An Examination of the Relationship Between Minimum Competency Test
Performance and Dropping Out of High School

Bryan W. Griffin
Georgia Southern University

Mark H. Heidorn Florida
Department of Education

(Published in Educational Evaluation and Policy Analysis Fall 1996.)

Bryan W. Griffin, Department of Curriculum, Foundations, and Research, Georgia Southern University, P. O. 8144, Statesboro, GA 30460 (E-mail: bwgriffin@gsvms2.cc.gasou.edu); Mark H. Heidorn, Statewide Assessment Program, Suite 701, Florida Department of Education, Tallahassee, Florida 32399.

An earlier version of this paper was presented at the 1993 meeting of the American Educational Research Association, Atlanta, Georgia. We thank Dr. Cordelia Douzenis and several anonymous reviewers for their helpful comments.

Correspondence concerning this manuscript should be sent to the first author.

Abstract

Many states now require students to demonstrate basic skills as a requisite for high school graduation, and this often means students must achieve passing scores on a minimum competency test (MCT). Educational researchers have speculated that increased academic standards for graduation, as manifested in MCTs, will have adverse effects on students, particularly at-risk, disadvantaged students. The purpose of this study was to examine the relationship between MCT performance and high school dropout behavior. The results indicated that failure on an MCT did provide a statistically significant increase in the likelihood of leaving school, but only for students who were doing well academically. Students with poorer academic records did not appear to be affected by MCT failure; similarly, minority students did not demonstrate an increased likelihood of leaving school as a result of failing an MCT.

An Examination of the Relationship Between Minimum Competency Test
Performance and Dropping Out of High School: A Research Note

Many states require students to achieve passing scores on tests that measure basic skills as a requisite for high school graduation. Tests of basic skills have been referred to as minimum competency tests (MCTs). For the purposes of this paper, MCTs will be understood to mean minimal competency tests to which graduation requirements are attached. Typically, MCTs are administered to students initially in grades 8 - 11, and students who fail all or part of an MCT on their first attempt are provided additional opportunities to retake the test. Passing standards established for the tests commonly result in passing rates of 60 to 80 percent for students taking the tests for the first time (Catterall, 1989). The percentage of students failing to pass MCTs in the final year of high school has been estimated by Serow (1984) to be about one percent of those students who have taken the test at an earlier grade level. This does not imply that the balance of the student population eventually passes MCTs, however, since many students drop out of school between the time of initial MCT testing and the final high school year.

A basic concern about MCT programs is that failure to pass an MCT may contribute to students' decisions to leave school. This concern was expressed when MCT programs were first established in the 1970s, and again was identified as a research issue in the 1980s in relation to later reform efforts that called for increased standards for academic courses, use of time in school, and student achievement (LeCompte & Dworkin, 1991; McDill, Natriello, & Pallas, 1987). The effect of MCT failure on dropping out continues to be a relevant issue in relation to current assessment practice. MCT programs remain in effect in many states, and at least one state, Michigan, has recently established a new MCT requirement. Revised MCTs representing more challenging test content are currently being developed in Florida and Georgia. Current reform efforts that call for the development of authentic tests involving higher-level problem-solving tasks that integrate content from several disciplines could also result in much higher standards of competency for graduation from high school.

The precise nature of the relationship between increased academic standards and dropping out behavior is relatively unclear, especially with regards to MCTs. Speculation, however, does abound. Archer and Dresden (1987), for example, surmised that MCTs, at least in Texas, will likely lead to more high school dropouts. Moreover, Archer and Dresden anticipated that academically disadvantaged and other at-risk students would be the most probable candidates to leave school after poor performances on MCTs. McDill, Natriello, and Pallas (1987) drew a similar conclusion concerning the adverse effects of MCTs on academically disadvantaged students. Kreitzer, Madaus, and Haney (1989) also argued that failure on MCTs would result in at-risk students leaving school more often, especially "racial and language minority children" (p. 137).

