Lloyd - Concurrent Prediction of Dropout and Grade of Withdrawal

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983

CONCURRENT PREDICTION OF DROPOUT

AND GRADE OF WITHDRAWAL’

DEE NORMAN LLOYD

Mental Health Study Center

National Institute of Mental Health

EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT1976, 36, 983-991.

A multiple regression was used to predict the grade in which

307 male and 200 female secondary school dropouts would leave

school. Predictors were twenty measures derived from sixth-gradeschool records. Results indicated that a combination of four

measures would significantly predict grade of dropout two to six

years in advance of the time students left school. Comparison ofresults with measures previously found to differentiate dropoutsfrom graduates showed considerable overlap in the prediction of

(a) grade of dropout and (b) the outcome of high school dropout vs.

graduation. It was concluded that the more inclusive concept, level

of educational attainment, can account for both the differences

between dropouts and high school graduates and the differences

between dropouts who leave at different points in their secondaryschool education.

OF the many studieson

the characteristics of high school dropouts,few have used partialling techniques to determine independent rela-

tionships of variables to school dropout or graduation or the poten-tial multiple prediction from a group of variables. In the few studies

in which multiple correlation or discriminant function analyses were

used (Childers, 1965; Livingston, 1958; Opstad, 1958; and Urdal,

Cech, Hamreus, and Workman, 1963) the predictive value of the

studies has been limited because data were obtained from grades in

1

Requestsfor

reprintsand referenced

supplementarydata should be sent to Dee N.

Lloyd, Mental Health Study Center, NIM H, 2340 University Boulevard, East, Adelphi,Maryland 20783.

Copyright © 1976 by Educational and Psychological Measurement

at MICHIGAN STATE UNIV LIBRARIES on June 13, 2015epm.sagepub.comDownloaded from

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984 EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT

which dropouts begin to leave school (grades 8 and 9). Lloyd (1974),however, found that prediction of similar magnitude to that realized

in these four studies could be obtained when data were limited to

information available in the sixth grade. Another focus of dropout studies has been to compare dropoutsfrom early grades with dropouts from later grades (e.g., Moore,

1967; Nachman, Getson and Odgers, 1964). The general finding of

these studies has been that dropouts from later grades show a greater

similarity to high school graduates than do dropouts from earlygrades. Compared to late dropouts, early dropouts are characterized

by a higher number of course failures, more school grades repeated,lower median IQ scores, a higher rate of absence, parents with lower

educational and occupational levels, a higher frequency of brokenhomes, and lower achievement test scores. However, only one study(Stroup and Robins, 1972) has attempted to predict grade level of

withdrawal from a combination of measures.

The present study is an extension of the previous discriminant

prediction of dropout vs. graduation (Lloyd, 1974). It uses only the

dropout subjects from that study. The two major purposes were (a)to determine whether variables based on information available at the

sixth grade level would predict the grade at which dropouts withdrew

from secondary school, and (b) to compare the relationship betweenthe predictors of grade level of withdrawal with the composite pre-

viously found to predict the outcome of dropout vs. graduation.

Method

Subjects

Subjects were 507 dropouts, 307 male, 200 female, drawn from a

larger cohort of 4,075 students, who were followed from the 6th gradeto transfer, withdrawal, or graduation from high school. All subjectswere White (non-Negro).2

Subjects were classified as dropouts if they received official school

codes for withdrawal other than those specifying a transfer to another

school. This group combined what are referred to as voluntary and

involuntary withdrawals. Most dropouts, however, would be consid-

ered as voluntary with only 5% being classified in the categories of

(a) committed to an institution, (b) special case, (c) physical disability,or (d) economic reasons. The most common reason for dropout listedon the school records was the catch-all term, &dquo;16 years of age or over,&dquo;

2 Data for two smaller samples of Black students were also analyzed. Results are

available on request from the author.








985DEE NORMAN LLOYD

which was applied to approximately 90% of the male dropouts and

approximately 75% of the female dropouts. Dropouts with missingdata on any of the variables were not included in the analysis (27.9% ofthe males, 30.3% of the females).

