigation, which included number of treatment groups, degree of population skewness, nature of the pairing of variances and group sizes, and nonnull effects of varying sizes, we recommend that researchers use trimmed means and Winsorized variances with either the Alexander and Govern, James, or Welch tests to test for mean equality.

A natural source of heteroskedasticity in many kinds of data is group membership: observations in the sample may be a priori defined as members of groups, and the variance of a series may di!er considerably across groups. This concept will also apply to the errors from a linear regression. The assumption of homoskedasticity in the relationship may reasonably hold within each group, but not between groups. This assumption most commonly arises in cross-sectional datasets. In economic data, for instance, the groups may correspond to firms in di!erent industries or workers in di!erent occupations. It could also apply in a time-series context: for instance, the variance of daily temperature may not be constant over the four seasons. In any case, a test for heteroskedasticity of this sort should take this a priori knowledge into account. How might we test for groupwise heteroskedasticity in a variable or in the errors from a regression? In the context of regression, if we can argue that each group’s regression equation satisfies the classical assumptions (including that of homoskedasticity), the s 2 computed by regress (see [R] regress )i s ac onsistent estimate of the group-specif ic variance of the disturbance process. For two groups, an F test may be constructed, with the larger variance in the numerator; the degrees of freedom are the residual degrees of freedom of each group’s regression. Conducting an F test is easy if both groups’ residuals are stored in one variable, with a group variable indicating group membership (in this case 1 or 2). The third form of sdtest may then be used, with the by(groupvar) option, to conduct the F test. What if there are more than two groups across which we wish to test for equality of disturbance variance, for instance, a set of 10 industries? We may then use the robvar command (see [R] sdtest), which like sdtest expects to find one variable containing each group’s residuals, with a group membership variable identifying them. The by(groupvar) option is used here as well. The test conducted is that of Levene (1960) labeled as W0, which is robust to nonnormality of the error distribution. Two variants of the test proposed by Brown and Forsythe (1974), which uses more robust estimators of central tendency (e.g., median rather than mean), W50 and W10, are also computed. We illustrate groupwise heteroskedasticity with state-level data: 1 observation per year for each of the six states in the New England region of the United States for 1981‐ 2000. We first apply robvar to the state-level population series to examine whether the variance of population is constant across states.

In this paper, we study a nonparametric spatial pattern test statistic, the D statistic. The D statistic is an effective test statistic for testing spatial patterns in regional health data. Comparison studies of the D statistic with fixed weights and random weights are illustrated on the atlas of the Chinese cancer mortality rates and on other cancer atlas. Some social, economic and environmental reasons for statistically significant spatial autocorrelations of the Chinese cancer mortality rates were given in the discussion section. The method for calculating the mean and the variance of the randomly weighted D statistic is given in the appendix.

The nested analysis of variance (ANOVA) model is often recommended for analysis of educational data in which students receive treatments within classrooms. The Type I error rate and statistical power of the F test for groups-within-treatments effects associated with such nested ANOVA designs were evaluated in a Monte Carlo study. Data were generated for ANOVA models comprising two and three levels of the treatment variable; two, three, and five groups nested within each treatment; and 3, 10, and 30 observations within each group. The intraclass correlation among scores within groups was controlled at levels ranging from zero (independent observations) to .50, and the F test for groups-within-treatments effects was conducted at nominal alpha levels ranging from .05 to .30. The results indicated that the test for groups within treatments did not indicate sufficient power, even at the most liberal alpha level examined, to detect intraclass correlation in the sample data. The procedure was not effective in supporting decisions to use individual observations rather than group means as the unit of analysis.

The inflation of Type I error rates caused by the testing of multiple null hypotheses in factorial analyses of variance (ANOVAs) is a problem that is often not recognized in the behavioral sciences. Fletcher, Daw, and Young (1989) described the problem and conducted a limited simulation study to investigate the effectiveness of two strategies to correct the problem: use of an overall F test and use of a Bonferroni adjustment. Unfortunately, two limitations in the design of their simulation led these authors to conclusions about the overall F test that do not hold under all conditions. The present study was designed to overcome these limitations and to provide a more complete evaluation of such strategies. Our results indicated that the overall F test is effective only when all effects in the ANOVA are null. In contrast, the Bonferroni adjustment and recent modifications of the procedure control the Type I error rate regardless of the number of true null hypotheses in the ANOVA.

With two judges and a two-point rating scale, the test statistic for Kappa is the same as Pearson's chi-square statistic applied to the 2 × 2 table of paired observations. This equivalence allows a quick test of the null hypothesis of no agreement, as Pearson's chisquare statistic is much less cumbersome to compute than the Kappa statistic and its variance. A simple formula for the null hypothesis variance is also derived.

This study examined the priorities for theory application and for theory development of 149 students from four different undergraduate occupational therapy curricula. Data were analyzed using Kruskal-Wallis one-way analysis of variance by ranks and again using the F test followed by Duncan's Multiple Range Test. Results of the two analyses were consistent. Compared to registered occupational therapists, undergraduate students hold higher priorities for theory application and lower priorities for theory development. The data support a developmental sequence for theory valuing: value for theory application → value for research → value for theory development.

