Use of demographic and quantitative admissions data to predict academic difficulty among professional physical therapist students.

Professional physical therapist education programs use a variety of measures of academic performance, aptitude, and affective characteristics when selecting students for admission. (1,2) Of these, grade point average (GPA) and standardized test scores are commonly used quantitative indicators. (1) In a survey of allied health education programs, physical therapist program directors ranked overall preadmission GPA and GPA in prerequisite courses as the most important factors for admissions decisions. (1) Although many authors (3-16) have studied the utility of these measures, little guidance exists on whether or how such data may be used to predict performance of individual students in physical therapist education programs. Prediction of academic performance could potentially be important because academic programs could estimate the resources that may be needed for students who eventually encounter academic difficulty. In addition, programs could consider early educational interventions for at-risk students in hopes of reducing students' risk for academic difficulty.

Numerous authors have studied the relationships among preprofessional GPA, standardized test scores, and academic performance in professional physical therapy curricula. Some early studies examined standardized tests that are now rarely used by physical therapist education programs, such as the Allied Health Professions Admissions Test (4) or the Scholastic Aptitude Test. (7) Other, generally more recent, studies have examined the use of GPA and scores on different portions of the Graduate Record Examination (GRE) to predict professional program GPA (6,8,11,16,17) or raw scores on the National Physical Therapist Examination (NPTE). (6,16) Day (17) conducted the only study we found that examined student data from more than one physical therapist education program. Using linear regression, Day found that preprofessional GPA, scores on the analytic portion of the GRE (aGRE), and race or ethnicity accounted for less than 20% of the variance in GPA among 522 students from 4 schools.

We found no studies that accounted for differences based on sex or ethnicity. In other fields, it has been suggested that sex or ethnic differences exist in performance on the GRE, (16,18-20) but such differences do not relate to academic performance. (21,22) Because previous studies have relied on relatively small samples, the effect of demographic characteristics, such as sex and race or ethnicity, on prediction of physical therapist student performance is unclear.

Recruiting and retaining students who are likely to succeed is an important goal for physical therapist education programs. In 2003, 12% of students admitted to physical therapist education programs did not graduate within 150% of the normally expected time frame. (23) When students struggle academically, programs may utilize more resources in providing remedial learning experiences and ensuring student competence. The purpose of this study was to investigate the utility of quantitative admissions data in predicting whether physical therapist students encountered academic difficulty during the professional academic program. Because academic programs make admissions decisions using only prematriculation data, we examined variables for which data were collected prior to students enrolling in professional programs. Data for variables obtained after matriculation (eg, professional program GPA) would potentially confound the findings for prematriculation variables. For the purposes of this study, academic difficulty was defined as being placed on probation, suspension or dismissal from the education program, or repeating courses or units due to poor academic performance.

By collecting data from a national sample of professional Master of Physical Therapy (MPT) and Doctor of Physical Therapy (DPT) programs, we examined the following questions: (1) can preadmission demographic data, GPA, and verbal and quantitative Graduate Record Examination scores (vGRE, qGRE), either in isolation or in combination, be used to predict physical therapist student risk for academic difficulty on a national scale, and (2) does the extent of prediction of academic difficulty vary by program?

Method

Program Recruitment

Physical therapist education programs were eligible for recruitment if they used the GRE in their admissions processes and if they had estimated class sizes of at least 30 students per year for the graduating classes of 2000 to 2004. We chose the years 2000 to 2004 because the most recent data were available for these years; we adjusted for "year" within the analysis to control for any variations among cohorts. Because we were interested in assessing predictors both among and within programs, we recruited only those programs that admitted at least 30 students to allow for a within-program analysis. We estimated that at least 30 students per year (for a total of 150 students) would be the minimum number required to generate reliable predictions in our within-program analysis. Given the number of variables that we examined, this number of students would allow for a minimum of 5 cases per cell in most cases.

The online directory of accredited programs compiled by the Commission on Accreditation in Physical Therapy Education (24) was used to identify accredited programs. Of the 209 programs accredited in 2004, (23) the online directory of accredited programs (24) provided profiles and contact information for 191 programs. The Internet Web sites for all 191 programs were reviewed to identify those programs that used the GRE and that reported an estimated enrollment of at least 30 students each year. Ninety-five programs were eligible.

Programs were recruited for participation using quota sampling. In quota sampling, subjects are enrolled based on the proportion of key characteristics in the population of interest. (25) We planned to recruit one fourth (n=24) of the 95 eligible programs. This approach allowed us to draw a sample that was representative with respect to geography and degree level. Recruiting 24 programs also would provide data on an adequate number of students for statistical analysis. (26)

The 95 eligible programs were classified into 4 geographic categories (Northeast, South, Midwest, and West) which corresponded to US Census Bureau regions. (27) Within each geographic category, programs were further categorized by degree level. Programs that had conferred professional DPT degrees in the years 2000 through 2004 were classified as DPT programs. Programs that conferred professional MPT degrees in the years 2000 through 2004 were classified as MPT programs. Programs that were conferring MPT degrees in 2000 but began conferring DPT degrees during any of the next 4 years were classified as "transition" programs (Tab. 1).

