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The identification of high-school dropouts identified as learning disabled: evaluating the utility of a discriminant analysis function.

* The impact of young people leaving high school without graduating presents an urgent issue for educators. In terms of functioning in society, Rumberger (1987) noted that young people who have dropped out, or have been released from school, generally have "serious educational deficiencies that will impair their economic well being throughout their adult lives" (p. 101). Reports from other major studies consistently describe a bleak outlook for individuals with incomplete basic educations (Edgar, 1987; Hess 1986; Kunisawa, 1988; Levin, 1972; Rumberger, 1987; Wehlage & Rutter, 1986). A consideration of this bleak outlook underscores the importance of developing a means to accurately identify students before they leave school as dropouts.

Despite the considerable attention afforded this issue, we are still searching for a consensus about what the term "high-school dropout" encompasses (Barber & McClellan, 1988; Hahn, 1987; Wehlage, 1986; Wehlage & Rutter, 1986). Some educators object to referring to any person as a dropout because of generally negative connotations, but the term has been used widely in earlier research. Within this study, use of dropout as a classification is not to imply any lack of respect for individuals in that group; the term should be considered synonymous with "person who has dropped out of school" or "person who has been dropped out of school." A person's status at the time he or she leaves school is recognized as being only one identifying characteristic, and no value judgment is implied. Furthermore, we consider the decision to leave school or that of being pushed out of school to be revocable. Many drop-outs do in fact return to school McMillian, Balow, Widaman, Borthwick-Duffy, & Hendrick, 1990) or complete a general educational development exam (Kirsch & Jungeblut, 1986; Kolstad & Owings, 1986; "News You Can Use," 1990):

Another key problem is defining what actions or conditions would cause a person to be included in the dropout classification. Hammack (1986), in a study of urban districts, summarized this problem in noting that "the most important conclusion of this [study] is that there is no single or standard definition [of dropout] utilized by the school systems contacted" (p. 337). Morrow (1986) helped to address this issue by offering a set of three criteria on which to determine dropout status: "(1) Is the student actively enrolled; (2) If not, has the student's enrollment been formally transferred to another legitimate institution; and $) Has the student been awarded a high-school diploma or its equivalent?" (p. 344). Those individuals for whom all three questions are answered in the negative are considered "dropouts." In this study, we employed this criteria to identify likely school dropouts during the 1987-1988 academic year.

In the present study, the issue of high-school dropout is examined in a subset of high-school students, those students who are identified as having learning disabilities (LD). Generally this subset comprises 4% to 5% of the total student population and is often characterized by having serious academic achievement problems and difficulties with social skills (see Reschley, 1988). In the district of study, the LD population accounts for 75% of the special education students at the secondary level and 75% of those who drop out of school.


Since research on students who drop out of school is extensive, though largely limited to samples of nondisabled youth, this review will be limited to research directly related to those variables employed in this study. These variables were selected based on a decision to employ a limited set of variables that represented individual, family, and school-level factors that were determined to be theoretically relevant to school dropout. The final selection was further limited by the need to utilize only those that were both readily available and determined to be accurate. Readily available variables were limited to those compiled in one of the school district's main computer databases. Variables such as school attendance, while supported by research (see e.g., Eckstrom, Goertz, Pollack, & Rock, 1986; Lloyd, 1976), were not utilized as the district does not provide for a central accounting of individual student attendance patterns. Of note is that accessible variables were also limited to only the most current information, as earlier information was routinely discarded (e.g., the family's socioeconomic status [SES] from the previous school year . Some variables, such as indicators of discipline problems, while also supported by research (Hahn, 1987; Levin, Zigmond, & Birch, 1985) were available but administration and staff had expressed serious concerns about their accuracy (Holland, personal communication, November 1989). Another example is that of student course failure or grade-point average- each was determined to offer an inadequate portrayal of actual performance because the majority of special education students in the district of study are graded on a nonstandard scale.

Research Relating to Ethnicity and Reading Ability

While it is true that a student is not born a "school dropout," he or she may have characteristics that are likely to be associated with or eventually contribute to his or her propensity to leave school prior to graduation. One such characteristic is that of race or ethnicity, an unalterable feature that may be related to dropping out of school. A second characteristic is the ability to read; the student who fails to develop this skill is at a distinct disadvantage in trying to succeed or survive in the school setting.