An empirical study of the power of the F test in normal populations with variances proportional to the cell means is reported. The results indicate that the power of the test can be approximated by the noncentral F distribution with a modified parameter of noncentrality.

This exploratory investigation concerned the effects of both auditory and visual stimulus variations on the accuracy of mental solutions to addition problems presented on a computer screen (CRT). 5 intensities of background noise and 5 background hues were presented randomly to 123 undergraduate volunteers as they mentally summed 25 numerals ranging from 1 to 5 at rates of either 1 sec. or 3 sec. per numeral timed from the onset of the previous numeral. A 2×2×5 mixed split-plot factorial analysis of variance gave a significant difference in errors between rates of digit presentation with greater accuracy associated with the 3-sec. rate. There was no significant difference in mean errors for auditory vs color modalities, yet a post hoc Newman-Keuls paired-comparison test of decibel levels at the 1-sec. rate of digit presentation gave a significant difference in mean errors between 60-dB and 70-dB sound-pressure levels (SPLs) of white masking noise. Also, a post hoc F test on differences between successive stages indicated significant differences suggesting a “learning set.” Comparisons between ‘everyday’ instances of these noise levels are made with implications for optimal computational environments.

The principal component regression (PCR) and partial least-squares (PLS) methods are used to calibrate and validate models for quantitative prediction of the composition of mixtures from FT-IR spectra. An experimental system of two- and three-component mixtures of xylene isomers was sampled with the use of statistical experimental designs. For two-component mixtures, the prediction error of independent validation samples decreased with increasing numbers of design points in the calibration. Four design points were needed to achieve a prediction accuracy of 0.0013 weight fraction. For three-component mixtures, a Scheffé {3,3} simplex lattice design, which has ten design points, achieved an equivalent accuracy of 0.002 weight fraction. There was little difference in performance between PLS and PCR computations. The results demonstrate the application of statistical methodology to the calibration of infrared spectra and show the importance of including an adequate number of samples in the calibration. The F test on the residual spectrum is shown to be a valuable tool for the identification of spurious data.

This paper describes a simple computer program for calculating the power of the F-test. The approach is based upon two independent approximations—the first, a normalization of the non-central F distribution and the second, an integration of the normal distribution. Comparison of the calculated values of power with exact values revealed a high degree of accuracy.

This investigation examined the postural-sway response of a matched group of learning-disabled and normal subjects. The subjects were evaluated on a force platform both with their eyes open and with their eyes closed. Four dependent variables, the measures of sway, were subjected to multivariate analysis of variance (MANOVA), with group as the independent variable. The analysis revealed F= 4.25 ( p

An alternate procedure is presented for testing the trial-by-subject interaction in the Shine Combined ANOVA. This new procedure is designed to get around the independence and distributional problems of the original F test.

The statistical analysis of trials in which individuals are evaluated repeatedly at several time points is examined. For the case in which correlations between observations follow a specified pattern, a conservative F test is applied to test for the effects of time and for the interaction between time and treatment groups.

Systematic assignment procedures are sometimes advocated as contributing to experimental designs that will result in more nearly precise estimates of treatment effects than those with completely random assignment. Several maintain that this systematic assignment is counter-productive because it reduces the power of statistical tests relative to random assignment. To help resolve these positions, the variance of the sample difference and the power of the F test for mean differences were studied under group matching on covariates and also under random assignment. This procedure was followed for all combinations of (1) one or three covariates; (2) small, medium, or large error variance; and (3) simple analysis of variance (ANOVA) or analysis of covariance (ANOCOVA). ANOCOVA with group matching always resulted in the correct Type-I error, yielded the greatest power in 5 of 6 situations, and gave the smallest variance of sample differences in 5 of 6 situations. However, the superiority of ANOCOVA with group matching over ANOCOVA with random assignment was small. It is concluded that there is little to choose between these two methods when a model of linear regression obtains. If it does not, matched assignment is a judicious technique.

This article presents a theoretical extension of the problem associated with multiple comparisons among means-the increasing rate of false rejection errors-to multiple F tests of effects in multifactor ANOVAs and regression analyses. The authors empirically confirmed the prediction of such errors through an experiment in which 32% of 100 random computer-generated three-factor ANOVAs had one or more false rejections for the usual seven F tests for main and interaction effects (30% were expected), yet only 6% of the overall F ratios-which tested all effects simultaneously-were falsely declared significant (5% were expected). In contrast, the Bonferroni procedure produced false rejections in 11% of the ANOVAs. The authors conclude that researchers can control the predictable rates of false rejection of errors inherent in multifactor analyses by extending the Fisher protection procedure and requiring the overall F to be significant. The article concludes with hypothetical experiments illustrating how researchers can use the procedure.