Within each of the 12 geographic and degree-level groups, eligible programs were assigned random numbers. These random numbers established the order in which programs would be invited to participate. The target sample included the number of programs in each category noted in the bottom panel of Table 1. In each category, programs were contacted and invited to participate until the target number of programs in that category was achieved. Overall, 19 programs declined, citing time constraints or difficulty compiling the requested information as reasons for not participating. In one of the categories, all of the eligible programs were either recruited or declined before the target number of programs was reached. Therefore, a total of 23 programs initially agreed to participate in the study. Eight of these programs required approval from their own institutional review boards. Human subjects approval was obtained from all 8 institutions using exempt criteria.

Subjects

Participating programs were asked to provide data regarding all students matriculating into the classes scheduled to graduate in the years 2000 through 2004. Three of the participating programs withdrew from the study because of difficulty compiling the needed data. The remaining 20 programs provided data on 3,585 students.

Data Collection

Academic difficulty was the dependent variable in the study. Programs were asked to indicate whether each student encountered academic difficulty in the academic program. As listed in Table 2, program directors or their designee assigned each student to 1 of 6 categories describing the student's progress in the program. We used categorical rankings of academic difficulty instead of professional program GPA because curricula, grading scales, and academic standards may vary from program to program. We believe that categorical ratings of academic difficulty reflect the range of relevant student outcomes. Other authors (10,28,29) have used similar approaches.

Independent variables included undergraduate GPA (uGPA), vGRE, and qGRE. The aGRE was changed from multiple choice to an essay-based assessment in 2002. (30) Because most students enrolled in physical therapist education programs during the study period would have taken the older version of the aGRE, this variable was not included in the study. Student demographic data and program degree level also were recorded. These independent variables are outlined in Table 3.

Procedure

After agreeing to participate in the study, program directors were sent a data collection spreadsheet and instructions for completion. Each program completed the spreadsheet and returned it as a password-protected electronic mail attachment. No names, birth dates, or other data that could be used to identify individual students were returned to the investigators.

Data Analysis

Prior to analysis, uGPA was transformed by multiplying by 10, which we believe allows for a clearer interpretation of the odds ratios produced by the logistic regression. Instead of describing a change in odds for every 1.0 change in uGPA (say from a 2.0 to a 3.0), the transformed variable produces an odds ratio based on an uGPA change of 0.1. Similarly, GRE scores were transformed by dividing by 10. The verbal and quantitative portions of the GRE are scored in 10-point increments. (31) The transformation allows for interpretation of the odds ratios based on these 10-point increments. Data screening procedures included assessment of missing data, ratio of cases to variables, and multicollinearity. (26,32)

Between-program analysis. Logistic regression procedures were used for the entire sample. Logistic regression, for our study, was useful for determining whether independent variables (eg, uGPA or GRE scores) predicted the dichotomous dependent variable of academic difficulty. The dependent variable was dichotomized into students who encountered academic difficulty (ie, academic problems, dismissal, or academic withdrawal; see Tab. 2) and those who did not (ie, graduate, nonacademic delay, or nonacademic withdrawal; see Tab. 2). We dichotomized academic difficulty because there were very few subjects in some categories, notably students who were dismissed (n=51) and students who withdrew for academic reasons (n=21).

Advice on the sample size required for logistic regression is scarce. (33,34) However, Norman and Streiner (33) recommended having 10 times as many subjects as independent variables. This is consistent with Tabachnick and Fidell, (26) who recommended having at least 5 subjects per cell. Our study was designed to meet or exceed these recommendations. Prior to logistic regression analysis, cross-tabulations of all combinations of nominal independent variables were performed. To avoid potential errors due to small cell sizes, (26) ethnicity was recoded from 7 to 5 levels (black/African American, Hispanic, white/non-Hispanic, Asian/Pacific Islander, and "other"; "white/non-hispanic" was used as the referent category). Because we used program as a control variable, the other program-level covariables (ie, institutional Carnegie classification as listed in the directory of accredited programs (24) and geographic region) resulted in cells with no data; thus, they could not be used in the main logistic regression analysis.

We used hierarchical logistic regression because we wanted to control for certain variables before other variables were entered into the model. Hierarchical regression requires entry of variables into the regression model in a prespecified order based on theoretical or evidence-based grounds. (35)

Specifically, we were interested in the influence of GPA and GRE scores after controlling for potential confounding variables. First, we wanted to control for the effects of the different years in the data set, as well as the different programs and degree levels, so we entered these variables into the model. (36) Given that programs vary in the methods used to train students, we suspected that there was variation in the relationship between academic difficulty and GPA and GRE scores across programs, degree levels, and years. These variables are all "group-level" variables. Next, we entered variables measured at the level of the individual--student age, sex, and race or ethnicity. Studies in physical therapy (9,16,17) and other fields (22,37,38) indicate that prediction of academic performance may be influenced by these demographic factors. Lastly, we entered uGPA, qGRE, and vGRE into the model. We entered these variables as a final step because we wanted to control for the previously mentioned group-level and individual-level variables before assessing the effect of uGPA and GRE scores.