Criterion

Codes assigned for Grade of Withdrawal covered three time periodsin each grade from grades seven through twelve: summer prior to the

grade, first semester, and second semester. Codes ranged from 01 for

the summer prior to the seventh grade to 18 for the second semester of

the twelfth graded The distributions of dropouts by Grade of With-

drawal are presented in Table 1. The modal Grade of Withdrawal was

the tenth grade for both sexes. A higher percentage of females than of

males, however, remained into the eleventh grade.

Predictor Variables

A total of 20 independent variables was derived from information

on elementary school permanent record cards or on classroom record

sheets for standardized test scores.

Age in months in the sixth grade (Age) was used largely as a

measure of the number of nonpromotions in elementary school

grades. A dichotomized variable of regular progression vs. retention in

one or more grades from the first to sixth grade (Retention) was also

included as a measure of retention.

The educational level of both the father and the mother and the

occupational level of the father as of the sixth grade were used as

measures of socio-economic background. Education of Father and

TABLE 1Grade of Withdrawal for Male and Female Dropouts

3 Grade of Withdrawal was coded to allow investigation of differences between season

of dropout as well as grade of dropout. It was not presumed that an 18-interval scale

would detect significant variance among dropouts better than a 6-interval scale repre-

senting the six secondary school grades.









Education of Mother consisted of three categories: elementary, highschool, and beyond high school. Occupation of Father consisted of

seven categories adapted from the Hollingshead occupational scale of

the Index of Social Position.’

The number of siblings of the subject, whether or not the motherwas employed outside of the home (Employment of Mother), and

marital status of parents were measures of family characteristics.

Number of Siblings was coded directly. Employment of Mother was

coded 1 if the mother was not employed outside the home and 2 if she

was employed. Marital Status of Parents was considered to be a gross

measure of intact or broken home. The two categories of the variable

indicated ( 1 ) that the subject’s natural parents were alive and married

or (2) that the natural parents were separated, divorced, deceased, or

remarried.

Marks received in the sixth-grade courses of reading, language,spelling, arithmetic, social studies, and science; the average of these

marks (Grade Point Average); and the number of days absent in the

sixth grade (Absence) were used as measures of school performanceand behavior. Course marks were coded on a 3-point scale represent-

ing below average, average, and above average performance as judgedby the course teacher. Absence was coded on an eight-category scale:

0-5, 6-10, 11-20, 21-30, 31-40, 41-60, 61-90, and more than 90 daysabsent.

The sixth-grade standardized test scores were the IQ score for Total

Mental Factors from the California Test of Mental Maturity (CTM MIQ score), elementary short form, 1950 edition; and the Total Read-

ing, Total Arithmetic, and Total Language scores from the California

Achievement Test (CAT), elementary battery, 1950 edition. The CAT

scores were grade-equivalent scores.

Results

Prediction of Grade of Withdrawal

Results of stepwise multiple regression analyses predicting the gradelevel dropouts left school are summarized in Table 2. Fifteen of the

twenty sixth-grade measures were significantly related to Grade of

Withdrawal for both males and females.

All standardized test scores, marks in sixth-grade courses, Absence,and Age were related to when a student would leave school. Only two

family background measures, however,were

significantly related to

4

Occupational codes are inverse with a code of I representing the highest occupa-tional level. Correlations have been reflected so that positive relationships are associatedwith higher levels.








987DEE NORMAN LLOYD

TABLE2

Zero-Order Correlations and Beta Coefficients for Multiple Correlations with Grade of Withdrawal

. Not significant at the .05 level.

Grade of Withdrawal. Education of Father had a significant correla-

tion with the criterion in both samples, and Number of Siblings was

related to the criterion only in the male sample. Although significant,these correlations were low, the highest being -.16. A combination of four variables produced a significantly higher

prediction of Grade of Withdrawal than did any single variable.Multiple correlations were .503 for males and .442 for females. Each

variable in the regression equations had a significant beta weight (p <

.05) and each increased the total variance accounted for in the crite-

rion by more than 2%. The standard errors of estimate indicate that

approximately two-thirds of the dropouts withdrew within a range of

one grade before to one grade after their predicted grade of with-

drawal.

