Format Card Research Articles

Transformation of variables to linear combinations

There exist many research situations in which linear combinations of an original set of measures are desirable. For instance, the calculation of subscale scores from items on a test, the selection (a priori or a posteriori) of a valid combination of a larger set of variables, or the contrasts among a set of scores may all be considered cases for which a solution lies in the application of a suitable transformation matrix to the observations of each subject. Indeed, the research design for which a linear combination of the original variable(s) would prove most helpful is the frequently used one in which each subject is repeatedly sampled on one or more criterion variables, what is often referred to as a withinsubjects or repeated-battery design. In this case, the application of an appropriate contrast matrix to the outcome measure(s) produces linear combinations of the original variable(s) that can be used in profile analysis or growth-curve analysis (for example, see Harris, 1975;Timm, 1975). Description. The programs consist of a brief main routine and several subroutines. The MAIN routine simply controls program flow. POLYN reads the metric of the polynomial contrast matrix, if the user has indicated the metric is unequally spaced, and then calculates the polynomial contrast matrix. USERD reads a user-defined contrast matrix. ORTHO performs a GramSchmidt orthonormalization on the rows of polynomial contrast matrix, or, if requested by the user, on the rows of the user-defmed contrast matrix. INPUT reads the input data, subject by subject, and applies the contrast matrix to it. The transformed data are temporarily stored in binary form on a peripheral device. RORDER reorders the input data prior to the application of the contrast matrix, if requested by the user. OUTPUT prints the contrast matrix applied to the data, reads and prints, and punches and/or writes to an alternate medium the transformed data, as requested by the user. . Input. Input to the program consists of (1) a title card, containing any 80 alphanumeric characters, (2) a parameter card, indicating the number of subjects, number of variables, number of input and output format cards, type of tranformation matrix to be read or generated, and various other program options, (3) variable format card(s) describing the input data, (4) variable format card(s) indicating how the transformed data are to be written, (5) the input data. The input data may reside on some medium other than cards that follow immediately in the input card stream. Output. The printed output includes the job title, program options selected, and the transformation matrix applied to the input data. It is also possible to have the transformed data listed on the printed output. In addition, the transformed data can be written onto an alternate output device (e.g., tape, disk), punched onto cards, or both. Technical Information. The program is written in 1966 ANSI standard FORTRAN N and should be compatible with any mainframe or minicomputer FORTRAN compiler with few if any modifications. All computations are in single-precision arithmetic, and core storage requirements on an IBM3032 are approximately 70 KB. This includes 30 KB for program storage and 40 KB for array storage. Array storage consists entirely of a singly subscripted array stored in COMMON. This array is subdivided at execution time according to the various program options chosen, through the use of integer pointers that allocate various portions of the array. Thus, the program is quite flexible in terms of the variety of programs it can handle. The formula detailing the limitations in core storage is complicated and, thus, is not presented here. As a rough guideline, the number of observations available on each subject must not exceed 100. This limitation can be altered easily by changing three statements in the MAIN routine. Moreover, one peripheral storage device is used as a binary scratch unit, and one peripheral device can be allocated for permanent storage of the output data set. The units numbers for these devices, as well as the card reader, printer, punch, and an alternate device that might contain the input data set, are assignable within the BLOCK DATA subprogram. Currently, these devices are assigned the numbers 1,4,5,6, 7,andO,respectively. Availability. Reprints of this paper and an annotated source listing can be obtained at no charge from Kevin E. O'Grady, Department of Psychology, University of New Mexico, Albuquerque, New Mexico 87131.