Ethnicity. Descriptive research examining the issue of school dropout relative to ethnicity is abundant. Rumberger (19$7), for instance, presented census data for 1984 with respect to school dropout among 16- to 19-year-olds. For the ages of 16-17 and 18-19, respectively, the following are dropout rates by ethnicity: Caucasian males (7.3% and 15%) and females (6.9% and 14%); Afro-American males (5.5% and 19.7%) and females (12.7% and 26%); and Hispanic males (13.6% and 26.2%) and females (12.7% and 26%). A second national study, a review of the High School and Beyond data set on the 1980 sophomore cohort sample (National Center for Educational Statistics, 1984), found the rate of school dropout to be the lowest among Asians (3%) and Caucasians (12%), while highest among Afro-Americans (17%); Hispanics (18%); and Native Americans (29%) (Peng, 1983). A third effort is presented in Hanimack's (1983) analysis of school district reports on school dropout in the Boston, Chicago, Los Angeles, Miami, New York City, and San Diego school districts. Across these districts, Hammack found a clear pattern that the dropout rate was highest among minority students and those with limited English language proficiency.

A number of less extensive efforts have also documented the rate of school dropout across measures of ethnicity. Hess (1986), for instance, found that for the 1982 class in the Chicago public schools, 47% of the Hispanics, 45% of the Afro-Americans, 35% of the Caucasians, and 18% of the Asians had left school without graduating. The Seattle public schools (1987) completed a study of school dropout and found the rate to be highest among Native Americans (42%), Afro-Americans (20%), and Hispanics (20%) and lowest among Asians (9%) and Caucasians (14%). A second study of the graduation and early school release patterns (i.e., school dropouts) of mildly disabled population students (learning disabled, behavior disordered, and mildly mentally retarded) in the Seattle schools (Blackorby, Edgar, & Kortering, in press) found the ratio of dropouts to graduates to be 2:1 among Afro-American, Hispanic, and Native American students, while the proportion was 1:1 or lower among Caucasian and Asian students.

Reading ability. A number of descriptive studies have portrayed the school dropout with respect to reading ability. Penty (1960) investigated the reading skills among 593 former high-school students from the Battlecreek, Michigan public schools, and found that the rate of school dropout was three times higher among "poor readers" (50%) than among "good readers" (15%). Voss (1966) reviewed the literature on school dropout and cited a study of male students who had dropped out of high school in the Rochester, New York public school district which found that dropouts had a median reading score at the 31 st percentile. Likewise, a study of school dropout in Ohio found that 75% had scored below the median age level in reading and that 53% scored in the lowest quartile Nachman, Getson, & Russell, (1963). More recently, Hammack's (1986) investigation of school dropout in the Chicago public schools found that the rate was 50% among students whose reading scores in the ninth grade were between the 4.7 and 6.7 grade level and 68% among those below the 4.7 grade level.

A number of studies have also compared the reading ability between samples of students who have dropped out of school to peers who have either stayed in school or graduated. Bledsoe (1959), in a 3-year study of one Georgia community, compared former 9th- and 10th-grade students who had dropped out of school to age peers who remained in school relative to scores on the California Reading Achievement Test. He found that those who dropped out of school had a mean level of reading that was one grade below that of peers. Combs and Cooley (1968) generated randomly selected samples of high-school dropouts and graduates from the Project TALENT database to compare reading ability. They found lower mean scores for the dropout sample on measures of reading comprehension (19 vs. 23.5) and table reading (1.9 vs. 5.5).

Curtis' (1983) study of school dropouts and graduates from Austin, Texas, relative to reading scores on the California Achievement Test found the dropouts to have a lower mean score (26th percentile) than the graduates (58th percentile). Likewise, an analysis of the High School and Beyond database (Alexander, Natriello, & Pallas, 1985) established that both the 1980 and 1982 sophomore cohorts who were identified as dropouts had lower mean grade level scores (4.8 and 5.3) than peers who remained in school in 1980 (7.2) and 1982 (8.5). Finally, Hahn (1987) reported that based on a national sample of noncollege-bound youth, those whose scores in reading and math fell in the bottom half were nearly nine times more likely to leave school as dropouts.

Correlational studies have also examined the relationship of reading ability and school dropout. Livingston (1958) utilized simple or direct correlational techniques to evaluate the relationship of staying in school to 24 elementary-level variables among a sample of 309 school persisters. He found a significant correlation between measured reading level and staying in school. Furthermore, in combination with variables representing participation in formal school activities, participation in informal activities, number of grades retained, and persons with whom the student resided, reading level accounted for 67% of the variance between the dropout sample and school persister sample.

Walters and Kranzler (1970) developed prediction equations for a sample of 414 school dropouts. The best equation determined that reading achievement, in combination with student intelligence quotient score, age, SES, and arithmetic achievement would accurately identify 91% of the dropouts. Lloyd (1976), meanwhile, performed a multiple regression analysis to predict the grade in which former students had dropped out of school. The results showed that reading achievement test scores, along with age, number of absences, and math achievement test score, could significantly predict, 2 to 6 years in advance, the grade level of leaving school. Finally, Hess (1986) reported that across the Chicago public schools' 63 comprehensive high schools for classes from the years 1982, 1983, and 1984, the percentage of students with below normal reading scores was the strongest predictor of school dropout (at a simple correlation of .854).