The -2 Log-Likelihood test (P<.05) was used to evaluate whether the final model represented improvement over the constant-only model. (34) The Hosmer and Lemeshow test (P>.05) was examined to evaluate how well the model fit the data. (26,34,39) Wald statistics and adjusted odds ratios were examined to identify the variables that contributed significantly to the prediction model. (34)

To provide an interpretation of the ability of uGPA and GRE to predict academic difficulty after adjusting for potential confounding variables, we used receiver operating characteristic (ROC) curves. Receiver operating characteristic curves provide an indication of how well a variable discriminates between students who encountered academic difficulty and students who did not. (40) For example, if one wanted to know whether a uGPA of less than 3.0 placed a student at increased risk for academic difficulty, a ROC curve could be used to determine whether this cut-point was important for estimating risk of academic difficulty. For a more thorough description of ROC curve analysis, see Deyo and Centor. (41) Receiver operating characteristic curves were plotted for those continuous variables (ie, uGPA, vGRE, qGRE, and age) that were identified as significant predictors of academic difficulty.

We used 2 strategies to develop cut-point thresholds for these variables. First, we divided uGPA, vGRE, qGRE, and age into tertiles, and then we tested the previously described model with the variables coded as tertile scores. We identified 2 cut-points for each variable because we wanted to examine the predictability for reasonably small ranges of scores for each variable (eg, uGPA of 3.0 or less versus a uGPA of 3.01 to 3.5 versus a uGPA of 3.51 or higher). If the tertile method did not result in significant differences among the 3 score ranges, the ROC curve was used to identify a single cut-point threshold that best discriminated between students who encountered difficulty and those who did not.

A final logistic regression model was fit using these discrete variables. This final model was examined for goodness of fit; main effects as well as all 2-way interactions were tested for significance. The variables contributing significantly to the final model were used to develop a prediction rule for academic difficulty.

Clinical prediction rules use clinical data to assist clinicians in making a diagnosis or predicting an outcome. (42,43) We use the term "prediction rule" rather than the term "clinical prediction rule" because, in our case, the prediction rule was designed to assist physical therapist academicians in the interpretation of applicant information. (43) We used the [beta] coefficients from logistic regression procedures to weight the importance of the variables predicting academic difficulty, an approach commonly used to develop clinical prediction rules. (44-46) Finally, we tested the prediction rule using the data from students from all programs.

Within-program analysis. To further clarify how prediction of academic difficulty may vary by program, the analyses performed on the entire data set were repeated with data from each program. The same variables were used as in the between-program analysis, with a few exceptions. First, controlling for program was not necessary. Second, some programs had few or no students from ethnic groups other than white/non-Hispanic. In these cases, ethnicity was collapsed into fewer categories or eliminated from the analysis, as needed. Similarly, some programs graduated students with only one type of degree (MPT or DPT) during the study period, so the degree variable was eliminated for these programs. Data were analyzed using the Statistical Package for the Social Sciences (SPSS), version 12.0. *

Results

Population Comparisons Where possible, the characteristics of the program and student sample were compared with those of the 95 programs eligible for the study. For the remaining population comparisons, we used the total population estimates from all accredited programs (23) because population estimates for the 95 programs that met the eligibility criteria were not available.

The geographic distribution of programs in the sample was similar to that of the 95 programs eligible for the study (Supplemental Fig. 1, available online only at www.ptjournal. org). In 2004, 53% of accredited programs offered the DPT degree. In the study sample, 45% of the programs conferred DPT degrees in 2004 (Supplemental Fig. 2, available online only at www.ptjournal.org). The sample included a slightly higher proportion of private institutions than did the populations of both accredited and eligible programs (Supplemental Fig. 3, available online only at www.ptjournal.org). The proportion of programs in the sample housed at doctoral, master's, and specialized medical or health sciences institutions was very similar to the population of accredited programs (Supplemental Fig. 4, available online only at www.ptjournal.org).

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The median age at admission of students enrolled in the sample programs was 23 years (range=18-52), which is similar to the median age reported by Goldstein and Gandy. (47) Women represented 65.9% of the sample. For the academic years 1999-2000 and 2001-2002, the sample had a slightly smaller proportion of women than did the population of all accredited programs (Tab. 4). The majority of students in the sample were white and not of Hispanic descent (Tab. 4). The sample had smaller proportions of African-American and Hispanic students than the population of students enrolled in all accredited programs.

Table 5 presents descriptive statistics regarding quantitative admissions data for students in the sample. The mean uGPA of students in the sample was between 3.40 and 3.50 for all 5 cohorts of students, which is consistent with the mean uGPA of students admitted to all accredited programs (23) (Fig. 1).

Three of the 3,585 students in the sample were missing data regarding academic difficulty, so they were excluded from further analysis. A total of 9.6% (n=345) of the 3,582 students encountered academic difficulty (Tab. 6). The percentage of students in the sample graduating on time without difficulty was the highest for the 2000 cohort (93.2%) and decreased each year. A similar trend was seen in the population of students enrolled in all accredited programs. Figure 2 compares the percentage of students in the study who graduated on time without difficulty with the graduation rates reported by the American Physical Therapy Association (APTA). (23) For all except the 2001 cohort, there was no significant difference (95% confidence interval [CI]) between the sample and population means.