The empirical link between MCT failure and dropping out has been difficult to establish due, to a large degree, to inadequate data; official high school dropout records often do not provide a means for tracking students following MCT testing. Catterall (1987) attempted to investigate the impact of MCTs on dropping out indirectly by associating state MCT policy with state graduation rates and other educational and demographic variables; his results, however, were inconclusive. Another indirect analysis of the impact of MCT programs on dropout rates using state-level data was reported by Kreitzer, Madaus, and Haney (1989). They compared the MCT testing policies for states with the highest and lowest dropout rates and reviewed other information that related to both MCT and dropping out, including descriptions of at-risk populations, retention rates, and perceived effects of MCTs on curriculum. They indicated that school effects were likely when considering the impact of MCT performance on dropping out since variability in dropout rates could be explained, in part, by school-level characteristics. They concluded, however, that empirical data or other clear evidence of the impact of competency testing on dropping out did not exist, but, as mentioned above, indirect information suggested that MCTs may increase the likelihood of at-risk students dropping out school.

In a second study Catterall (1989) used a different approach to provide indirect evidence of a relationship between MCT failure and students' decisions to leave school. He conducted a survey in four states of school district personnel and grade 9 and 11 high school students in which he asked students to indicate their MCT experience and their self-perceived chances of leaving school without graduating. In Catterall's sample of 736 students, 38% reportedly had taken an MCT. Of those who had taken an MCT, 10% claimed to have failed initially but subsequently to have passed, and 5% reported to have failed.

Catterall (1989) constructed a model that related family background, school context, and school performance variables to the students' self-perceived chances of dropping out of school. Results of his analysis indicated that socio-economic status, grades, and having failed an MCT were statistically associated with students reporting that there was some chance of dropping out. Catterall therefore concluded that failing an MCT potentially contributes to student doubts about finishing school, which could subsequently be associated with actually dropping out.

MacMillan, Balow, Widaman, and Hemsley (1990) provided the only study to date that examined the association between MCT performance and actual dropout behavior of students. Their study, which consisted of approximately 1,200 students in California, focused primarily on learning handicapped and educationally marginal students. They did include, however, a sample of regular students (i.e., non-learning handicapped and non-educationally marginal) to serve as a reference group in the study. MacMillan et al. found that failure on an MCT corresponded with substantially higher dropout rates for the learning handicapped and educationally marginal students, and a slightly higher rate for the reference group. In modeling the dropout rates between the three groups, MacMillan et al. did not provide statistical control for any potentially confounding correlates of dropout behavior (e.g., academic performance or behavioral problems), so it is not clear whether students from the reference group who failed the MCT and dropped out were also at-risk of dropping out due to their academic performance, age, problem behaviors, etc.

How competency testing affects students' decisions to drop out remains largely an unanswered question. While many have argued that increased standards are likely to result in higher dropout rates (Kreitzer, Madaus, & Haney, 1989; McDill, Natriello, & Pallas, 1987), research on the relationship between MCT performance and leaving school is, at best, inconclusive. The purpose of this study was to examine more thoroughly the relationship between MCT performance and dropout behavior. Since prior research has indicated that academically disadvantaged and minority students are especially likely to be adversely affected by MCT requirements, the specific relationships between MCT performance and dropping out for these students were also explored. In sum, the following questions were investigated: (a) what is the nature of the relationship, if any, between MCT performance and dropout behavior; (b) do academically disadvantaged students who fail the MCT show an increased risk of dropping out relative to those who pass the MCT; and (c) are minority students differentially affected by MCT performance in terms of dropping out of school relative to White students?

Method

Sample

The data for this study were provided by the Florida Department of Education and consisted of a cross-sectional, random sample of high school students from fourteen school districts in Florida.¹ The data reflect the standing of the students as of the 1990-1991 school year. Only grade 10, 11, and 12 students who had participated in the state-mandated MCT during the preceding five years were included in the study. The sample was restricted to these grade levels since students in Florida first take the MCT in grade 10. Since most students included in the sample had taken the MCT prior to the 1990-1991 school year, MCT performance records for all students were examined during the five year span of 1986 to 1991. The total sample consisted of 76,664 students enrolled in 75 high schools. Racial and ethnic classifications were limited to White (61.6%), Black (22%), and Hispanic (16.4%) students due to the small sample sizes for the other racial and ethnic groups.

Variables of Interest

The two variables of central importance in this study were DROPOUT, whether the student left school or not, and MCT, whether the student failed either the written (communication) or mathematics portion of the competency test. For the purposes of this study, DROPOUT was an indicator variable coded 0 for students who remained in school (96.6% in this sample) through the 1990-1991 academic year, and 1 for students who left school for any reason identified by the Florida Department of Education (1992) that constituted a high school dropout.² The dropout rate for the sample was 3.4%³.