Family Socioeconomic Statug and Intactness

Family influence as a force for or against school continuation has been extensively studied in a number of ways; the most common factors studied are family SES and intactness. Steinberg, Blinde, and Chan (1984) summarized the findings of such studies on family SES as follows: "Virtually every study that has included social class as an independent variable has indicated that the lower SES strata are more likely to drop out of school than their more economically privileged peers" (p. 126). Schreiber (1963), meanwhile, emphasized that the home provides an environment in which "a child's attitude toward school is developed and nurtured" (p. 217). Masters (1969) and Mare (1980) further underscored the importance of family intactness by indicating thai students from broken homes are not likely to find the support and encouragement they need to keep them in school.

Family SES. From a descriptive point of view, Hollingshead's (1949, 1975) classic study of adolescents from one midwestern city portrayed a clear image of the school dropout relative to family SES. In this study, 100% of the students in the top two social classes and 92% of those in the middle class had remained in school throughout the duration of the study, yet only 11% and 59% of those from the lowest and second lowest SES class had done so. Tessner and Tessner (1958) reviewed 20 studies on school dropout and found that between 72% and 84% of all dropouts had come from low-income families. Similar evidence was found in Thomas' (1954) study: 37% of students whose parents were reported to be general laborers or factory workers were drop-outs, and 14% of those whose parents were white-collar or retired were dropouts. Kowalski and Cangemi (1974) reported that eight of nine dropouts came from the lowest social class. Young (1982), in a study of the school enrollment status of a national sample of 14- to 24-year-olds, found that based on a calculation of a within-race family income median, over 67% of Afro-American students and Caucasian students who had dropped out of high school came from families whose income was below the median of their respective ethnic group.

A number of studies have used measures of family SES to compare samples of school dropouts to peers who have either stayed in school or graduated. For example, Hathaway, Reynolds, and Monachesi (1969a; 1969b) found a higher rate of school dropout among male (38%) and female youth (32%) who had come from families of farm laborers than among youth from professional families (5%). Nam and Folger (1965) in their investigation of a national sample, established that 80% of the youth from families whose income was over $5,000 graduated, a sharp contrast to those from families with an income below $3,000 in which only 50% did so.

In a more recent study, Shaw (1982) reported that school dropout was much higher among a sample of female former students who had come from families with an income of $4,000 or less (39% and 55% for Caucasian and Afro-American, respectively) than among those from families with an income of $8,000 or more (15% and 26% for Caucasian and Afro-American, respectively). Peng (1983) found a higher rate of dropout (17%) among low SES former students than among former students from middle SES (9%) and upper SES (5%) families. Finally, the William T. Grant Foundation (1988) reported in a national study of noncollege-bound youth that three times as many students who drop out of high school come from families receiving welfare than do students who graduate.

A number of correlational studies have also examined the relationship of school dropout and family SES. Nam, Rhodes, and Harriott (1968), in a study of national census data on 16- and 17-year-old youth, found that low SES (along with variables representing non-Catholic religious identification and residence in the south) were significantly associated with dropping out of high school. Masters' (1969) study of representative census data from 1960 determined that dropping out of high school by age 16 or 17 was six times more likely among students from families whose parents had less than a fifth-grade education and a reported income of less than 3,000 (33%) than among students from families of parents who had graduated and reported family incomes of $19,000 or more (2%).

Walters and Kranzler (1970) employed it discriminant analysis function, utilizing family SES along with a math achievement test score to correctly identify 89% of the dropouts and graduates from among 414 students. For a sample of 1,400 students, Lloyd (1978) found that he could construct a discriminant analysis function that would correctly identify 60% to 70% of all school dropouts by utilizing data from the third-grade level on variables such as family SES, school achievement, and grade retention. Rumberger (1983) examined various predictors of school dropout and concluded that family factors, including SES, accounted for "almost all the racial difference in dropout rates" (p.199). Likewise, Wehlage and Rutter (1986), in another analysis of the High School and Beyond database, reported that after controlling for family SES, race "is not a variable that predicts dropout" (p. 376). In his study of the Chicago public schools, Hess (1986) also found a significant correlation between the dropout rate and the reported poverty rates among students as they entered high school.