Between-Program Analysis

The results of the hierarchical logistic regression indicated that age, ethnicity, uGPA, vGRE, and qGRE contributed to prediction of academic difficulty after controlling for program, cohort, degree, ethnicity, and sex (Tab. 7). Odds ratios indicate that, as uGPA decreased by 0.10 (ie, from 3.1 to 3.0), the odds of encountering academic difficulty were increased by 15%. As vGRE and qGRE decreased by 10 (ie, from 420 to 410), odds of academic difficulty were increased by 3% and 4%, respectively. Age and ethnicity also contributed significantly to the model. As age at admission increased by 1 year, odds of academic difficulty increased 10%. Odds of academic difficulty were 200% higher for students from ethnic groups other than white/non-Hispanic.

Receiver operating characteristic curves were plotted for uGPA, vGRE, qGRE, and age. The area under each curve (Tab. 8) was significantly greater than 0.5 (P<.001), indicating that these variables significantly discriminated among students who did and did not have academic difficulty. Table 9 presents the final logistic regression model after converting age, uGPA, vGRE, and qGRE into discrete variables. Based on ROC curve analyses, uGPA was recoded into 3 discrete categories (3.15 or lower, 3.16-3.49, and 3.50 or higher). Both vGRE and qGRE were recoded into dichotomous variables (vGRE: 400 or lower versus 410 or higher; qGRE: 530 or lower versus 540 or higher). In addition, race or ethnicity was dichotomized into 2 levels representing white/non-Hispanic and "other." We dichotomized the race and ethnicity variables because the students who did not fit the white/non-Hispanic category all had reasonably similar increased risks of academic difficulty (Tab. 7). Being older than 26 years of age, being from a racial or ethnic group other than white/non-Hispanic, having a uGPA of 3.15 or lower, having a vGRE of 400 or lower, and having a qGRE of 530 or lower all were associated with increased odds of academic difficulty. Having an uGPA of 3.50 or higher was associated with a reduced risk of academic difficulty. The model indicates that an interaction between age and uGPA exists: students who were older and who had low uGPA scores were at an increased risk of difficulty, as were students who were older and had higher uGPA scores.

Table 10 presents the individual items in the prediction rule created by rounding the [beta] coefficients to the nearest 0.5 from the final logistic regression model presented in Table 9. For example, students with a low uGPA (3.15 or lower) had an increased incidence of academic difficulty with a [beta] coefficient of 0.357. We rounded this coefficient to +0.5 for the prediction rule. The risk was even more pronounced for older students. A uGPA of 3.51 or higher had a protective effect in younger students, with a [beta] coefficient of -1.113. We rounded this coefficient to -1.0 for the prediction rule. Older students, however, had a higher incidence of difficulty, even when uGPA was 3.51 or higher. Each student's predicted score was calculated, and then the predicted scores were cross-tabulated with the student's actual difficulty status. The results of the combined scores from the prediction rule are shown in Table 11.

Within-Program Analysis

In the between-program models, prediction of academic difficulty varied by program, as evidenced by the [beta] coefficients in Tables 7 and 9. When logistic regression was applied to data of each program individually, a variety of models emerged. After controlling for covariates, uGPA was the most consistent predictor of academic difficulty, contributing to prediction of difficulty in 12 programs (alone in 7 programs, in combination with vGRE in 3 programs, and in combination with qGRE in 2 programs). Quantitative GRE score alone contributed to prediction of difficulty in 2 programs. For 2 programs, an adequate model could not be fit. For 4 other programs, the logistic regression model included only control variables, such as age and cohort.

The logistic regression output and prediction rules for 3 selected programs are presented in Supplemental Tables 1, 2, and 3 (available online only at www.ptjournal.org). These 3 programs were chosen to illustrate the variation in prediction across the entire sample of participating programs.

Discussion

Between-Program Analysis

The logistic regression analyses indicate that uGPA, vGRE, and qGRE are independently predictive of academic difficulty when controlling for program, cohort, degree level, ethnicity, and age. These results are consistent with other research in physical therapy and other fields. For instance, Huff and Fang (38) found that low scores on the Medical College Admission Test (MCAT) and low preadmission GPA were predictive of academic difficulty in 13,118 medical students. As preadmission GPA increased by 0.1 point, risk of academic difficulty was reduced by 6.7%. (38) Rosenfeld et al (48) used discriminant function analysis and found that preadmission GPA and MCAT scores correctly classified the difficulty status of 76% of the 223 students in their study. Thomas and Draugalis (49) used multiple regression analysis to develop an equation that predicted 43% of the variance in first-year GPA in a group of 159 pharmacy students; the prediction equation included GPA in prerequisite courses and scores on the Pharmacy College Admissions Test.

Day (17) found that uGPA, scores on the analytic GRE, and ethnicity accounted for 20% of the variance of professional program GPA for a sample of physical therapist students. Thieman et al (16) found that prerequisite course GPA, GRE scores, and age accounted for 37% of the variance in professional program GPA. Work by Day (17) and Thieman et al (16) support the notion that previous academic performance and GRE scores are related to performance in physical therapist professional education. The major difference is that these studies were conducted on relatively small samples. Our study appears to be the first study to suggest that GPA and GRE scores provide reasonably stable population-based estimates of risk. Substantial program-to-program variation exists, however, which suggests to us that individual programs should generate their own risk estimates.