For the analysis, MCT was a dummy variable that took the value 0 if the student passed both portions of the competency test on their first sitting of the examination, and 1 if the student failed either portion of the competency test. The state-wide passing rate for first-time takers on the mathematics portion of the competency test during the 1987-1991 years ranged from 75 to 82%, and for the communication portion of the test the rate ranged from 85 to 88% (Florida Department of Education, 1991a). The combined passing rate observed in the sample was 70.4%.

The MCT instrument used in Florida during the time of the sample was a state-mandated competency test that students first took in grade 10 (Florida Department of Education, 1991b). Unsuccessful students had five opportunities to retake the test in subsequent years (Florida Department of Education, 1991b). As noted above, the MCT consisted of two sections: mathematics and communication skills. The instrument used was designed to "assess the practical application of certain academic skills" which represented "real-world situations and problems requiring a student to use the basic skills acquired throughout the school years" (Florida Department of Education, 1991b, p. 14). Some skills assessed include the following:

(a) Determine equivalent amounts of up to one hundred dollars using coins and paper currency.

(b) Solve real-world problems involving comparison shopping.

(c) Determine the main idea stated in a paragraph.

(d) Obtain appropriate information from indexes, tables of contents, or dictionary entries.

(e) Include the necessary information when writing messages to make a request, to supply information, or to note an assignment. (Florida Department of Education, 1991b, pp. 14-16)

The reported reliabilities (KR-20) for the instrument were .935 for the mathematics section and .918 for the communication section (Florida Department of Education, 1990). The content validity of the Florida MCT was addressed, and established, in the Debra P. v. Turlington (1979; 1981; 1983) court cases. In these cases, the Florida Department of Education demonstrated that test-item construction procedures ensured both curricular and instructional validity. In addition, the Florida Department of Education (1990) developed procedures (e.g., review boards) to prevent the use of items that may be "biased against any student because of sex, race, ethnicity, or geographic region" (p. 4).

Covariates

Previous research on high school dropouts has identified several factors that either contribute to the decision to leave school or are strong predictors of dropping out. To gain a better understanding of the relationship between MCT and DROPOUT, a number of correlates of dropping out were included in the analysis as control variables.

One of the strongest predictors of dropping out is high school academic performance (Ekstrom, Goertz, Pollack, & Rock, 1987; Pallas, 1986; Wehlage & Rutter, 1987). High school grade point average, GPA, which ranged from 0 to 4 (4 = highest), was included in this study as a measure of academic performance (M = 2.34, SD = .727). Another important indicator of potential dropouts is the student's age relative to his/her classmates (Frase, 1989; Kreitzer, Madaus, & Haney, 1989). Students who are considerably older than their classmates, due, for example, to grade retention, are more likely to leave school. The variable OVERAGE was dichotomously coded and took the value 1 for students who were considerably older than their classmates (e.g., older than 17 and in grade 10), and 0 otherwise. Approximately 4.8% of the students in the sample were overage.

Other important correlates of dropping out include limited English proficiency, behavioral problems, and race or ethnic origin (Ekstrom, Goertz, Pollack, & Rock, 1987; Hammack, 1986; Pallas, 1986). Students of limited English proficiency (1.7% in sample) were included in the analysis by the dummy variable ENGLISH. This variable took the value 1 for students classified as having limited English proficiency, and 0 for students not classified with limited English proficiency. The indicator variable BEHAVE was assigned the value 1 for students with behavioral problems (21.7%), and 0 for students not experiencing behavioral problems. Students were recorded as having behavioral problems if they experienced any of the following: an in-school suspension, a court appearance, or an expulsion from school. McDill, Natriello, and Pallas (1987), as well as others (Ekstrom, Goertz, Pollack, & Rock, 1987; Fine, 1991) found that racial/ethnic differences existed in dropout rates. To capture this effect, two dummy variables were created, BLACK (equal to 1 for Black students and 0 for non-Black students) and HISP (1 for Hispanic students and 0 for non-Hispanic students), and included in the model.

Florida, like other states, has dropout prevention and retrieval programs. If a student was enrolled in a dropout prevention or retrieval program (4.7% in the sample), the dummy variable DOP took the value 1, otherwise 0. The Florida dropout prevention and retrieval programs during the time of the sample were classified into one of five categories: educational alternatives, disciplinary, teenage parent, youth services, and substance abuse. A more detailed description of each of these can be found in Florida Department of Education (1991c). Finally, an indicator variable for sex, MALE (1 for males, 0 for females), was also included in the analysis (males comprised 49.4% of the sample).