Family Intactness. From a descriptive viewpoint, Brewer (1950) concluded from exit surveys with students who had voluntarily withdrawn from school that coming from broken homes was a major reason for students leaving school. In Maryland, Williams (1963) found that 20% of the students who had dropped out of school did not live with either of their natural parents and that an additional 10% lived with only one of their natural parents. Schreiber (1963) in a review of the findings relative to 10 characteristics related to school dropout, reported that more school dropouts than graduates come from physically and psychologically" broken homes. Finally, Beachum's (1980) investigation of 116 students who had been identified as potential dropouts found that only 58% of the males and 46% of the females lived with both of their parents, the remainder with one parent or in a foster or guardian situation.

Comparative studies on family intactness and school dropout date back to Cook's (1956) examination of 95 high-school withdrawals and 200 school nonwithdrawals. in this study, he found that personal family adjustment of the withdrawals was significantly poorer than the family adjustment reported by those who had stayed in school. Livingston (1959) reported that among a sample of former students from Illinois the graduates were much more likely to have parents who were still married than were those who had dropped out of high school. Similarly, a study of school persistence among students in Kentucky found that those who dropped out of school were more likely to have come from broken homes than were those who stayed in school (Martin, 1981). Shaw's (1982) study of school attendance patterns of young women found that only 13% and 36% of those from Caucasian and Afro-American families, respectively, who had always lived with both parents failed to complete school. Among those from Caucasian and Afro-American families that had been nonintact at one or more points in time, the rate of noncompletion rose to 23% and 41%, respectively.

Correlational studies on school dropout and family intactness began with Livingston g (1958) examination of 24 variables and school dropout. He found that the variable of family intactness in elementary school was not significantly related to school dropout. In contrast, Duncan (1967) found that, based on 1962 census data on 20- to 64-year-old-males, 30% of the variance in educational attainment was a function of four family variables' family intactness, family SES, family head's income, and number of siblings. Lloyd (1976), in an analysis of 507 secondary students who had dropped out of school, reported that parental marital status did not predict school dropout. However, an examination of the third-grade records of 788 boys and 774 girls who were known dropouts yielded a significant correlation between the marital status of parents and attendance in elementary and high school (Lloyd, 1978). Mare (1980) stated in his study of 33,500 males born before 1950 that school dropout was definitely correlated with "family origins," as measured by family intactness, level of income, and father's type of occupation. More recently, a classification function employing measures of family SES, placement IQ, and the presence of a two-parent household correctly classified 27 of 31 LD students who had dropped out of school (Zigmond, Thomton, & Kohnke, 1987).

School Transfers and District-Initiated Interruptions

Wehlage and Rutter (1986) and Fine (1986) emphasized the need to examine school-related processes if one truly wants to understand the problem of school dropout. Hess' (1986) study of school dropout among Chicago public school students pointed out that "efforts to diminish unnecessary [school] transfers and to give special treatment to students transferring into a school are obvious implications of this [finding as to the high dropout rate among transfer students]" (p. 46). Goodlad (1984) also noted the presence of an institutionalized process of "pushing out" unwanted students or an exercising of what he called the "hidden curriculum."

School Transfers. The study by Hess (1986) found that students who transferred from one high school to another had a higher rate of school dropout (56%) than did peers who did not transfer (40%). In the 63 comprehensive schools, those with 21% or more of their entering freshmen as transfers had a higher rate of student dropout (56%) than did schools with 20% or less of their entering freshmen as transfers (32%). Cook's (1956) comparative study of students who withdrew from high school and peers who persisted found that withdrawing students had more highschool transfers. In their study of school dropout and graduation among mildly disabled students, Blackorby et al. (in press) found those youth who graduated in 1986 and 1987 averaged fewer transfers (.42 and.45, respectively) than did peers who dropped out of high school during the 1986-87 school year (1.3).

Two correlational studies also offer information on school transfers and school dropout. The study by Livingston (1958), involving 163 graduates and 116 dropouts found that the number of elementary school transfers was not related to eventual graduation or dropout. However, Stroup and Robins (1972) found in their study of 400 Afro-American students who had dropped out of school that the number of elementary school transfers was significantly correlated to eventual school dropout.

District-Initiated Interruptions. Peng (1983) found in his examination of the High School and Beyond 1980 and 1982 sophomore cohorts that 13% of the males and 5% of the females who had dropped out of school in the 10th grade or later left because they were suspended or expelled; another 21% and 10% of the males and females, respectively, reported leaving because they had not gotten along with their teachers. The Children's Defense Fund, as cited by Hahn (1987), reported that 25% of all dropouts had been suspended from school at least one time prior to their final decision to leave school; another 20% had been designated as "behavior problems" by their classroom teachers. A survey of California school administrators showed that 32% agreed or strongly agreed that special education students drop out of school "because they [had] been suspended or expelled" (p. 27) (Jay & Padilla, 1987). The study of school dropout among mildly disabled youth found that those who were exited as graduates had fewer releases from school (.30) than had peers who were released under codes suggesting school dropout (2.24) Blackorby et al., in press). Felice's (1981) investigation of 226 Afro-American school leavers and 400 ethnic peers who stayed in school found that the proportion of students who had been placed on suspension or expelled significantly contributed to discriminating between the two groups.