Three of the four variables in the equations were the same in both

samples: Age, Absence, and CAT Arithmetic score. The additionalvariables were similar in that each was a measure of achievement.

CAT Reading score appeared in the equation for males, Mark in

Spelling for females. The direction of the relationships indicated that









dropouts from earlier grades were older, absent more days, and lower

on tested arithmetic achievement than were dropouts from later

grades. In the male sample, dropouts from earlier grades had lower

reading achievement scores than did dropouts from later grades.

Among females, early dropouts had lower marks in spelling than didlate dropouts.

Relationships to Prediction of Dropout or Graduation

With the finding that sixth-grade information would predict Grade

of Withdrawal, one possibility would be to use this information in

connection with the findings from the prediction of dropout or gradu-ation (Lloyd, 1974) to calculate the joint probability that an individual

may become a dropout and if so, an early dropout. Although thisapproach would be prediction of failure, the technique is the same as

that used in personnel classification to predict jointly occupationalplacement and success in that occupation (Rulon, Tiedman, Tatsuoka,and Langmuir, 1967). Similarity in the results with those previouslyfound to predict dropout or graduation, however, raised the questionof whether a joint prediction was warranted or required. In each

sample, two of the four variables predicting Grade of Withdrawal

were among the most powerful predictors of dropout (Age and CAT

Arithmetic for males, Age and Absence for females). The significantcorrelations of other measures in the battery with both criteria also

suggested similarity in the indirect contributions of variables to both

predictions. When one predicts whether a student will become a drop-out or a graduate is one also predicting the grade level at which he will

withdraw?

To test the overlap between the two predictions, a score on the

discriminant variate that differentiated dropouts from graduates(Lloyd, 1974) was calculated for each of the dropouts. This discrimi-

nant was composed of the following variables listed in Table 2: (a) 1, 3,4, 5, 6, 12, 19, and 20, for males, and (b) 1, 3, 4, 5, 6, 14, 16, and 20, for

females.

The following equations give the normalized scaled coefficients for

the discriminant variates Vm (for males) and V, (for females):

~ = -.599zi + .196z3 - .349z,

+ .219z6 - .205z, + .197z,2 + .435z1s + .404z2o (1)

~ = -.402~ + .189z3 - .301 z,+ .164zs - .319ze + .472zI4 - .5252i<, + .291z2o (2)

In the previous study, these discriminants produced an overall cor-








989DEE NORMAN LLOYD

rect classification of dropouts and graduates of approximately 75% in

each sample and had multiple correlations predicting dropout vs.

graduation of .532 and .482 for males and females, respectively.

The discriminant variate was added to the original battery of inde-pendent variables and a stepwise multiple regression with Grade of

Withdrawal was recomputed. As hypothesized, the correlation of the discriminant variate with the

criterion was the highest in the set, .467 for males and .382 for females.

Alone it accounted for only 3.5% (males) and 4.9% (females) less

variance in Grade of Withdrawal than was afforded by the equationsshown in Table 2. Variables making a significant prediction of Grade

of Withdrawal in combination with the discriminant were Absence in

the male sample, and the Mark in Spelling and Age in the female

sample. The multiple correlations associated with these equations were

.486 for males and .425 for females, only slightly lower than the

multiple correlations produced by the optimum equations for predict-ing Grade of Withdrawal.

Discussion

The first

analysisrevealed that

dropoutsdiffer on characteristics in

such a way that the grade in which they will leave school can be

predicted from sixth-grade data. The second analysis showed that

there was considerable communality between the prediction of

whether a student will become a dropout (or graduate) and the predic-tion of the grade level of his withdrawal. When one is predicted, to a

large extent, the other is also forecast.

The implication of the close relationship between the two criteria is

that there may be one dimension underlying both of these predictions.