Data Analysis

Since the outcome variable, DROPOUT, is binary, logistic regression was used for analysis of the data. However, before estimating the logistic model for DROPOUT, a series of contingency tables, i.e., DROPOUT by MCT, were examined across various levels of GPA. Of the 11,372 students in the sample with GPAs greater than 3.10, only 2 failed the MCT and dropped out of school. Since such a limited number of students with high GPAs both failed the MCT and left school, the logistic regression analyses described below were estimated only for students with GPAs less than 3.11. This restriction was included to eliminate the possibility of unreliable estimates resulting from extremely small cell sizes (Agresti, 1990; Hosmer & Lemeshow, 1989)⁴.

To better assess the complexity of the data, all possible two-way and three-way interactions between the covariates, and the covariates and MCT were examined in the logistic models. A model building and selection strategy similar to those outlined by Hosmer and Lemeshow (1989) and Larntz (1993) for logistic regression was employed. After estimating a series of models with varying levels of complexity in terms of the number and types of interactions involved, the best fitting and most parsimonious model was selected.

Results

The final logistic model adopted is presented in Table 1. The results indicate that students who performed poorly on the competency test were more likely to leave school. This relationship, however, was moderated by student academic performance (GPA). Figure 1 provides a pictorial display of the relationship between MCT performance, GPA, and DROPOUT. The two solid lines show the predicted probability of dropping out across various levels of GPA. The thicker of the two solid lines represents the predicted probability of dropping out for students who failed the MCT, and the thinner solid line depicts the predicted probability of dropping out for those who passed the MCT.

Table 1

Logistic Regression Results for Dropping Out

Note. Deviance = 18296.93; n = 65,292; pseudo-R2 = 0.156.

* p less than .001.

First, note that the relationship between GPA and DROPOUT was negative--as academic performance increased, the predicted probability of dropping out of school rapidly decreased. These probabilities also revealed more clearly the nature of the relationship between MCT performance and the likelihood of leaving school. At lower levels of GPA there were no statistical differences, at the 5% level, in the predicted probabilities of dropping out between students who passed and failed the MCT.⁵ But for higher levels of GPA, the relationship was more defined--students who failed the test had a statistically higher risk of leaving school prematurely than students who passed the MCT.

How did the risk of dropping out change across the range of GPA for students who failed the MCT? The third, dashed line in Figure 1 represents the relative risk or risk ratio (RR; Agresti, 1990) of dropping out for students who failed the MCT. The RR is defined as the predicted probability of dropping out for students who failed the MCT, p(dropout|fail), divided by the predicted probability of dropping out for students who passed the MCT, p(dropout|pass). That is:

RR = p(dropout | fail) / p(dropout | pass).

The RR can be interpreted as follows. If RR is equal to 1, then the predicted probability of dropping out is the same for students who failed and passed the MCT. For example, if p(dropout|fail) = .07 and p(dropout|pass) = .07, then RR = .07/.07 = 1. If RR is less than one, then students who passed the MCT have a higher risk of dropping out (i.e., they are more likely to leave school before graduation), and if RR is greater than 1, then students who failed the MCT have the higher risk of dropping out.

As Figure 1 illustrates, the RR is just under 1 for low levels of GPA. This indicates that students who passed the MCT were more at risk of dropping out than were students who failed the MCT. However, as previously noted the difference in predicted probabilities between the two groups of students for low levels of GPA was not statistically significant at the .05 level; thus, the RR does not depart, statistically, from a value of one. This means that the predicted dropout rates are statistically indistinguishable for low-achieving students who passed or failed the MCT.

Note in Figure 1 the correspondence between the RR and GPA, i.e., increases in GPA are associated with increases in the RR. The increase in the RR suggests that students who had relatively high GPAs and who also failed the MCT were more likely to drop out than students with similar GPAs who passed the MCT. Despite the fact that the overall probability of dropping out decreases sharply with increases in GPA, failure on the MCT appears to increase the odds of dropping out as achievement levels increase. For example, for students with GPAs of 3.0 the predicted probability of dropping out is .014 for those who failed the MCT, and for students who passed the predicted probability of becoming a dropout is .008. The RR for this group of students is .014 / .008 = 1.75. Therefore, students who failed the MCT were estimated to be 1.75 times more likely to leave school before graduation, and this difference was statistically significant at the .05 level. In sum, these results suggest that academically at-risk students were not statistically more likely to leave school prematurely as a result of failure on the MCT. But failure on the MCT did appear to statistically increase the risk of dropping out for more academically successful students.