The purpose of this study was to determine if an urban school district could make an accurate discrimination between LD students who are released as high-school dropouts and their LD peers who are released as high-school graduates. The basis of this discrimination is a linear discriminant function. If successful, the procedure would provide a first step in the effort to reduce the number of high-school dropouts--a determination of whether local districts can identify those LD students who are at risk of dropping out. In addition, the study made an initial comparison of LD school dropouts and LD graduates across variables that have been used in the literature to contrast regular education dropouts and graduates. Finally, the study offered local districts an opportunity to examine one technique that could be employed toward identifying likely school dropouts.


District Setting

Subjects for this study were from a large urban school district in the northwestern United States. The school district had an October 1987 enrollment of 45,119 students-4,160 (9%) of whom received special education or related services under the Education for All Handicapped Children Act. The school-age population for special education students was 45% white, 39% Afro-American, 7% Asian, 5% Latino or Chicano, and 4% Native American. As a measure of the family SES for district students, 34% of the students received either free or reduced-priced school lunches during the 1987-88 school year.

Sample Characteristics

The subjects were from two exhaustive populations of district students: 213 LD students who had their schooling interrupted under codes considered suggestive of school dropout and 100 LD students who graduated from high school. Subjects were assigned to either population when their school status reflected a change during the 1987-88 school year. The status change informs us that the students had been released from active student status due to a school-initiated release that reflects having been either dropped or graduated from school. This school district typifies other urban districts (see e.g., Hahn 1987; Hammack, 1986; Hess, 1986) by utilizing a number of release codes to remove students from active status with no one code to signify "dropout." For the purpose of identifying likely high-school dropouts the following release codes were utilized: unable to locate pupil, expulsion, habitual disruptive behavior, delinquent behavior, irregular attendance, suspension from building, age over mandatory attendance, completion of ninth grade, and exempted for poor/nonattendance. The presence of any one of these codes indicated that a student was no longer enrolled in school, had not formally transferred to another legitimate educational institution, and had not been awarded a high-school diploma or its equivalent. Furthermore, the majority of these students, under conditions of their release, could not come back to a comprehensive high school in the district for at least the remainder of the semester. Release codes that did not indicate high-school dropout are represented by the following: enrollment in public (or private) school outside (or inside) the district, moved out of the district, marriage, supervision by public agency, temporarily unavailable, and certificate of competency. The school release code of "graduated from high school" was used to identify high-school graduates.

The mean chronological age at the time of study was 18.3 years (SD =.75) for the LD graduate sample and 17.2 (SD = 1.4) for the LD dropout sample. The mean age and grade level at referral was 11.5 (SD = 3.5) and 4.8 (SD = 2.8) for the graduate group and 10.7 (SD = 3) and 4.8 (SD = 2.8) for the dropout group. Both groups had similar intelligence scores at the time of referral; they were within the lower part of the normal range. Specifically, the graduate and dropout groups had mean full scale scores of 89.4 (SD = 11.6) and 89 (SD = 10.3), respectively. Mean verbal (87.8 and 87.3) and performance (93.9 and 93.2) scores were also similar. At the time of school exit, the majority of both samples were enrolled in special education for 2 or more hours per day. The majority of graduates (77.5%) and dropouts (78.6%) were male.


Six discriminating variables were utilized in this study. All variable information was collected from the school district's databases and manipulated through the computer program, the Statistical Package for the Social Sciences (SPSS) (Norusis, 1986).

Individual Characteristics

Student ethnicity was obtained by accessing the main student database. Within this database, one variable field assigns the ethnicity of individual students into one of two categories: white or nonwhite. For the purposes of statistical analyses and measurement, a "I" was assigned to those students identified as nonwhite and a "O" was assigned to those identified as white.

The second variable, reading ability, was available within the district's special education database. Variable information was represented by the student's most recent reading score on the Wide Range Achievement Test, Level Two (Jastek Assessment Systems, 1984). Within the district, special education students are administered this test each fall and spring. Normal curve equivalency scores were utilized as measurements of reading ability.

Family Characteristics

The variable of family SES was accessed within the district's main student database. This information was provided through the use of the proxy--student eligibility for free or reduced-priced lunch programs. To qualify for either the free or reduced-priced lunch programs, parents must annually complete a two-page form that requests information on household size and weekly, monthly, or annual gross income and they must meet the stipulated income requirements. The annual income limits for the free lunch program ranged from $7,150 for a family with one child to $17,030 for a family with five children. The corresponding income limits for the reduced priced lunch program were $10,175 to $24,235. For measurement purposes, variable information was coded as a "2" for students qualifying for the free lunch program, a "1" for those on the reduced-priced lunch program, and a "0" for those paying full price for their school lunches.

