The study seeks to determine the robustness and power of parametric analysis of covariance and analysis of covariance using rank transformation to violation of the assumption of normality. The study employs a Monte Carlo simulation procedure with varying conditions of population distribution, group size, equality of group size, scale length, regression slope, and Y-intercept. The procedure was performed on raw data and ranked data with untied ranks and tied ranks.

This study is concerned with the effect of placing text into a mediated structure form upon the generation of test items for analysis level domain referenced test construction. The item writing methodology used is the linguistic (operationally defined) item writing technology developed by Bormuth, Finn, Roid, Haladyna and others. This item writing methodology is compared to 1) the intuitive method based on Bloom's definition of analysis level test questions and 2) the intuitive with keywords identified method of item writing. A mediated structure was developed by coordinating or subordinating sentences in an essay by following five simple grammatical rules. Three test writers each composed a ten-item test using each of the three methodologies based on a common essay. Tests were administered to 102 Composition 1 community college students. Students were asked to read the essay and complete one test form. Test forms by writer and method were randomly delivered. Analysis of variance showed no significant differences among either methods or writers. Item analysis showed no method of item writing resulting in items of consistent difficulty among test item writers. While the results of this study show no significant difference from the intuitive, traditional methods of item writing, analysis level test …

The problem of this study was to determine the differences in experimentwise and comparisonwise Type I error rate among six multiple comparison procedures when applied to twenty-eight combinations of normally distributed data. These were the Least Significant Difference, the Fisher-protected Least Significant Difference, the Student Newman-Keuls Test, the Duncan Multiple Range Test, the Tukey Honestly Significant Difference, and the Scheffe Significant Difference. The Spjøtvoll-Stoline and Tukey—Kramer HSD modifications were used for unequal n conditions. A Monte Carlo simulation was used for twenty-eight combinations of k and n. The scores were normally distributed (µ=100; σ=10). Specified multiple comparison procedures were applied under two conditions: (a) all experiments and (b) experiments in which the F-ratio was significant (0.05). Error counts were maintained over 1000 repetitions. The FLSD held experimentwise Type I error rate to nominal alpha for the complete null hypothesis. The FLSD was more sensitive to sample mean differences than the HSD while protecting against experimentwise error. The unprotected LSD was the only procedure to yield comparisonwise Type I error rate at nominal alpha. The SNK and MRT error rates fell between the FLSD and HSD rates. The SSD error rate was the most conservative. Use of the harmonic mean of …

The study seeks to determine the degree of accumulation of Type II error rates, while violating the assumptions of normality, for different specified levels of power among sample means. The study employs a Monte Carlo simulation procedure with three different specified levels of power, methodologies, and population distributions. On the basis of the comparisons of actual and observed error rates, the following conclusions appear to be appropriate. 1. Under the strict criteria for evaluation of the hypotheses, Type II experimentwise error does accumulate at a rate that the probability of accepting at least one null hypothesis in a family of tests, when in theory all of the alternate hypotheses are true, is high, precluding valid tests at the beginning of the study. 2. The Dunn-Bonferroni procedure of setting the critical value based on the beta value per contrast did not significantly reduce the probability of committing a Type II error in a family of tests. 3. The use of an adequate sample size and orthogonal contrasts, or limiting the number of pairwise comparisons to the number of means, is the best method to control for the accumulation of Type II errors. 4. The accumulation of Type II error is irrespective …

Educators who use criterion-referenced measurement to ascertain the current level of performance of an examinee in order that the examinee may be classified as either a master or a nonmaster need to know the accuracy and consistency of their decisions regarding assignment of mastery states. This study examined the sampling distribution characteristics of two reliability indices that use the squared-error agreement function: Livingston's k^2(X,Tx) and Brennan and Kane's M(C). The sampling distribution characteristics of five indices that use the threshold agreement function were also examined: Subkoviak's Pc. Huynh's p and k. and Swaminathan's p and k. These seven methods of calculating reliability were also compared under varying conditions of sample size, test length, and criterion or cutoff score. Computer-generated data provided randomly parallel test forms for N = 2000 cases. From this, 1000 samples were drawn, with replacement, and each of the seven reliability indices was calculated. Descriptive statistics were collected for each sample set and examined for distribution characteristics. In addition, the mean value for each index was compared to the population parameter value of consistent mastery/nonmastery classifications. The results indicated that the sampling distribution characteristics of all seven reliability indices approach normal characteristics with increased sample size. The …