The final question of interest is whether the effects of MCT performance differentially impacted minority students' decisions to leave school. If, indeed, MCT performance had a different effect on minority students relative to White students, then an interaction between MCT and RACE would be found in the data. To test the proposition that race and MCT were linked in terms of dropping out, a two-way interaction between MCT and race, and a three-way interaction between MCT, race, and GPA were estimated. The three-way interaction was included since GPA and MCT interacted and since GPA and race interacted (see Table 1). The statistical results indicate that the interactions contributed little to the model. The likelihood ratio test⁶ (Agresti, 1990; Griffin & Douzenis, 1994; Hosmer & Lemeshow, 1989) for the inclusion of these two interaction terms was not statistically significant (DDEV = 4.28, df = 4, p = .369). Note that the power to detect an interaction between race and MCT exceeded .99; therefore, it should be clear that MCT performance did not differentially impact minority students' decisions to leave school, at least in this sample.

Discussion and Conclusions

Numerous researchers have argued that competency tests are likely to have adverse affects on academically at-risk and minority students (Archer & Dresden, 1987; Kreitzer, Madaus, & Haney, 1989; McDill, Natriello, & Pallas, 1987). The results of this study do not support these hypotheses. First, there was no statistically significant difference in dropout rates between low achieving students who passed and failed the MCT. While academically disadvantaged students are more likely to leave school overall, it did not appear that MCT performance provided any additional impetus to drop out for these students.

Second, there appears to be a gap in the predicted dropout rate between those who passed and failed the MCT for students with better academic records. But this gap, denoted by the RR in Figure 1, did not differ between Blacks, Whites, and Hispanics. In short, these data did not support the notion that minority students are adversely affected, in terms of dropping out, by the MCT in a manner that is different from Whites.

Lastly, there does appear to be some relationship between MCT performance and dropping out of school. While MCT performance is not the strongest predictor of dropping out, competency testing does appear to play a minor role in students' decisions to leave school. Apparently it is those students one would least expect to be affected by competency test performance who suffer the most from MCT failure -- students with strong academic records. This relationship may be partially explained by the perceived stigma attached to MCT failure. Following a competency test failure, students may experience a substantial drop in self-esteem, or they may feel embarrassed in front of their peers. And such experiences might be especially acute for students with a proven record of academic success. As a result, failure on a competency test may also foster a sense of alienation, and as LeCompte and Dworkin (1991) contend, alienation may ultimately lead to the abandonment of school for these students.

What implications do these findings hold for future research? First, note that the non-experimental nature of the data preclude any causal inferences in this study (Rumberger, 1983); thus we cannot assume that a factor such as MCT performance actually contributes to a student's decision to leave school. At best, the present study can only indicate possible linkages between MCT performance and dropping out. Therefore, additional studies should be conducted using data from other states to determine whether the findings outlined above replicate elsewhere. Should these relationships persist, case studies of academically successful students who failed the MCT and left school without graduating will be needed to determine the causes behind such decisions to leave school. Through such research, appropriate policies can be developed for addressing any possible adverse effects on students who fail competency tests.

References

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Archer, E. L., & Dresden, J. H. (1987). A new kind of dropout: The effect of minimum competency testing on high school graduation in Texas. Education and Urban Society, 19, 269-279.

Catterall, J. S. (1987). Toward researching the connections between tests required for high school graduation and the inclination to drop out of school (Grant No. G008690003). Los Angeles: University of California, Los Angeles, Center for the Study of Evaluation. (ERIC Document Reproduction Service No. ED 293 886)

Catterall, J. S. (1989). Standards and school dropouts: A national study of tests required for high school graduation. American Journal of Education, 98, 1-34.

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Debra P. v. Turlington, 564 F. Supp. 177 (M.D. Fla. 1983).

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Fine, M. (1991). Framing dropouts: Notes on the politics of an urban high school. Albany, New York: State University of New York Press.

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Florida Department of Education (1991c). Dropout prevention: Second biennial report of program effectiveness for the 1989-90 school year: Volume 1. Tallahassee, FL: Author.

Florida Department of Education. (1992). Assistance paper for identifying and reporting dropouts for grades pk-12. Tallahassee, FL: Author.

Frase, M. J. (1989). Dropout rates in the United States: 1988. Washington DC: National Center for Educational Statistics.