ORDER2: A program to perform ordering-theoretic data analysis

ORDER2: A program to perform ordering-theoretic data analysis

A FORTRAN IV program for the estimation of missing data

XI is of order n by PI and X 2 is of order n by P2. The partitioned correlation matrix is: standardized regression coefficients into unstandardized coefficients and by computing the intercepts. Before estimating missing data by Equation 1, the correlation matrix R must be estimated. Two methods can be used: Wilks (1932) proposes substituting the corresponding column mean for each missing entry; Glasser (1964) estimates R from all available pairs of scores for each pair of variables. The estimates obtained from Equation 1 can be improved by iteration. The estimates from one iteration can be used to improve the estimate of the correlation matrix for use in a next iteration. The program, however, becomes very expensive to run when the number of iterations is large. This procedure depends on the assumption that the data are missing at random and the estimates will be quite unsatisfactory when the missing variables do not correlate highly with at least one of the available variables and/or when the proportion of missing entries is large. Description. The main program uses a set of FORTRAN IV subroutines. These routines implement the estimation procedure and all supplementary operations. The subroutine WILKS computes the correlation matrix R by Wilks' (1932) method; GLASSER computes R by Glasser's (1964) method; TRANSF draws R 1 and RII from the relevant parts of R-I; REGRES estimates the missing entries according to Equation 1; CORR computes correlations and standard deviations; XMISS generates a data presence-absence matrix; GRINV is a matrix inversion routine that was published by Kaiser and Dickman (1972). The set also includes a matrix printing and punching routine. Input. The job deck consists of the following cards. Card 1 is the alphameric title; Card 2 specifies the number of rows (N) and columns (NP) of the data matrix; Card 3 contains the choice of procedure for computing R (NR) and the number of iterations (NRUN) , and it contains an option for punching the data matrix with estimated missing entries (NPU); Card 4 is the data format card (F-type variable format); Card 5 contains the code for missing entries. The next cards contain the raw data matrix. Each row of the data matrix must begin on a new card. The use of more than one card per row is permitted. Output. The printed output includes the titling information and, for each iteration, the correlation matrix, the data matrix with estimated missing entries, and corresponding means and standard deviations. The proportion of missing entries is also reported; the program gives a warning when this proportion exceeds the limit of .20. The data matrices with estimated missing entries can be punched as desired. Restrictions. The data matrix may not have more than 200 rows and 10 columns. These limits can easily (2) (1)

A transformation program for normalizing data

A central concern in the use of parametric statistics is the extent to which deviations from the basic assumptions erode the power of a statistical test. Numerous empirical studies have been performed (Boneau, 1960; Donaldson, 1968; Lindquist, 1953; Norris & Hjelm, 1961) that demonstrate the substantial robustness of most univariate tests. It is hopeful to assume that univariate robustness will generalize to the multivariate case, but at this time empirical proof is in short supply (Davidson, 1972; Olson, 1976). As a result of this situation, it behooves the multivariate investigator to be somewhat more sensitive to scaling, normality, and homogeneity of variance considerations than his univariate brethren. Winer (1971), in a discussion of measurement and transformation, suggests three basic monotonic transformations: square root, arcsin, and logarithmic. All of these are effective in stabilizing variances. However, these transformations, with the exception of the logarithmic and square root in the case of positive skewness, are not notably effective in normalizing distribu tions. Thurstone (1959) suggested a monotonic transformation to create scores of ranked data. The transformed value is the difference in the height of the normal curve at the upper [f(Xk)] and the lower [f(XkdJ bounds of the corresponding interval, divided by the area (Pk) bounded by the curve within that interval: ZT' [f(Xk_ d f(Xk)] IPk, where ZT is the transformed value. It can be shown that this transformation sets the means to zero, the variances are homogenized with the upper limit approximately equal to one, and the maximum possible normalization of the distribution occurs under the scale limitations. Thus some normalization occurs with distributions of any shape, and this suggests greater generality than either the logarithmic or square-root transformations. This program accepts input data, transforms them according to the preceding formula, and outputs the new values. Input. The input consists of (1) raw data, (2) format card, and (3) program parameter cards, including (a) the number of cases, (b) the total number of variables, (c) the number of variables to be transformed, (d) the maximum number of missing values for any variable, (e) a flag indicating whether missing values should lead to deletion of the entire case or just the particular missing value for the case at hand, (f) the value to be substituted for all missing values, and (g) an estimate of the sum of the number of different values for each variable to be transformed. Output. As the program is currently written, the transformed values are output as punched cards in the prespecified format. Computer and Language. The program is written in PL/I and currently is operating on an IBM 360/65 under the OS/MVT-HASPsystem. Portability. The program should be operable on systems with PL/I by modifying the job control language appropriate to the facility. The source listing includes sample input and output to assist in this process. Availability. The source listing and documentation may be obtained by writing John E. Langhorne, Jr., at the Iowa Mental Health Authority, University of Iowa, Oakdale Campus, Oakdale, Iowa 52319.