We developed a prediction to identify students who are at risk for academic difficulty. In this sample, nearly 40% (95% CI=32.3-45.1) of students with high prediction rule scores (scores of 2 or higher) encountered academic difficulty. Using this rule would allow early identification of students at risk, enabling programs and students to develop strategies to maximize the chances for student success. Academic programs interested in using this prediction rule should recognize that "program" was an important predictor in our study. The most accurate prediction rule for an individual program would be developed using data collected from that program. In lieu of a program developing its own prediction rule, we suggest the prediction rule reported in Table 10 as a reasonable, though less accurate, alternative.

Influence of Covariates on Academic Performance

Program was an important covariate in the prediction of academic difficulty. There is no prescribed curricular format for physical therapist education programs, (50) so curricular variation may affect the prevalence of academic difficulty at individual programs. Programs also are responsible for setting their own policies for grading and academic performance requirements, which in turn may affect the number of students encountering academic difficulty as defined in this study. Despite these differences in curricular design and policy, vGRE, qGRE, and uGPA still were predictive of academic difficulty, which suggests that these scores are reasonably powerful predictors of academic difficulty across a broad array of program types in different geographic regions.

Because we could not control for geographic region and Carnegie classification in our main analyses, these variables were tested in separate post hoc analyses. Each of these 2 variables was entered into a single logistic regression model. The Northeast region and doctoral institutions served as the referent categories, respectively. Geographic region was associated with academic difficulty ([chi square]=32.81, P<.001). Students in the Midwest had reduced odds of academic difficulty compared with students in the Northeast (odds ratio=0.459, 95% CI=0.317-0.665). Carnegie classification also was associated with academic difficulty ([chi square]=7.38, P=.025). Students enrolled in programs at institutions classified as master's institutions had 1.3 times the odds of academic difficulty compared with students at doctoral institutions (95% CI=1.301-1.733). Students enrolled in medical or specialized health sciences institutions had 1.4 times to odds of academic difficulty compared with students at doctoral institutions (95% CI=1.076-1.952).

Student-level characteristics that were significant in the between-program logistic regression model were age and ethnicity. Age contributed to the prediction of academic difficulty (P<.001) in the first logistic regression model developed for all 3,582 students in the sample. The regression model created using dichotomized variables suggests that prediction of academic difficulty is age-dependent. A uGPA of 3.50 or higher was protective against academic difficulty; however, when interacting with age [greater than or equal to] 27 years, this relationship was reversed. Students with this combination of variables had more than twice the odds of difficulty (odds ratio=2.314, 95% CI=1.097-4.881) as compared with younger students with the same GPA. These findings suggest that older students may have other challenges beyond undergraduate academic preparation that affect their performance in graduate-level physical therapist education. For instance, older students may have experienced a longer gap between undergraduate and professional education than their younger counterparts. They also may have different work or family commitments. Programs should be aware that student age is a significant predictor of academic difficulty even after adjusting for program and other student-level variables.

Other studies support the notion that age may affect performance in physical therapist education. Both the studies by Dockter (6) and Thieman et al (16) showed that age contributed to the prediction of professional program GPA in linear regression models. Hayes et al (9) suggested that traditional measures of intellectual ability, such as uGPA and standardized test scores, may not be the best predictors of academic performance for older, nontraditional physical therapist students. In a study of 107 students in a baccalaureate physical therapist program, they found that grades in a gross anatomy course and preprofessional GPA predicted professional program GPA for younger students, whereas grades in a gross anatomy course and interview scores predicted professional program GPA for older students.

Some authors (1,2,51) have expressed concerns that GPA and test scores are not accurate predictors of academic performance for students from minority ethnic groups. Student ethnicity emerged as a significant predictor of academic difficulty. Interaction effects between race or ethnicity and the variables uGPA, vGRE, and qGRE were not detected, suggesting that the effects of race or ethnicity were independent of other variables in this study. However, fewer than 3% of the students in the sample were Hispanic or African American. Thus, the statistical power to detect significant interactions between ethnicity and the independent variables may have been limited.

The data collected do not allow inferences regarding why students in some ethnic groups had higher odds of academic difficulty. For example, the higher odds of academic difficulty for some racial or ethnic groups may be related to socioeconomic and educational factors that were not addressed by this study. Further research is needed regarding the relationships among race or ethnicity, quantitative admissions data, and academic difficulty to guide programs in the development and implementation of recruitment and retention strategies for minority students. Important disparities in the representation of some racial or ethnic minorities in physical therapy exist. For example, African Americans represent 12.3% of the US population, (52) yet only 1.9% of physical therapist members of APTA are listed as African American. (53) In our opinion, resolving these types of disparities should be priority issues for academic programs.

Within-Program Analysis

For students in 12 of the 20 programs, uGPA contributed to prediction of academic difficulty. Verbal GRE score was predictive of difficulty in 3 programs, and qGRE score was predictive in 4 programs. Variability in program-specific odds ratios, ROC curve areas, and prediction rules indicates that discrimination between students who had difficulty and students who did not varied widely within programs. These results suggest that program directors should analyze data from their own students to generate program-specific thresholds and rules for prediction of academic difficulty. If the number of students at an individual program is too small to conduct the analysis, we recommend using results from the between-program analysis because they represent the "typical student" in the study sample.

