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This report examines existing mathematical methods that have been utilized to develop educational enrollment estimates and analyzes the applicability of these methods in the community college setting. Models surveyed are based on (1) extrapolation--by either survival cohort or cohort-regression, (2) structural flow, and (3) Markov-type procedures. The paper then presents some of the theoretical and practical problems associated with the formulation and implementation of these models. The final chapter presents a rationale for developing enrollment estimates by institution or curriculum in community colleges. (Author)

Statistical procedures are presented for determining ordinal and disordinal aptitude-treatment interactions with linear and curvilinear data. The paper presents a method for testing the homogeneity of group regressions for a single aptitude and provides models for expanding this test to linear and curvilinear regression planes. Procedures are presented for constructing appropriate tests of significance and for isolating the specific source of interaction in complex aptitude-treatment interactions for which there are multiple aptitudes. (Author)

This paper shows that Garfinkel and Gramlich's conclusion about the average performance of the contractors is not supported by the data. The discussion focuses on three issues: (1) The study was conducted in such a way that performance contracting schools and the comparison schools were generally not comparable in terms of initial achievement, socioeconomic status, and a host of other demographic and social variables that may have influenced the results. Since the contractors were generally assigned to the schools with the lower achieving students, who also had lower S.E.S. and family income, the effect of the noncomparability of the comparison schools was to negatively bias the estimated effect of performance contracting. (2) The statistical adjustments used by Garfinkel and Gramlich were inadequate to offset these biases. (3) The data base was open to a wide variety of potential biases that were not assessed; e.g., the testing conditions (at some schools) were terrible, the tests may have been highly speeded and thus not measuring reading and mathematics ability per se, and there was no control on the control group in that they may have been trying harder to outdo the experimentals. (Author/JM)

This invitational conference was convened to report the principal findings of a six-year study of possible sources of bias in the prediction of job performance. The research was conducted jointly by Educational Testing Service and the U.S. Civil Service Commission, supported by the Ford Foundation. Data were gathered on test and job performance of ethnic subgroups in three occupations in the Federal Government. The design of the study permitted a detailed analysis of the differential validity of selected aptitude tests for several kinds of performance criteria. Speakers at the conference were asked to respond to a draft of the technical report, to be published in 1973. Following an introduction to the project and a presentation of the major findings, the papers are provided. The titles and authors of the papers are as follows: "Technical Critique" by Anne Anastasi, "Implications for Employers in Government" by Raymond Jacobson, "Implications for Employers in Industry" by Lewis E. Albright, "Implications for Blacks" by Roscoe C. Brown, Jr., "Implications for Spanish Americans" by Edward J. Casavantes, "Implications for Governmental Regulatory Agencies" by Robert M. Guion, and "Implications for Future Research" by S. Rains Wallace. (Author/DB)

In this paper problems caused by the existence of errors of measurement are identified for factor analysis, regression analysis, ANOVA, and ANCOVA. At least one detrimental effect is shown to exist for each type of analysis. When a researcher's interest is with infallible variables, he runs the risk of biased results from all of the procedures except ANOVA. The estimates of parameters in all four procedures suffer from inflated error variance. Some partial solutions are indicated, but clearly more work is needed on several of the problems. Most statistical procedures have been developed for models where variables are assumed to be free from errors of measurement. Since almost all educational research involves use of fallible variables, it is important that the effects of errors of measurement for the various models be understood and that the understanding be reflected in current research practice. (Author/GS)

This paper uses ordinary least squares regression to obtain probabilities for the post-graduation choices of high school seniors, and it presents an illustration of the use of these probabilities in calculating future income. Problems raised by the use of the least squares regression are discussed. The benefits of higher education and ways in which they may be used as predictors are considered. The estimates presented are based upon data collected by a questionnaire administered to 2453 public high school seniors in Dade County, Florida. (GS)

A relatively new area of psychological investigation is the identification of biographical and psychological variables which contribute to an individual's decision to move from or to stay in a geographical area. This study is an attempt to utilize biographical and psychological data on 50 college students in a multiple linear regression to predict a newly defined Mobility Index, which was derived from having subjects place themselves into groups according to mobility plans. Using the multiple linear regression (MLR) model, significantly better than chance prediction of Mobility Index was obtained from six biographical items, from three psychological scales, and from a combination of the psychological and biographical items. The variables investigated and the results obtained are summarized in tabular form. Using a hold-out cross validation sample (N=10), a cross validation R=.63 (RSQ=.40) was obtained. (Author)

Based on the assumption that inferential statistics can make the operant conditioner more sensitive to possible significant relationships, regressions models were developed to test the statistical significance between slopes and Y intercepts of the experimental and control group subjects. These results were then compared to the traditional operant conditioning eyeball technique analysis. (Author)