LEVTREND: A FORTRAN program for analyzing and displaying the results of repeated measures across multiple factors

LEVTREND is a FORTRAN program written to analyze and display in a ready-for-publication form the results of a N + 1 factor (either as levels or as groups) by N repeated-measures design. It uses a variable formatting technique that allows the user to either develop his own input data layout or use a free-form input format. Input. The number of factors (levels or groups), the number of subjects in each factor, and the number of repeated measures are read in from a parameter card. The second input card is the data input format. The data are then read from data cards using the format described in the data format card. Output. The output is displayed in two tables. Table 1 displays the marginal means and standard deviations for each level and repeated measure, as well as those for each I by J cell. Table 2 displays the analysis of variance summary table of the multiple-factor by repeated-measures design in a form that follows the American Psychological Association (1974) standards. Capacity. LEVTREND is set up to handle up to 200 subjects dispersed among N + 1 groups, with each subject having up to 40 repeated measures. The program's capabilities may be enlarged by user alterations of the appropriate dimension statements. A minimum of 20K words of memory is needed to load the program. Compiling time is less than .0006 h. Load and execution time varies depending on the amount of data. Computer. LEVTREND may be used with a Honeywell 66/60, Honeywell 635, or any IBM computer that supports a WATFN compiler. Table 1

A generalized nonparametric ANOVA program (Version 2)

The program discussed in this paper is designed to (1) compute various nonparametric ANOVA statistics (Cochran, 1950; Friedman, 1937; Kruskal & Wallis, 1952), (2) compare the value of a given statistic with the chi-square values required for significance at the .05 and .01 levels, (3) perform a priori or post hoc trend analyses (Ferguson, 1965, 1971; Marascuilo & McSweeney, 1967), and (4) carry out post hoc multiple comparisons (Dunn, 1964; Rosenthal & Ferguson, 1965; Nemenyi, Note 1). Input. The job deck consists of some subset of the following cards (depending upon the analyses requested by the user: problem card, contrast matrix format card, contrast matrix card(s), levels format card, levels card(s), data format card, sample size card(s), data deck, and last card. The problem card indicates the nonparametric ANOVA test desired, the number of samples (or experimental conditions), and the specific a priori or post hoc analyses to be performed. If post hoc comparisons (other than all pairwise comparisons) are desired, the contrast matrix format card is an F-type variable format card that indicates the location of the coefficients for the comparisons on the subsequent contrast matrix card(s). Similarly, if a post hoc trend analysis is desired, the levels format card (for unequal intervals) is an F-type variable format card that indicates the location of the level magnitudes on the accompanying levels card(s); for equal intervals, the levels format card and levels card(s) are omitted. The data format card is an F-type variable format card that indicates the location of the raw scores (or ranks) on the data cards. It is followed by a card (or cards) indicating the size(s) of the sample(s). The arrangement of the data deck varies according to the specific nonparametric ANOVA that is to be performed. Specifically, for the Kruskal-Wallis test, the data are punched by sample with the data for each sample beginning on a new card. However, for the Friedman test and the Cochran test, the data are punched by subject (or group of matched subjects) with the data for each subject (or group of matched subjects) beginning on a new card. Finally, if the user wishes to terminate the program, the last card must have the word FINISH punched in columns 1-6. On the other hand, if the user wishes to analyze another set of data, the last card is a blank card and the job deck is arranged sequentially (as described

A computer program for Likert format questionnaire analysis

On college and university campuses, Likert format questionnaires are used for student evaluation of diverse aspects of courses, often with multiple items ~rouped into ~ets with a common referent (e.g., instructor, assignments, presentations, etc.). Contrary to summated rating scales which yield a total score to place a respondent somewhere on a continuum of agreement-disagreement toward the attitude being measured (Kerlinger, 1973), course evaluation questionnaires are typically analyzed to obtain respondent group means to each item or to sets of items. Moreover, the instructor examines the number and percentage of respondents selecting each al~er.native and makes comparisons among items within a set and between sets of items to determine relative strengths and weaknesses of the course. While subprograms of larger statistical analysis packages, such as SPSS (Nie, Hull, Jenkins, Steinbrenner, & Bent, 1975), will perform analyses such as those described, they are often inappropriate because they (1) require a computer system large enough to support the entire package, (2) cannot perform an analysis of individual items and sets of items. simultaneously, and (3) generate more output than IS necessary while requiring extensive variable and parameter definition. The program described in this paper performs the an~lyses typically sought for Likert format questionnam~s ~suc~ as ~ourse evaluations) while overcoming the Iimitations Imposed by larger generalized statistical analysis packages. Input. The job deck consists of the following: title card~, a. problem. parameters card, item group specification card, Item group label cardts), optional question and response choice label cards, a data format card, data deck, and a last card. The first three cards describe the problem in a text which is reproduced on the output. The problem parameters card indicates the number of respondents, the population size, the number of item sets, and user preference for optional alphanumeric labeling. The next card specifies the number of items in each set (or the total number of items if they are ungrouped) and is followed by item group labels (one per card to a maximum of 80 characters). If the user selects alphanumeric output labeling, the next cards contain the questions (one per card to a maximum of 80 characters) and the response alternatives (one per card to a maximum of 20 characters) in the same