Implications for Academic Programs in Physical Therapy

In 2004, Oeffner (54) suggested that uniform requirements for physical therapist education programs should be developed. That same year, the Education Section of APTA developed a list of recommended admissions requirements for physical therapist education programs. (55) These recommendations are broad in that they do not specify minimum GPA requirements, nor do they recommend any single standardized test. The Education Section's recommendations (55) state that programs should consider a variety of intellectual, nonintellectual, and demographic factors when selecting students. The current study provides strong evidence to support the use of uGPA, vGRE, and qGRE as part of students' overall admissions portfolio.

Many physical therapist education programs use the GRE in their admissions processes, although it is a general test and is not designed specifically for physical therapist students. An admissions test with content more relevant to physical therapy may improve the ability of the test to predict which students might have difficulty completing physical therapist education. Until a better alternative is identified, this study suggests that vGRE and qGRE scores should be used by academic programs to assist in making admissions and academic training decisions. We are not suggesting that the prediction rule be used, in isolation, to decide which students should or should not be offered admission to an academic program. There was too much unexplained variance in our prediction rule to recommend that it be used for this purpose. Rather, we contend that if programs are aware of a prospective student's modest increase or decrease in risk for academic difficulty, the program will be in a position to better plan that student's educational experience and increase the likelihood of success. All programs need to balance admissions decisions with policies, program and university missions, and societal needs. It is our contention that program missions and societal needs should be given high priority. We believe that the clinical prediction rule we describe can assist programs in better utilizing their educational resources to optimize the chances of success for all students while complying with institutional missions and societal needs.

Limitations

Despite controlling for program, cohort, degree level, and student demographic characteristics, the logistic regression models accounted for only 24% of the variance in odds of academic difficulty. We suspect that a variety of variables that we did not measure explain the remaining variance. First, the analyses did not control for the rigor of students' undergraduate education. Studies of medical students (38,56,57) have used indexes for this variable to adjust uGPA in their analyses. In addition, programs may have calculated preadmission GPAs in different ways, especially when applicants attended more than one undergraduate institution. Applicants may have taken the GRE more than once. We asked programs to report the scores they used in making their admissions decisions. Consistency in recording these data may have improved the strength of our predictive models.

Our study did not attempt to control for students' socioeconomic status or psychosocial factors. Studies of students in other fields, such as medicine, suggest that these variables may contribute to academic performance. Fadem and colleagues (37) found that parental income was related to performance of 192 medical students on both the MCAT and medical licensure examinations. The authors suggested that students from poorer families may have had fewer educational advantages than their wealthier counterparts. Furthermore, students from families with fewer financial resources may be more likely to work during medical school, which may affect learning and performance. (37) In a study of 175 medical students, Hojat and colleagues (58) demonstrated that measures of psychosocial factors, such as anxiety, depression, locus of control, stress, and self-esteem, improved the prediction of medical school grades over the use of preadmission GPA and MCAT scores. More research of physical therapist students is needed to clarify which socioeconomic and psychosocial factors potentially contribute to students' performance and he occurrence of academic difficulty.

Other study limitations are related to potential sampling and historical biases. Because it is not possible to determine the specific demographic makeup of the student bodies at the 95 eligible programs, we compared he sample to the population of all students at all accredited programs. Because only larger programs that use the GRE were eligible for the study, these comparisons may not be valid.

With respect to historical bias, it is possible that the results were affected by the profession's rapid transition to the DPT. However, degree level (MPT versus DPT) did not contribute to the prediction of academic difficulty. Concurrently with the transition to the DPT, the number of students applying to physical therapist education programs declined in the early part of the decade. (23) The mean uGPA of students admitted to physical therapist education programs declined slightly over the years of this study. Therefore, changes in the applicant pool may also have introduced bias. This was addressed statistically by controlling for cohort in the between-program analyses and, when possible, in the within-program analyses as well.

Recommendations for Future Research

Because large proportions of the variance in odds of academic difficulty were unexplained in the results of this study, future research should consider other program and student characteristics. A valid method for adjusting for academic rigor would be an important contribution to the program level analysis. In addition, qualitative research methods may help identify additional variables that contribute to prediction of academic difficulty. This approach also may help clarify reasons why students who are older or from minority ethnic groups are at higher risk for academic difficulty than younger students.

The study sample was drawn from a population of 95 programs that were selected for eligibility based on their size and their use of the GRE. These eligible programs represent only half of the accredited physical therapist education programs in the United States. Future research should investigate whether previous grades or other measures of intellectual ability predict academic difficulty for students in programs with smaller class sizes or that use standardized tests other than the GRE.

Conclusion

Physical therapist education programs are charged with the task of producing graduates who can fulfill society's needs for high-quality, contemporary physical therapy care. (50) This study confirms the utility of uGPA and GRE scores as well as age and race or ethnicity in predicting difficulty among students enrolled in physical therapist programs. However, we concur with other authors (2,31,55,59) who have suggested that previous grades and standardized test scores should be considered in light of other information when making admissions decisions. Because the prediction of student performance varies by program, individual institutions should study their own data to develop guidelines for predicting students' risk for academic difficulty.

All authors provided concept/idea/project design, writing, and data analysis. Dr Utzman provided data collection. Dr Utzman and Dr Riddle provided project management and fund procurement. Dr Riddle and Dr Jewell provided consultation and manuscript review.