This study compared three methods of detecting test item bias, the chi-square approach, the transformed item difficulties approach, and the Linn-Harnish three-parameter item response approach which is the only Item Response Theory (IRT) method that can be utilized with minority samples relatively small in size. The items on two tests which measured writing and reading skills were examined for evidence of sex and ethnic bias. Eight sets of samples, four from each test, were randomly selected from the population (N=7287) of sixth, seventh, and eighth grade students enrolled in a large, urban school district in the southwestern United States. Each set of samples, male/female, White/Hispanic, White/Black, and White/White, contained 800 examinees in the majority group and 200 in the minority group. In an attempt to control differences in ability that may have existed between the various population groups, examinees with scores greater or less than two standard deviations from their group's mean were eliminated. Ethnic samples contained equal numbers of each sex. The White/White sets of samples were utilized to provide baseline bias estimates because the tests could not logically be biased against these groups. Bias indices were then calculated for each set of samples with each of the three …

This study dealt with shrinkage in multiple correlation coefficients computed for sample data when these coefficients are compared to the multiple correlation coefficients for populations and the effect of the ratio of utilized predictors to original predictors on the shrinkage in R square. The study sought to provide the rationale for selection of the shrinkage formula when the correlations between the predictors and the criterion are known and determine which of the three shrinkage formulas (Browne, Darlington, or Wherry) will yield the R square from sample data that is closest to the R square for the population data.

This study examined the statistical consequences of employing various methods of computing and cumulating effect sizes in meta-analysis. Six methods of computing effect size, and three techniques for combining study outcomes, were compared. Effect size metrics were calculated with one-group and pooled standardizing denominators, corrected for bias and for unreliability of measurement, and weighted by sample size and by sample variance. Cumulating techniques employed as units of analysis the effect size, the study, and an average study effect. In order to determine whether outcomes might vary with the size of the meta-analysis, mean effect sizes were also compared for two smaller subsets of studies. An existing meta-analysis of 60 studies examining the effectiveness of computer-based instruction was used as a data base for this investigation. Recomputation of the original study data under the six different effect size formulas showed no significant difference among the metrics. Maintaining the independence of the data by using only one effect size per study, whether a single or averaged effect, produced a higher mean effect size than averaging all effect sizes together, although the difference did not reach statistical significance. The sampling distribution of effect size means approached that of the population of 60 studies …

Short-to-medium projections were made of student semester credit hour enrollments for North Texas State University and the Texas Public and Senior Colleges and Universities (as defined by the Coordinating Board, Texas College and University System). Undergraduate, Graduate, Doctorate, Total, Education, Liberal Arts, and Business enrollments were projected. Fall + Spring, Fall, Summer I + Summer II, Summer I were time periods for which projections were made. A new regression analysis called "cycle regression" which employs nonlinear regression techniques to extract multifrequential phenomena from time-series data was employed for the analysis of the enrollment data. The heuristic steps employed in cycle regression analysis are similar to those used in fitting polynomial models. A trend line and one or more sin waves (cycles) are simultaneously estimated using a partial F test. The process of adding cycle(s) to the model continues until no more significant terms can be estimated.

This study compared the estimates of reliability made using one, two, three, four, five, and unlimited consecutive failures as ceiling rules in scoring a mathematics achievement test which is part of the Iowa Tests of Basic Skill (ITBS), Form 8. There were 700 students randomly selected from a population (N=2640) of students enrolled in the eight grades in a large urban school district in the southwestern United States. These 700 students were randomly divided into seven subgroups so that each subgroup had 100 students. The responses of all those students to three subtests of the mathematics achievement battery, which included mathematical concepts (44 items), problem solving (32 items), and computation (45 items), were analyzed to obtain the item difficulties and a total score for each student. The items in each subtest then were rearranged based on the item difficulties from the highest to the lowest value. In each subgroup, the method using one, two, three, four, five, and unlimited consecutive failures as the ceiling rules were applied to score the individual responses. The total score for each individual was the sum of the correct responses prior to the point described by the ceiling rule. The correct responses after the ceiling …

This study was designed to determine whether chis-quared based tests for independence give reliable estimates (as compared to the exact values provided by Fisher's exact probabilities test) of the probability of a relationship between the variables in 3 X 3, 3 X 4 , and 3 X 5 contingency tables when the sample size is 10, 20, or 30. In addition to the classical (uncorrected) chi-squared test, four methods for continuity correction were compared to Fisher's exact probabilities test. The four methods were Yates' correction, two corrections attributed to Cochran, and Mantel's correction. The study was modeled after a similar comparison conducted on 2 X 2 contingency tables and published by Michael Haber.