This dimensioncan

be best describedas

level of educational attain-ment. The distribution of discriminant scores used to predict Grade of

Withdrawal was a truncated distribution, excluding the scores of

graduates. If the criterion were expanded to include eventual level of

educational attainment of graduates, would the prediction be in-

creased ? Several lines of evidence suggest that it would. First, amongthe predictors of withdrawal grade were achievement test scores and

teachers’ marks, which traditionally have been found to be the best

high school predictors of college performance. Although the measures

in this study were from the last grade in elementary school, the highintercorrelations of teachers’ marks and achievement scores longitudi-nally would support the existence of some predictive relationship over

a more extended period of time. Stronger evidence comes from the

study of Bachman, Green, and Wirtanen (1971) who hypothesized a









continuum of educational attainment that would hold across three

groups: high school dropouts (from the tenth grade on), high school

graduates, and high school graduates continuing to college. Consist-

ent, significant relationships found in this study support the con-

tention that factors predicting educational attainment in high school

can be extended to prediction of educational attainment beyond highschool. An additional study (Stroup and Robins, 1972), which is

intermediate in point of data collection between the Bachman, Green,and Wirtanen study and the present study, provided a high multiplecorrelation (.64) between pre-ninth-grade predictors and a criterion of

five groups, dropouts from grades nine to twelve and a group of highschool graduates.

Although &dquo;dropout&dquo; has been a useful concept for research, its ill-defined nature has produced confusion as well as inappropriate con-

notations. Because of the association of dropout with delinquency and

unemployment, there have been confusions of cause and effect in these

relationships. The stigma associated with dropout also presents the

danger that labeling students as potential dropouts will have the

negative consequence of making them the victims of the very efforts

designed to help them. Viewing dropout in terms of level of educa-

tional attainment may reduce the stigma by putting the focus on the

real problems involved-the factors in a child’s capacity, his social

background, and importantly, the school system-that limit or en-

hance his educational development. Evidence that prediction of with-

drawal from secondary school can be made from elementary school

data, three years prior to the time when dropouts leave in substantial

numbers, clearly indicates dropout is only an event marking the end of

a long, developing process. There is also evidence that the high school

dropout phenomenon is not as exceptional as might be thought.

Rather,it contains the elements that influence

developmentover the

entire range of educational attainment.

REFERENCES

Bachman, J. G., Green, S., and Wirtanen, I. D. Dropping out—

Problem or symptom? Ann Arbor, Michigan: Braun-Brumfield,1971.

Childers, R. D., Sr. The identification of potential school dropouts by

discriminant analysis

.

(Doctoral dissertation, University ofGeorgia) Ann Arbor, Michigan: University Microfilms, 1965, No.65-2462.

Livingston, A. H. High-school graduates and dropouts—A new lookat a persistent problem. School Review, 1958, 66, 195-203.

Lloyd, D. N. Analysis of sixth grade characteristics predicting high








991DEE NORMAN LLOYD

school dropout or graduation. JSAS Catalog of Selected Docu-

ments in Psychology, 1974, 4, 90.

Moore, J. W. Reducing the school dropout rate—A report on the holdingpower project. Albany, New York: The University of the State of

New York, The State Education Department, Bureau of Guid-ance, 1967.

Nachman, L. R., Getson, R. F., and Odgers, J. G. Ohio study of highschool dropouts, 1962-63. Columbus, Ohio: Division of Research

and Division of Guidance and Testing, State Department of Edu-

cation, 1964.

Opstad, P. E. Non-scholastic factors associated with drop-outs frompublic school in Iowa. (Doctoral dissertation, University of Iowa) Ann Arbor, Michigan: University Microfilms, 1958, No. 58-2977.

Rulon, P. J., Tiedeman, D. V., Tatsuoka, M. M., and Langmuir, C. R.

Multivariate statistics for personnel classification.New York: Wi-

ley and Sons, 1967.

Stroup, A. L. and Robins, L. N. Research notes: Elementary school

predictors of high school dropout among Black males. Sociologyof Education, 1972, 45, 212-222.

Urdal, L. B., Cech, E. J., Hamreus, D. G., and Workman, D. J.

Dropouts: An analysis ofpersonal variables within the school situa-

tion. Olympia, Washington: Office of State Superintendent of Pub-lic Instruction, Research Department, 1963.


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Lloyd - Concurrent Prediction of Dropout and Grade of Withdrawal