This work was completed in partial fulfillment of requirements for Dr Utzman's PhD degree in Health Related Sciences, Medical College of Virginia Campus, Virginia Commonwealth University.

The Institutional Review Board of Virginia Commonwealth University approved this study.

This research was presented at the annual meeting of the Federation of State Boards of Physical Therapy; September 10, 2006; Portland, Ore.

This work was funded, in part, by the Federation of State Boards of Physical Therapy.

This article was received August 8, 2006, and was accepted April 18, 2007.

DOI: 10.2522/ptj.20060221

References

(1) Agho AO, Mosley BW, Williams AM. A national survey of current admission practices in selected allied health educational programs. J Allied Health. 1999;28:8-14.

(2) Scott AH, Chase LM, Lefkowitz R, et al. A national survey of admissions criteria and processes in selected allied health professions. J Allied Health. 1995;24:95-107.

(3) Baker J, Douphrate D, Ridley D. The use of the Revised PSB-Health Occupations Aptitude Examination as a predictor of success in physical therapy students. Journal of Physical Therapy Education. 1996;10(2): 63-67.

(4) Balogun JA, Karacoloff LA, Farina NT. Predictors of academic achievement in physical therapy. Phys Ther. 1986;66:976-980.

(5) Balogun JA. Predictors of academic and clinical performance in a baccalaureate physical therapy program. Phys Ther. 1988;68:238-242.

(6) Dockter M. An analysis of physical therapy preadmission factors on academic success and success on the National Licensing Examination. Journal of Physical Therapy Education. 2001;15(1):60-64.

(7) Gross MT. Relative value of multiple physical therapy admissions criteria in predicting didactic, clinical, and licensure performance. Journal of Physical Therapy Education 1989;3(1):7-14.

(8) Guthrie MR. Physical therapy student selection: analysis of the variables. Journal of Physical Therapy Education. Spring 1990:31-36.

(9) Hayes SH, Fiebert IM, Carroll SR, Magill RN. Predictors of academic success in a physical therapy program: is there a difference between traditional and nontraditional students? Journal of Physical Therapy Education. 1997;11(1):10-16.

(10) Jewell DV, Riddle DL. A method for predicting a student's risk for academic probation in a professional program in allied health. J Allied Health. 2005;34:17-23.

(11) Kirchner GL, Holm MB, Ekes AM, Williams RW. Predictors of student success in an entry-level master in physical therapy program. Journal of Physical Therapy Education. 1994;8(2):76-79.

(12) Rheault W, Shafernich-Coulson E. Relationship between academic achievement and clinical performance in a physical therapy education program. Phys Ther. 1988;68:378-380.

(13) Roehrig SM. Prediction of licensing examination scores in physical therapy graduates. Phys Ther. 1988;68:694-698.

(14) Roehrig SM. Prediction of student problems in a baccalaureate physical therapy program. Journal of Physical Therapy Education. 1990;4(1):26-30.

(15) Templeton MS, Burcham A, Franck L. Predictive study of physical therapy admission variables. J Allied Health. 1994;23: 79-87.

(16) Thieman TJ, Weddle ML, Moore MA. Predicting academic, clinical, and licensure examination performance in a professional (entry-level) master's degree program in physical therapy. Journal of Physical Therapy Education. 2003; 17(2): 32-37.

(17) Day JA. Graduate record examination analytical scores as predictors of academic success in four master's degree physical therapy programs. Phys Ther. 1986;66: 1555-1562.

(18) Gallagher A, Bridgeman B, Cahalan C. Effect of Computer-Based Tests on Racial/ Ethnic, Gender, and Language Groups. Princeton, NJ: Educational Testing Service; 2000. Report no. 96-21P.

(19) Gallagher A, Levin J, Cahalan C. Cognitive Patterns of Gender Differences on Mathematics Admissions Tests. Princeton, NJ: Educational Testing Service; 2002. Report no. 96-17P.

(20) Grandy J. Trends and Profiles (Second Edition): Statistics About General Test Examinees by Gender, Age, and Ethnicity. Princeton, NJ: Educational Testing Service; 1999. Report no. RR-99-16.

(21) Attiyeh GM. Determinants of Persistence of Graduate Students in Ph.D. Programs. Princeton, NJ: Educational Testing Service; 1999. Report no. 95-18R.

(22) House JD. Gender differences in prediction of grade performance from Graduate Record Examination scores. Journal of Psychology. 1994; 128:695-698.

(23) American Physical Therapy Association. Fact Sheet: Physical Therapist Education Programs, 2005. Available at: http://www. apta.org/AM/TemplateRedirect.cfm?tem plate=/CM/ContentDisplay.cfm& Conten tID=23836. Accessed February 12, 2006.

(24) Commission on Accreditation in Physical Therapy Education. Accredited Physical Therapy Programs, 2004. Available at: http://www.apta.org/Education/accreditation/ dir_acc_PT_ed_prog. Accessed May 2, 2004.

(25) Portney LG, Watkins MP. Sampling. Foundations of Clinical Research." Applications to Practice. 2nd ed. Upper Saddle River, NJ: Prentice Hall Health; 2000: 113-152.