The variable of family intactness was available within the main student database and was measured by the number of parents who were reported to be living with the student at the time of school registration for the most current school year. The school district annually records this information by assigning students to one of six categories: living alone, living with both parents, living with father only, living with mother only, living with guardian, living with agency, or living with spouse. In terms of measurement, the categories were coded as follows: a "0" was assigned to those students living with both parents or with spouse, a "1" was assigned to those living with their mother or father, and a "2" was assigned to those living with a guardian or agency or living alone.

School-related Factors

School transfer information was available within the district's school history database. This database records the students' school history while enrolled in the school district of study. Within the district, individual school transfers were denoted by the presence of I of I I transfer codes. The most frequently used codes included change in educational placement, parent request, promoting racial balance, and professional recommendation. Measurement of this variable was provided by a numerical count of the number of school transfer codes that actually resulted in the student having to change schools. Not included are those codes reflecting changes in the educational programming that may not have resulted in having the student actually transfer to another school or a school transfer for academic promotion, for example, going from a middle to a high school or elementary to a middle school.

The variable of district-initiated interruptions was also accessed in the district's school history database. Variable information was available on the number of times students had their education interrupted. As with school transfers, the information was limited to interruptions while the student was enrolled in the school district of study. These interruptions were represented by the presence of those same release codes used to indicate district-initiated interruption or likely school dropout. As with transfers, interruptions were measured by a count of the number of times that the student had been released from school. The final release code of interest was not counted as an interruption for the dropout sample since it represented the criterion for group membership. Likewise, codes that reflected school interruptions that were not initiated by the school (e.g., parents moving) were not counted.


Univariate Analysis

The set of six independent variables was analyzed individually to determine which variables, in isolation, were related to the criterion status of dropout or graduate. The presence of these relationships was evaluated with the t-test statistic. To control for Type I errors, each test was evaluated at the .01 level of statistical significance, making for an experiment-wise error rate of less than .06.

Discriminant Analysis

Discriminant analysis was utilized to evaluate whether the six variables could, in combination, construct a linear discriminant function that would differentiate between LD students who drop out of school and those who graduate. The procedure can be summarized for conceptual purposes by the following formula:


In this formula [D.sub.x] represents the score on the discriminant function, the b series are weighting coefficients (similar to beta weights in multiple regression), and the Z series are the standardized values of the variables. In the successful discriminant function, the discriminant scores are similar across members of the same group but yield respective group centroids that are sufficiently different. Similarly, individual scores on the discriminant function are sufficiently different to allow the equation to accurately distinguish, using the individual's discriminant scores, between the members of different groups. In other words, individual cases are assigned to the group that their discriminant score most closely approximates, and it is hoped that this classification is accurate.

The present study employs the "direct method of analysis," which simultaneously employs all of the variables. This method was chosen over the "stepwise method," which utilizes only those variables that in isolation prove to differentiate between the two groups at a statistically significant level. The "direct method" was deemed appropriate for this study because it allows the researcher to evaluate the interaction of all the theoretically relevant variables.


Univariate Analysis

The t-test was employed to evaluate the relationship between the criterion groups and each of six independent variables. The resulting group means, standard deviations, and corresponding t-values are summarized in Table 1. [TABLE 1. OMITTED] For three variables (ethnicity, reading, and family SES), differences between the two groups were determined not to be statistically significant. For the remaining three variables (family intactness, transfers, and releases), differences were found to be statistically significant at the .01 level.

When considering common rhetoric (i.e., dropouts come from minority groups, poor families, and have lower academic skills), the lack of differences between LD students who drop out of school and cohorts who graduate across measures of ethnicity, family SES, and reading appears noteworthy. Any inferences from these findings, however, should be tempered with consideration for several possible explanations. First, and perhaps foremost, despite the rhetoric, LD dropouts and LD graduates may be similar across measures of ethnicity, reading, and family SES. Second, the design of this study had limitations. For example, ethnicity was recorded as Caucasian or non-caucasian. It was speculated that this measurement might not adequately distinguish between advantageous and non-advantageous ethnic membership. This presumption, however, was addressed by analyzing the data with respect to specific ethnic group membership. Across the following five ethnic groups the proportion of dropouts and graduates was as follows: Asian (2% and 9%, respectively); Caucasian (36% and 34%); Hispanic/Latino (4% and 1%); Afro-American (54% and 51%); and Native American (4% and 5%). While differences were apparent between Asian students and Hispanic/Latino students, the size of these cells was too small 10 and 15, respectively) to substantially impact the findings. Similarly, family SES was limited to three levels of measurement. It is possible that finer scaling (e.g., family income in dollars) would have yielded more discerning information. Finally, the variable of reading was evaluated with the student's most recent score on the reading vocabulary subtest of the Wide Range Achievement Test (Jastek, 1984). It is possible that the reading vocabulary score did not adequately portray the students' reading ability.