This paper investigates the effects of school on learning as exhibited in this research. In all three studies, there were regressional analyses carried out in which the total variation to be accounted for was that between school averages, and regression analyses in which the total variation to be accounted for was the full variation between individual students. In examining overall effects of school variables, the between-student analysis should be used even though it includes a lot of variance due to individual differences within schools. It appears better to recognize that school variables can account only for that fraction of the total variance that lies between schools, and to use the between-student analysis for the study of effects of school variables. In the use of the between-student analysis, six countries are focused on which engaged in testing in literature, reading, and science: Chile, England, Finland, Italy, Sweden, and the United States. In addition, the analysis is confined to the 10 and 14 year-olds. Several general results are useful to state. For all three subjects, the total effect of home background is considerably greater than the total direct effect of school variables. Comparisons between ages 10 and 14 show a slightly higher total direct effect of schools at age 14 than at age 10 but a smaller proportion of it independent of home background. The data show fairly conclusively that reading achievement is more fully an outgrowth of home influences than are either of the two subjects, less a function of what takes place at school. (Author/JM)

Four computer programs using the general purpose multiple linear regression program have been developed. Setwise regression analysis is a stepwise procedure for sets of variables; there will be as many steps as there are sets. Covarmlt allows a solution to the analysis of covariance design with multiple covariates. A third program has three solutions to the two-way disproportionate analysis of variance: (a) the method of fitting constants, (b) the hierarchical model and (c) the unadjusted main effects solution. The fourth program yields three solutions to the two-way analysis of covariance, with or without proportionality, and with multiple covariates. The three solutions are similar to those described for a two-way analysis of variance with disproportionate cell frequencies. (Author)

This paper discusses the use of contrast coefficients in multiple linear regression models, and shows how they can provide for a logical method of analysis in both the analysis of variance and the analysis of covariance. (CK)

The major objectives of this study were: to determine whether information feedback provided during a difficult task would reduce State-Anxiety (A-State) and whether learner control of feedback would lead to further reductions in A-State. Another objective was to attempt to bridge cognitive and affective domains by examining relationships of the task variables of feedback and learner control by examining the relationships of the task variables of feedback and learner control with anxiety and cognitive abilities, specifically reasoning ability (R) and associative memory (Ma). Three objective-related hypotheses were investigated. Prior to taking the CAI course, each subject received a battery of five tests administered to small groups. The course contained a series of eight sets of three examples and three test items, illustrating eight consecutive rules comprising the task. A varimax factor analysis conducted on the ability scores produced two factors, R and Ma. A second analysis of variance, multiple linear regression analysis, a two covariable analysis of covariance, and a single covariable analysis were also performed. It was found that real reductions in A-State can be obtained through increased use of feedback. While feedback generally seems to reduce A-State, high A-State appears to interfere with the learner's capacity to utilize the feedback information effectively in performing the task requirements. Learner control seems to offer definite advantages both in terms of anxiety reduction and performance. (CK)

This study utilized linear multiple regression analysis with dummy variables to isolate one component of an educational accountability system, the contribution of the individual teacher to student achievement. Independent variables consisted of measures of each student's past academic record, the size of the class and a dummy variable to represent the student's instructor. The dependent variable was scores on a Social Science departmental final examination. Results revealed the effectiveness of this approach in isolating and rank ordering each instructor's contribution to student achievement. Obtained regression coefficients for instructors paralleled department chairman perceptions of their contribution. The discussion considered the possibility of this method for faculty evaluation and included some recommendations for those contemplating its use. (Author)

Thirty-four papers on educational statistics which were presented at the 1971 AERA Conference are summarized. Six major interest areas are covered: (a) general information; (b) non-parametric methods; (c) errors of measurement and correlation techniques; (d) regression theory; (e) univariate and multivariate analysis; (f) factor analysis. (MS)

A survey of recent literature was undertaken to locate validity studies of paper-and-pencil tests which met the following criteria: (1) Studies were conducted in a business or industrial (i.e. non-education, non-military) setting; (2) Separate statistics were available for blacks and whites; (3) Race was not confounded with some outside variable which would preclude meaningful interpretation; (4) Necessary data were reported to enable a test of homogeneity of regression between racial groups. For each of 20 studies which met these criteria, a homogeneity of regression analysis was conducted on each predictor-criterion pair to determine if there were significant differences between blacks and whites in standard errors, slopes, or intercepts of the regression lines. The number of significant differences in standard errors and in slopes was less than would be expected by chance, indicating that tests do not have differential validity between white and black groups. For intercepts, significant differences in excess of chance were obtained. The direction of the differences was such that job performance of blacks was overestimated by tests. (Author)