The problem considered involved assessing willingness of educators to participate in a study offering monetary incentives. Determination of willingness was implemented by sending educators a packet requesting return of a postcard to indicate willingness to participate. The purpose was twofold: to determine the effect of a monetary incentive upon willingness of educators to participate in a research study, and to analyze implications for mail questionnaire studies. A sample of 600 educators was chosen from directories of eleven public schools in north Texas. It included equal numbers of male and female teachers and male and female administrators. Subjects were assigned to one of twelve groups. No two from a school were assigned to different levels of the inducement variable.

The purpose of this study was to determine if leniency and halo error in student ratings could be reduced by training the student raters and by using a Behaviorally Anchored Rating Scale (BARS) rather than a Likert scale. Two hypotheses were proposed. First, the ratings collected from the trained raters would contain less halo and leniency error than those collected from the untrained raters. Second, within the group of trained raters the BARS would contain less halo and leniency error than the Likert instrument.

Behavioral data are frequently plagued with highly intercorrelated variables. Collinearity is an indication of insufficient information in the model or in the data. It, therefore, contributes to the unreliability of the estimated coefficients. One result of collinearity is that regression weights derived in one sample may lead to poor prediction in another model. One technique which was developed to deal with highly intercorrelated independent variables is ridge regression. It was first proposed by Hoerl and Kennard in 1970 as a method which would allow the data analyst to both stabilize his estimates and improve upon his squared error loss. The problem of this study was the application of ridge regression in the analysis of data resulting from educational research.

This study sought to determine boundary conditions for robustness of the Tukey HSD statistic when the assumptions of homogeneity of variance were violated. Box's coefficient of variance variation, C^2 , was utilized to index the degree of variance heterogeneity. A Monte Carlo computer simulation technique was employed to generate data under controlled violation of the homogeneity of variance assumption. For each sample size and number of treatment groups condition, an analysis of variance F-test was computed, and Tukey's multiple comparison technique was calculated. When the two additional sample size cases were added to investigate the large sample sizes, the Tukey test was found to be conservative when C^2 was set at zero. The actual significance level fell below the lower limit of the 95 per cent confidence interval around the 0.05 nominal significance level.

This study compared three methods of selecting the best discriminating test items and the resultant test reliability of mastery/nonmastery classifications. These three methods were (a) the agreement approach, (b) the phi coefficient approach, and (c) the random selection approach. Test responses from 1,836 students on a 50-item physical science test were used, from which 90 distinct data sets were generated for analysis. These 90 data sets contained 10 replications of the combination of three different sample sizes (75, 150, and 300) and three different numbers of test items (15, 25, and 35). The results of this study indicated that the agreement approach was an appropriate method to be used for selecting criterion-referenced test items at the classroom level, while the phi coefficient approach was an appropriate method to be used at the district and/or state levels. The random selection method did not have similar characteristics in selecting test items and produced the lowest reliabilities, when compared with the agreement and the phi coefficient approaches.

A Monte Carlo simulation technique was employed in this study to determine if the r transformation, a test of homogeneity of variance, affords adequate protection against Type I error over a range of equal sample sizes and number of groups when samples are obtained from normal and non-normal distributions. Additionally, this study sought to determine if the r transformation is more robust than Bartlett's chi-square to deviations from normality. Four populations were generated representing normal, uniform, symmetric leptokurtic, and skewed leptokurtic distributions. For each sample size (6, 12, 24, 48), number of groups (3, 4, 5, 7), and population distribution condition, the r transformation and Bartlett's chi-square were calculated. This procedure was replicated 1,000 times; the actual significance level was determined and compared to the nominal significance level of .05. On the basis of the analysis of the generated data, the following conclusions are drawn. First, the r transformation is generally robust to violations of normality when the size of the samples tested is twelve or larger. Second, in the instances where a significant difference occurred between the actual and nominal significance levels, the r transformation produced (a) conservative Type I error rates if the kurtosis of the parent population …