As with those results that proved nonsignificant, one should consider several concerns with the remaining findings. First, the variable of family intactness was limited to the parental response about whom the student was living with at the time of school registration. This measure does not account for those home situations wherein one or more of the parents may not be present for a duration of the school year, nor does the measure provide for a determination of the nature of previous living situations. Second, the variables of school transfers and school-initiated interruptions are limited to the student's history while he or she was enrolled in the school district of study. Third, the use of a straight numerical count of transfers and releases may have underestimated the degree of group differences in that the typical graduate had been in school for a least 1 more year than had the typical dropout. A more discerning measure might have been to divide the number of years in school by the number of interruptions. Finally, school-initiated interruptions did not include those school interruptions identified as parent-initiated (e.g., moved from district or enrolled student in a private school).

Multivariate Analysis

Discriminant analysis was employed as a means to evaluate the relationship between the criterion of dropout status and graduate status and, in combination, the six independent variables. This evaluation was based on the termination of whether a linear discriminant function, composed of information from the six independent variables, could be employed to distinguish between LD dropouts and LD graduates. Specifically, the function initially solves for weights to use to combine all variable scores in order to construct the linear discriminant function that optimally differentiates between the two groups. Within this function, the relative importance of each variable is signified by the size of its standardized weighting coefficient. These coefficients are then multiplied by the respective group means (i.e., centroids) to yield a group discriminant score for each respective group. Next, these same coefficients are multiplied by the respective variable values for each individual case yielding a discriminant score for each case. Individual cases are then classified into the criterion group that their discriminant score most closely approximates. This analysis was performed using 267 (88%) of the study sample, with 86% and 91% of the dropout and graduate groups being represented, respectively. The 38 cases that were not utilized had missing information on one or more variables.

The discriminant function constructed weighted the variables of school-initiated interruptions, family intactness, and school transfers most heavily. The standardized coefficient values (see Table 2) offer a depiction of the individual variable contribution to the discriminant function. These coefficients, however, offer an evaluation of each variable relative to its absolute contribution and do not adequately reflect the impact of variable interdependency. The within-group correlation matrix indicated relatively how degrees of intercorrelation existed within the function. The largest degree of interdependency was found to exist between the variables of school transfers and school interruptions (r = .28) and family intactness and ethnicity (r = .26). The size of these correlations indicates that while some of the contribution offered within these respective variable pairs was shared, it was insufficient to present the problematic condition of multicolinearity.

In evaluating the accuracy of the discriminant function, actual group membership was compared to predicted group membership (see Table 3). The present function correctly classified a large majority of the dropout group and a near majority of the graduate group providing an overall accuracy rate of 72%. The finding that the function classified only a near majority of the graduate group suggests the presence of two or more distinct types of graduates. For procedural purposes, A Wilks's lambda statistic was employed to evaluate whether the amount of separation (i.e., between-group variance summed over total variance) produced across the six variables was statistically significant. This procedure determined that the between-group variance, while accounting for 15% of the total variance, was significant [2.sup.X][6, N = 267] = 42.75, p <.00).

In evaluating the utility of a discriminant function by the number of correctly classified cases, one must appreciate that there is a likelihood that the function will fit the sample on which it has been constructed better than it will some other sample. This feature suggests the likelihood that the derived accuracy overestimates the actual utility of the function. A cross-validation study was conducted on a separate sample of LD dropouts and LD graduates to address this concern and to establish information about whether the function could be employed to predict high-school dropout and high-school graduation among other samples. This cross-validation study was conducted on a representative sample of LD students who had been either released as dropouts or graduates under the same codes as noted earlier during the 1986-87 school year. These samples were not significantly different from the original study samples on measures of intelligence, gender, age at exit, and ethnicity. The function correctly classified 70% (97) of the available LD dropouts and 90% (63) of the available LD graduates.


The results of this study compel us to consider a number of implications for schools and future research. First, the findings suggest that among LD students in this urban setting the rate at which they are leaving school by avenues other than graduation is alarmingly high.