In view of the queries raised about the validity of the 16 P.F. factors when applied to a large New Zealand sample (vide Adcock & Adcock 1977), it was decided to make a study of individual items which did not seem to be satisfactory in the light of three criteria: inadequate loadings on any of the factors found in the analysis; gross failure to yield any indication of face validity; and failure to gain appreciable loading on group factors as defined by group factor analysis of the correlational matrix sectioned in accord with the scoring material. Consideration of these items indicates that many are greatly affected by cultural and temporal differences and by test climate.

The program presented computes a chi-square statistic for testing pattern hypotheses on correlation matrices. The statistic is based on a multivariate generalization of the Fisher r-to- z transformation. Monte Carlo studies have demonstrated that this statistic has small sample performance which is superior to an analogous likelihood ratio statistic obtained via the analysis of covariance structures.

If each of k predictor variables is correlated with a criterion variable, the use of multiple t tests to assess pairwise differences between r's will compound Type I error. This note describes an overall F test for determining the significance of differences between r2's which provides an error term for use in conventional ANOVA follow-up procedures.

This paper describes a computer program which performs a randomization test called the t'-test. Formally known as Fisher's Test of the Difference Score Population Symmetry About Zero, this test is appropriate when a matched-group t test would be appropriate but the data cannot meet the required distributional assumptions. The data must, however, be at least interval level.

Summary.-An alternative procedure to the use of farnilywise error rates is described that rerains an experimentwise error rate for the entire experiment. The procedure uses Dunm's (1961) test, considering each source of variation as a planned contrast and testing for significance with Dunn's cables. Most of the literature regarding error rates in experimental design has been directed to the one-way analysis of variance situation. Three different kinds of error rates have been faisly widely discussed: per comparison, experimentwise, and per experiment error rates. Ryan (1962 ) has argued effectively for the two latter error rates when interpreting an experiment. A fourth kind of error rate which has received somewhat less attention is the familyzuise error rate. Because the farnilywise error rate has rarely been discussed in textbooks (one notable exception is Miller, 1966), despite the fact that the concept was described much earlier by Tukeyl it would be worthwhile to describe the concept briefly. In the two-way (or higher) analysis of variance, an investigaror might formulate a prio~i hypotheses separately for each source of variacion (rows, columns and interaction), and each source of variacion is viewed as being a separate experiment. In a two-way analysis, when comparisons are made within levels of the A factor at the a level and then comparisons are made separately within the B factor at the a level, the error rate is being controlled at the a level familywise, but at the 2a level experimentwise. It then becomes impocanc for an experimenter to understand the differences between a farnilywise error rate and an experimentwise error rate for the entire experiment. The difference is in one sense mainly conceptual; if the experimenter is willing to interpret each source of variacion as being a separate experiment, chen the farnilywise error rate would be appropriate. While the term farnilywise has usually been given to the multiple comparisons following the main effecc tests, it is useful to extend the term to the main effects and interaction tests rhemselves. When analyzing data in a two-way layout, typically the F test for each main effect and for the interaction are tested independently, using the tabled F values to determine the significance of each separate source of variation in the experiment. The effecc of this practice is to consider each F test as a separate experiment. If each test is performed at the a level, the experimentwise error rate is not held at the u level, but rather at the 1 - ( 1 - a) level. The a level can, 'J. W. Tukey, The problem of multiple comparisons. (Unpublished Notes, Princeton Univer., 1953)

The effect of instruccional methods on students' performance has been a concern of American colleges and universities. One aspect is encompassed within the term "personalized instruction" which often includes giving frequent examinations on relatively small portions of material. The present study was designed to examine the effect of frequency of tests on mastery of general subject-area by 84 students, enrolled in the introductory psychology course at Davidson College. Ss were randomly assigned to three groups (28 Ss each). At the outset each group received a standard test of psychological knowledge ( 2 ) to establish a baseline for their individual knowledge in the area. Throughout the subsequent 10-wk. term, group procedures varied as follows: Group 1 took 6 tests on material in the cextbook (1) ; Group 2 rook 3 tests on that material; and Group 3 (comparison) utilized the same textbook without periodic tests during the term. Groups 1 and 2 had similar classroom experience. Group 3 received equivalent classroom time; another professor taught the course and used the same textbook. At the conclusion of the 10-wk. term, each group received an alternate form of the standard test they had taken initially. With maximum possible score of 100, group means and standard deviations were: Group 1 (pre-term, 44.18 and 5.88; post-term, 65.46 and 6.22), Group 2 (pre-term, 45.39 and 5.88; post-term, 65.32 and 5.06), and Group 3 (pre-term, 44.89 and 7.27; post-term, 59.61 and 11.55). Data were analyzed using a 3 X 2 analysis of variance (conditions, trials). An F test for simple effects indicated no significant difference between the performance of the 6-test and 3-test groups, but these groups differed significantly from the Comparison Group ( F = 5.04, df = 2/81, p < .01). While general mastery seemed unaffected by the frequency of testing, the fact that both tested groups performed significantly higher than the comparison group raised the possibility that periodic testing may have affected mastery. Regular assessment may be more important than the frequency of regular assessment. In effect, established pacing may be more imporcanc than the existence of a final "day of reckoning." The question deserves further systematic research.