This paper uses the data from the 1966 Educational Opportunities Survey (EOS) to investigate regional and racial inequalities in education by applying a definition of inequalities that incorporates both school inputs and educational outcomes. Inequalities in school inputs are weighted by their importance for educational outputs, in order to empirically assess the extent and source of inequalities experienced by different racial and regional groups. A particular racial or regional group is said to experience inequalities relative to another group if its educational achievement is shown to change significantly when its own school inputs are replaced by the school inputs of the other group, while retaining its own family resources. Multiple regression techniques are used to obtain estimates of predicted average achievement for a racial or regional subgroup when they are assigned the average school resources from another group. The difference between the observed mean achievement and the predicted average achievement indicates the degree and direction of the inequality. (Author/JM)

The purposes of this study were (1) to provide an objective description of the supervisor-teacher conference behavior in a micro-teaching situation, (2) to determine the combinations of teacher and supervisor characteristics that predict conference behavior and conference effectiveness, and (3) to determine the supervisor characteristics that predict supervisors who change their behavior toward a more indirect and supportive conference. Test results, along with conference data and personal data, were used as supervisor and teacher variables for the statistical analysis. Through the use of the multiple regression technique, full and restricted models were tested to determine significant predictor sets. (Author)

This study involved two phases: first when classification was based on the calibration sample, and second in a cross-validation setting. Computer-generated data were used. Results obtained from rules based on probabilities of group membership were compared for accuracy when classifying in the discriminant space and in the predictor variable spaces. In the first phase accuracy was greater in the predictor variable spaces, while the reverse was true in the second phase. In general, rules based on probabilities of group membership were approximately equally accurate, and more accurate than a rule related to a multiple regression analysis. Other findings are also discussed. (Author)

The objective of the study was to predict potential procrastinators in a self-pacing instructional system. Seventy-five entering college freshmen were randomly selected to participate in a large scale individually-paced program. Those students (25) who procrastinated were classified as "no-start-procrastinators" (NSP); the remainder (52) were classified as "satisfactory progressists" (SP). This binary variable (NSP vs. SP) was regressed via step-wise multiple regression on the following predictors: ACT scales, Nelson-Denny scales, SSHA scales, Cooperative Algebra Test, Cooperative Trigonometry Test, high school percentile rank and "under-over" achievement. The multiple regression yielded a multiple correlation of .58. (Author)

Longley proposed a set of data for use in testing regression programs. This paper shows that the numerically accurate solution is likely to be an unreasonable estimate of the regression coefficients for this problem. This is true because the accuracy of the data and appropriateness of the model may affect the solution more than the computational method. An easily computed index is derived that can be used to indicate such computational instability. The basic conclusion is that a concern about highly accurate computational methods must be tempered with a concern for whether the data are accurate enough to make the results of such computation meaningful. (Author)

Perinatal variables were used to predict 7-year outcome for 538 children, 32% Negro and 68% white. Mother's age, birthplace, education, occupation, marital status, neuropsychiatric status, family income, number supported, birth weight, one- and five-minute Apgar scores were regressed on 7-year Verbal, Performance and Full Scale IQ, Bender, Wide Range Reading, Arithmetic and Spelling, ITPA Auditory Vocal Association, and Draw-A-Man or -Woman test scores. Regressions were calculated for each race, sex, and total group. With all groups combined, perinatal variables correlated significantly with all 7-year tests except Draw-A-Man, -Woman. Although not all 7-year test scores were predicted significantly for the total group, nor was any test predicted for all subgroups, the Bender test was significantly predicted for seven of the nine groups. (Author/CK)

This paper, a continuation of the analysis of data collected on 455 Negro and white medical technicians (see ED 035 018) as part of a study on fairness in selection testing, investigates the prediction of supervisors' ratings from aptitude tests. (AG)

Joreskog's general method for analysis of covariance structures was developed for estimating a model involving structures of a very general form on means, variances, and covariances of multivariate observations. This method achieves a great deal of generality and flexibility, in that it is capable of handling most standard statistical models as well as many nonstandard and complicated ones. This paper describes a computer program for the method. When the variance-covariance matrix of the observed variables is unconstrained, the method may be used to estimate location parameters and to test linear hypotheses about them. For example, the program may be used to handle such standard problems as multivariate regression, ANOVA, and MANOVA. A unique feature of the method is that it can also be used when the variance-covariance matrix is constrained to be of a certain form. Various other models involving correlated errors or errors of measurement can also be handled. An illustration of how input data is set up, and what the printout looks like for two small sets of data, are included. (Author/CK)