A computer program for randomization tests for predicted trends

When experimental treatments vary quantitatively along a dimension, experimenters may want to test hypotheses with tests sensitive to linear, quadratic, or other trends in the measurements over experimental treatments. Standard parametric trend analysis is sometimes used for that purpose, but the probability tables are based on a random-sampling model. This makes them inappropriate for the typical psychological experiment, in which there is random assignment to treatments but not random selection of subjects. A computer program for randomization tests for trend for both independent groups and repeatedmeasures designs has been written. The user can employ an exact randomization test that is based on all divisions of the data or, when the number of divisions is very large, an approximate randomization test based on a random sample of all possible divisions selected by a random number generator routine. An approximate randomization test is a perfectly valid test and is almost as powerful as an exact test (Edgington, 1969). . The randomization tests for predicted trends test the hypothesis that all levels of the independent variable have the same effect, that is, the null hypothesis of no treatment effect. Just as a predicted direction of difference can be incorporated into a t test to make it more sensitive, so can predicted trends make a test of a difference between treatments more sensitive when there are more than two treatments. Very specific predictions can be utilized. For example, instead of just predicting a linear trend, an experimenter can predict a linear downward trend if he expects the response measures to drop for higher values of the independent variable. Or, instead of simply predicting a quadratic trend, the experimenter, can predict aU-shaped quadratic trend of response measures and the value of the independent variable about which the response measures will be symmetrically distributed. Any standard mathematical functional relationship can be predicted. Also, the experimenter can use predicted trends that are not readily specifiable by any of the common mathematical functions, such as a trend in data from an earlier experiment that is being replicated. The experimenter indicates his predicted trend by providing numerical values (coefficients). Each coefficient is transformed into an expected mean value. The test statistic is where nk i! the number of subjects taking the kth treatment, Xk is the mean of the scores for the kth treatment, and EMk is the expected mean for the kth treatment. The test statistic is the weighted sum of squared deviations of the means (for any particular division of the data) from the corresponding expected means. The probability value (significance) associated with the experimental results is the proportion of the data divisions (randomizations) that provide a test statistic as small as the value associated with the obtained results. Randomization tests for trend are discussed in more detail elsewhere (Edgington, 1975), and examples of the application of such tests to experimental data can be found in an article by Price and Cooper (1975). Limitations. The program is limited to 20 treatments and a maximum of 1000 data points. Input. The setup for an analysis is as follows(1) Title and parameter card: columns 1-40 = title; columns 41-45 = number of treatments; columns 46-50 = number of data points per card, if repeated measures; for independent groups analysis, leave space blank; columns 51-55 = any nonzero digit for performing an exact randomization test. (2) Size of groups card: columns 1-4 = number of scores for Treatment 1; columns 5-8 = number of scores for Treatment 2, etc. (3) Coefficients card: columns 1-4 = coefficient for Treatment 1; columns 5-8 = coefficient for Treatment 2, etc. (4) Input format card: e.g., (F4.l). (5) Data deck. Output. The computer output for the program includes the title, the mean for each treatment, and the significance or probability value. Language and Computer. The program is written in FORTRAN IV and has been tested on a CDC Cyber 70. Because the random number function may not be standard for all systems using FORTRAN, the user should check his system for the random number function to call. Availiability. A source listing and user's manual, which includes sample problems, can be obtained free by writing E.S. Edgington, Department of Psychology, University of Calgary, Calgary, Alberta, Canada.