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Kreitzer, A. E., Madaus, G. F., & Haney, W. (1989). Competency testing and dropouts. In L. Weis, E. Farrar, & H. G. Petrie (Eds.), Dropouts from school: Issues, dilemmas, and solutions (pp. 129-152). Albany: State University of New York Press.

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MacMillan, D. L., Balow, I. H., Widaman, K. F., & Hemsley, R. E. (1990). A study of minimum competency tests and their impact: Final report (Grant # G008530208). Office of Special Education and Rehabilitation Services, U.S. Department of Education. (ERIC Document Reproduction Service No. ED 269 454)

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McDill, E. L., Natriello, G., & Pallas, A, M. (1987). A population at risk: Potential consequences of tougher school standards for student dropouts. In G. Natriello (Ed.), School dropouts: Patterns and policies (pp. 106-147). New York: Teachers College Press.

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Rumberger, R. W. (1983). Dropping out of high school: The influence of race, sex, and family background. American Educational Research Journal, 20, 199-200.

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Footnotes

¹The school districts included in the sample were Alachua, Columbia, Hernando, Hillsborough, Lake, Lee, Marion, Martin, Okaloosa, Osceola, Pinellas, St. Lucie, Seminole, and Suwannee.

²A dropout, according to the Florida Department of Education (1992), was any student who withdrew from school due to hardship, medical reasons, court action or pregnancy, to get married, or to join the military. Students expelled from school, withdrawn due to nonattendance, or whose whereabouts were unknown were also classified as dropouts. In addition, a dropout was any student who failed the statewide MCT and did "not receive any of the certificates of completion"; or who was "withdrawn from school because exceptional student education programs [were] unavailable due to the student's age" (p. 14). Finally, any student "who was expected to attend school, but did not enter as expected for unknown reasons," or who was "over compulsory attendance age" and left "school voluntarily with no intention of returning" was also classified as a dropout (p. 14).

³The official dropout rate for all 10, 11, and 12 grade students in Florida is 6.11% (Florida Department of Education, 1991, Profiles of Florida school districts 1990-91: Student & staff data [MIS Series 92-05, Statistical Report], Tallahassee, FL: Author.), which includes those student who have not yet taken the MCT. In the sample used for this study, a total of 99,432 students from grades 10-12 were selected. Of these students, 5,649 dropped out, for a sample dropout rate of 5,649/99,432 = .0568 or 5.68%, which is in general agreement with the official dropout rate of 6.11% for these three grade levels.

The sample dropout rate of 3.4% in this study is considerably lower than the dropout rates reported above. This reflects the filter or selection criterion used in our study--that students must have taken the MCT to be included in the analysis. Of the 99,432 10-12 grade students selected for this study, 22,768 did not take the MCT, for various reasons, prior to, or during, the 1990-1991 school year. Of these students, 3,054 dropped out of school. Removing these 22,768 students from the sample results in the reported sample size figure of 76,664. Also, removing the 3,054 dropouts who did not take the MCT lowers the number of dropouts from 5,649 to 2,595, and results in the reported sample dropout rate, i.e., 2,595/76,664 = .0338 or 3.4%.

⁴In addition to the reported logistic analyses on students with GPAs less than 3.11, separate logistic models with all students were estimated. The overall results obtained were nearly identical to those reported, and the specific findings from the two analyses concerning MCT were indistinguishable. Interested readers may obtain copies of the two analyses from the first author.

⁵Regions of statistical significance in the presence of interactions can be established in logistic regression using a computer procedure similar to the Johnson-Neyman technique discussed by Aiken and West (1991, pp. 132-133).

⁶The likelihood ratio test is the logistic regression analog of the partial F test in multiple linear regression and ANOVA. Like the partial F test, the likelihood ratio test can be used for testing the statistical significance of a subset of predictor variables in hierarchically nested models (Cohen & Cohen, 1983; Griffin & Douzenis, 1994; Maxwell & Delaney, 1990; Pedhazur, 1982). The symbol DDEV denotes the change in the deviance between two nested models in logistic regression, and it is also the likelihood ratio test statistic used for assessing difference in fit between two nested models. DDEV is distributed as a chi-squared variate with degrees of freedom equal to the difference in the number of parameters estimated in the two nested models (Agresti, 1990; Griffin & Douzenis, 1994; Hosmer & Lemeshow, 1989).

Copyright © 2000, Bryan W. Griffin

Last revised on 08 December, 2000 03:18 AM