A second implication, demonstrated by the results of a separate analysis of the school histories of LD students, highlights the dynamic nature of school dropout. For instance, 28% of the graduates had already been released from school, under this study's criteria, as dropouts one time prior to graduation; another 10% had been dropped out two or more times. As a caution, this finding informs us that the dropout sample may therefore be confounded with students who will eventually be graduated. Among the dropout sample, 28% had already been released one time prior to being identified as dropouts in this study and an additional 43% had dropped out two or more times. These findings suggest that the common perception of the school dropout as being a student who simply drops out or is dropped out of school never to return may not be valid. Future research must examine this dynamic nature of school dropout.

The results of this study, as well as a number of similar efforts on other populations of students (see Bledsoe, 1959; Cook, 1956; Felice, 1981; Hollingshead, 1949, 1975; Livingston, 1958; Lloyd, 1976, 1978; Penty, 1960; Stroup & Robins, 1972; Thomas, 1954; Walters & Kranzler, 1970), also suggest that schools may be able to contrast those students who are most likely to exit from high school as dropouts from their peers who are likely to graduate. This feature is an important first in trying to identify likely school dropouts before they leave school. In the present study, the basis for this contrast was a discriminant function employing six variables that were readily available within the district of study. Future research needs to extend these findings along two lines of inquiry. First, while those variables proving most useful-family intactness, school releases, and school transfers-were generated at the high-school level, it is likely that similar information could be collected at earlier points in time. Second, it is likely that other variables (e.g., attendance data at earlier points in time) could supplement or supplant the three variables used in this study. These lines of inquiry will allow us to determine the feasibility of developing even earlier identification models of school dropout. The potential benefits of such models are compelling.

School transfers and school-initiated interruptions were powerful factors in distinguishing between LD dropouts and LD graduates. When considering that these variables can be viewed as potentially alterable within a school setting, in contrast to a variable such as family intactness or family SES, one is faced with a perplexing question: What is the nature of the relationship between practices that interrupt a student's schooling and the increased likelihood of school dropout? A number of authors have brought attention to this role by examining the traditional operating procedures and hidden agendas that exist in schools (see Fine, 1986; Goodlad, 1984; Hammond & Howard, 1986; Hess, 1986; Hess, Wells, Prindle, Liffman, & Kaplan, 1987; Wehlage & Rutter, 1986). While not establishing a causal relationship, we feel it is time to contemplate these factors and evaluate their educational relevance with respect to our LD students.

The level of family intactness also represented a major bellwether for school dropout. A number of authors have presented findings and information that point out the important role that families play in a student's schooling (Fine, 1986; Hollingshead, 1949, 1975). This variable is typically beyond the influence of the school as an agent of social change, yet our efforts cannot ignore its implications. Similarly, the findings relative to family SES, while of limited power to distinguish between the groups, cannot be ignored as large proportions of both groups came from families that qualified for free or reduced-priced school lunches. Future efforts to identify and provide appropriate interventions for students who are potential dropouts must take into account these external factors.

Finally, despite the cursory appeal of conducting additional research, findings alone are seldom persuasive enough to bring about needed change. More precisely, the present research base and technology afford us the means by which we may be likely to characterize, and eventually identify at even earlier ages, those students who are apt to become high-school dropouts. This feature offers us both the opportunity to take a first step toward providing these students with the services necessary to keep them in school and an agent by which we can justify the directing of additional resources toward this end. Despite the ease with which such efforts could be implemented at the local level and the potential benefits, such action is not guaranteed. Likewise, we must respect that schools often drop students out of school in an effort to better manage and carry out their responsibility to educate students. An acceptance of this feature, however, must be balanced with a consideration of the ramifications associated with dropping students out of school before they have been afforded an adequate opportunity complete a basic education, and thus likely become a part of our nation's underclass. Therefore, the task that lies before us includes an examination of the barriers to improving the ability of our schools to carry out this crucial responsibility to these students, including organizational, community, teacher, and societal influences.
 Table 2
 Standardized Discriminant Function Coefficients
 Variable Standardized Value
 Ethnicity -.13826
 Reading .08170
 Intactness .54147
 Family socioeconomic status -.02456
 Transfers .25831
 Releases .69887
 Table 3
Group Hits Misses Hit Rate
Dropout 151 32 83%
Graduate 39 45 46%


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LARRY KORTERING (CEC DE Federation) is an Assistant Professor of Educational Studies at the University of Delaware, Newark. NORRIS HARING (CEC Chapter #389) is a Professor in the Department of Special Education, and ALAN KLOCKARS is a Professor in the Department of Educational Psychology at the University of Washington, Seattle.

We wish to thank Michael Boer and Sarah Kirk for their assistance in completing this manuscript.

Manuscript received September 1989; revision accepted December 1990.

Exceptional Children, Vol. 58, No. 5, pp. 422-435. [C] 1992 The Council for Exceptional Children.
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Author:Kortering, Larry; Haring, Norris; Klockars, Alan
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Date:Mar 1, 1992
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