A computer program for ordering-theoretic data analysis

Ordering theory, a measuremen t model which ex­ tends scalogram analysis to include nonlinear item or task hierarchies in unidimensional as well as multidimensional configurations, allows for both the determination of an item or task hierarchy and the testing of a hypothesized hierarchy among a set of items or tasks. The prerequi­ site relation employed to generate the hierarchy is derived from formal logic: Item i is prerequisite to item j if and only if the response pattern (0,1), where °rep­ resents a failure on item i and 1 represents a success on item j, occurs infrequently. That is, the response pattern (0,1) is disconfirmatory of the hierarchical relation, item i is prerequisite to item j. To overcome the deterministic limitation shared with scalogram analysis concerning an inability of the model to consider random error occurrences in the item or task response data, ordering-theoretic analysis in­ corporates preset tolerance levels to establish the num­ ber of disconfirmatory response patterns that will be accepted in defining a prerequisite relation between two items. A prerequisite relation, whether hypothesized a priori or generated by the analysis, is accepted only if the frequency of disconfirmatory response patterns is less than or equal to the frequency of such response patterns established by the tolerance level. Detailed discussions of ordering-theoretic data analysis have been provided elsewhere. Airasian and Bart (1973, Note 1) articulated the general nature of order­ ing theory. Bart and Krus (1973) described an ordering­ theoretic technique by which item or task hierarchies could be determined. Krus and Bart (1974) discussed an application of the technique to multidimensional item scaling. Moreover, the technique has been applied to diverse data, including Piagetian task responses (Bart & Airasian, 1974), propositional logic game item responses (Airasian, Bart, & Greaney, 1975), and various attitudinal data (Bart, 1972a, b). The program discussed in this paper searches out all of the prerequisite relations between all item pairs as described above, employing a user preset tolerance level(s) for each testing. Input. The job deck consists of the following cards: title cards, a problem parameters card, tolerance level card(s), output options card, a data format card, a

UMAVC: A program for computing comparisons in multifactor designs with unequal cell Ns

While some computer center libraries include programs that perform comparisons for multifactor analysis of variance (ANOVA) designs, these programs are usually limited to designs with equal Ns. Program UMAVC extends these basic capabilities to include factorial designs with unequal Ns (Keppel, 1973; Myers, 1972). The program employs unweighted means techniques to assess comparisons for main effects (example: Acomp) and for interactions (example: Acomp by B by C). Description. This program consists of two major segments. The first segment performs one-, two-, three-, or four-way unweighted means ANOVAs for standard factorial designs (fixed effect only) having either equal or unequal Ns; this program segment is similar in design to Veldman's (1967) AVAR23 program. The second segment performs comparisons requested by the user. These comparisons may be orthogonal or nonorthogonal, or tests for trend depending upon the coefficients that are specified. Input. Three program control cards precede the data: an ANOVA problem identification card, an ANOVA design card, and a data format card. The data is read in accordance with the user-specified format and is arranged with the subscript of the last factor varying the fastest. Cards containing the Ns are placed before each cell of data cards. A card containing the comparison problem identification immediately follows the data. Cards specifying the desired comparisons and their coefficients complete the deck setup. Output. Output from UMAVC consists of (l) a standard unweighted means ANOVA table including the probabilities of the computed F ratios, (2) means and Ns, and (3) a comparison table including sums of squares, degrees of freedom, mean squares and F ratios accompanied by their associated probabilities. Restrictions. The number of levels of each ANOV A factor must not exceed 10. The program can analyze only one comparison per factor in a given run; different comparisons for different factors may be analyzed in a single run. In the case of trend comparisons, for example, to investigate both linear and quadratic trends for factor A would require two runs, while a linear trend for factor A, a quadratic trend for factor B, a cubic trend for factor C, and a quartic trend for factor D could be investigated in a single run. Computer and language. The program is written in FORTRAN IV and was developed on an IBM 370{155 with virtual memory. It executes in approximately 192K of core; reducing the maximum number of levels for the ANOV A factors below the present value of 10 would greatly reduce the program's core requirements. Compilation time is approximately 30 sec. Data sets of average size may be analyzed in 5-10 sec of CPU time. Two direct access devices are required. The program consists of a mainline and 13 subroutines. Availability. A documented listing of UMAVC is available at no cost from the first author at: Southern College of Optometry, 1245 Madison Avenue, Memphis, Tennessee 38104.

An ANOVA program for Latin square designs involving order effects

By using a twoor three-factor Latin square design with repeated measures on two factors, the researcher can determine the variation due to order as well as that due to the by order interaction. In the two-factor design, the two factors would be treatment and order. In the three-factor design, the additional factor could be either a classification factor (e.g., grade level, sex, anxiety level. etc.) or another treatment. The characteristics of these designs and/or the computational procedures are described in statistics books commonly used by behavioral scientists (c.g., Bruning & Kintz, 1968, pp. 84-105; Lindquist, 1953, pp. 273-281, 285-288; Myers, 1972, pp. 286-300; Winer, 1971, pp. 712-717, 727-736). Gaito's (1961) comprehensive examination of the problems associated with repeated measurements designs includes a lucid discussion of the analysis of order effects by means of a two-factor Latin square design with repeated measures on both factors. The program discussed in this paper performs an ANOVA for Latin square designs of the types described above. Input. The job deck consists of the following cards: a problem card, a Latin square matrix format card, the Latin square matrix card(s), the label cards, a data format card, the data deck, and a last card. The problem card indicates the type of design, the number of levels for each factor, the number of groups, and the number of subjects in each group. The Latin square matrix format card is an F -type variable format card which includes the location of the numerals corresponding to the levels on the accompanying Latin square matrix card(s). Each row of the Latin square matrix contains a set of numerals that specify the order of presentation of the levels for a given group. In this matrix, there should be as many rows and columns as there are levels, The label cards (one per factor) contain the alphanumeric labels for the factors. The data format card is an Fvtype variable format card which indicates the location of the raw scores on the subsequent data cards, Each of the data cards must contain the data for one subject; however, the use of more than one data card per subject is permitted. Finally, if the user wishes to terminate the program, the last card must have the word FINISH punched in Columns 1-6. On the other hand, if the user wishes to analyze another set of data, the last card is a blank card and the job deck is arranged sequentially (as described above) beginning with the problem card Output. The printed output includes (a) the labels for the factors and (bl an analysis of variance summary table (i.e., sources of variation, sums of squares, degrees of freedom, mean squares, and F ratios) which is presented in a form similar to that found in many behavioral science statistics books (e.g., Bruning & Kirtz, 1968; Lindquist, 1953; Winer, 1971). Computer and language. The program is written in FORTRAN IV for processing by computers in the IBM 360 (or the CDC 6000) series. Well documented, it has variable names that are mnemonic, and correspond to the verbiage used in the computational steps outlined by Bruning and Kintz (1968, pp. 84-1(5), to facilitate modification by users. Restrictions. The program has the following limitations: (a) the design can have either two or three factors with repeated measures on two of the factors, (b) each factor can have a maximum of 10 levels, (c) the number of levels must be the same for the two repeated measures factors, and (d) there must be an equal number of observations in each cell. Availability. Copies of this paper, test data, and a source listing, which includes printed output for sample problems for twoand three-factor experimental designs, may be obtained without charge by writing to James 1. Roberge, Temple University, Department of Educational Psychology, Philadelphia, Pennsylvania 19122.

A regression program for Tukey’s test

where Xi = I is a member of Group 1. 0 otherwise: the bi are regression coefticients; and e is the error in prediction. Each of the k I models leaves a different Xi out of the equation. which allows the group left out to be compared to all other groups. The test of signiticance for each regression weight (a t test) is transformed to a value that can be compared to the Studentized range statistic by multiplication by >{i. Alternatively. the values in the tables of the Studentized range statistic could be divided by ..[2. and the t values could be assessed directly. The method used in this program is fully described in Williams (1974). The assumption is made when using Tukey's test that each group has the same number of scores. Moderate departures from this assumption do not render the test invalid. but rather cause the procedure to become approximatc. Description. This program performs a one-way analvsis of variance and Tukey's test for multiple comparisons. The data cards for each observation must contain the criterion score and k (where k IS thc numi}cr of groups) group membership variables. The group mcmhcrshlp <Inahlcs must be coded 1 to indicate membership in a grnup and (J ( thcrwisc. Input. thrcc cards prcccde thc data cards. Card 1 contains pn1h1em identification and allows Columns 1-80 for whatever description the USCI' preters. Card 2. a control card. requires the numbcr of obscrvations. thc numbcr of groups. and an option for printout of the data. Card 3 is a format card in F format. The criterion variable must be tirst. followed by the group membership vanahles. It \anables arc not punched in this order. use a T format to rcordcr.