(26) Tabachnick BG, Fidell LS. Logistic regression. In: Tabachnick BG, Fidell LS, eds. Using Multivariate Statistics. 4th ed. Boston, Mass: Allyn & Bacon; 2001:517-581.

(27) US Census Bureau. Census Regions and Divisions of the United States, 2004. Available at: http://www.census.gov/geo/ www/us_regdiv.pdf.

(28) Jones RF, Vanyur S. MCAT scores and student progress in medical school. J Med Educ. 1984;59:527-531.

(29) Schmalz GMA. The use of pre-admission data to predict levels of success in selected allied health students. Occupational Therapy Journal of Research. 1990;10: 367-376.

(30) GRE Analytical Writing Measure: An Asset in Admissions Decisions. Princeton, NJ: Educational Testing Service; 2004.

(31) 2005-2006 Guide to the Use of Scores. Princeton, NJ: Educational Testing Service; 2005.

(32) Tabachnick BG, Fidell LS. Cleaning up your act: screening data prior to analysis. In: Tabachnick BG, Fidell LS, eds. Using Multivariate Statistics. 4th ed. Boston, Mass: Allyn & Bacon; 2001:56-110.

(33) Norman GR, Streiner DL. Logistic regression. In: Norman GR, Streiner DL, eds. Biostatistics: The Bare Essentials. 2nd ed. Hamilton, Ontario, Canada: BC Decker Inc; 2000:139-144.

(34) Peng CJ, Lee KL, Ingersoll GM. Introduction to logistic regression analysis and reporting. Journal of Educational Research. 2002;96(1):3-14.

(35) Cohen J, Cohen P. Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences. Hillsdale, NJ: Lawrence Erlbaum Associates; 1983.

(36) Tabachnick BG, Fidell LS. Multiple regression. In: Tabachnick BG, Fidell LS, eds. Using Multivariate Statistics. 4th ed. Boston, Mass: Allyn & Bacon; 2001:111-176.

(37) Fadem B, Schuchman M, Simring SS. The relationship between parental income and academic performance of medical students. Acad Med. 1995;70:1142-1144.

(38) Huff KL, Fang D. When are students most at risk of encountering academic difficulty? A study of the 1992 matriculants to U.S. medical schools. Acad Med. 1999;74: 454-460.

(39) Munro BH. Logistic regression. Statistical Methods for Health Care Research. 4th ed. Philadelphia, Pa: Lippincott Williams & Wilkins; 2000:283-302.

(40) Hosmer DW, Lemeshow S. Applied Logistic Regression. 2nd ed. New York, NY: Wiley; 2000.

(41) Deyo RA, Centor RM. Assessing the responsiveness of functional scales to clinical change: an analogy to diagnostic test performance. J Chronic Dis. 1986;39: 897-906.

(42) Reilly BM, Evans AT. Translating clinical research into clinical practice: impact of using prediction rules to make decisions. Ann Intern Med. 2006;144:201-209.

(43) Wasson JH, Sox HC, Neff RK, Goldman L. Clinical prediction rules: applications and methodological standards. N Engl J Med. 1985;313:793-799.

(44) Wells PS, Anderson DR, Bormanis J, et al. Value of assessment of pretest probability of deep-vein thrombosis in clinical management. Lancet. 1997;350:1795-1798.

(45) Solomon DH, Avorn J, Warsi A, et al. Which patients with knee problems are likely to benefit from nonarthroplasty surgery? Development of a clinical prediction rule. Arch Intern Med. 2004;164: 509-513.

(46) Leung GM, Rainer TH, Lau FL, et al. A clinical prediction rule for diagnosing severe acute respiratory syndrome in the emergency department. Ann Intern Med. 2004; 141:333-342.

(47) Goldstein M, Gandy J. Applicants to professional physical therapist programs in 2000. Journal of Physical Therapy Education. 2001;15(3):9-15.

(48) Rosenfeld LM, Hojat M, Veloski JJ, et al. Delays in completing medical school: predictors and outcomes. Teach Learn Med. 1992;4:162-167.

(49) Thomas M, Draugalis JL. Utility of the Pharmacy College Admission Test (PCAT): implications for admissions committees. American Journal of Pharmaceutical Education. 2002;66(1):47-51.

(50) Commission on Accreditation in Physical Therapy Education. Evaluative Criteria for Accreditation of Education Programs for the Preparation of Physical Therapists. Alexandria, Va: American Physical Therapy Association; 2006.

(51) Chapman DM. Noncognitive variables as predictors of academic success for physical therapy students. Journal of Physical Therapy Education. Fall 1989:18-21.

(52) Grieco EM, Cassidy RC. Overview of Race and Hispanic Origin. Census 2000 Brief Washington, DC: Department of Commerce, Economics and Statistics Administration, US Census Bureau; 2000.

(53) American Physical Therapy Association. Cultural Competence Strategic Plan, 2002. Available at: http://www.apta.org/AM/ Template.cfm?Section=Reources5& CON TENTID=14668&TEMPLATE=/CM/Con tentDisplay.cfm. Accessed June 28, 2006.

(54) Oeffner JK. Uniform academic prerequisites: action required. Presented at: Combined Sections Meeting of the American Physical Therapy Association; February 4-7, 2004; Nashville, Tenn.

(55) Education Section of the American Physical Therapy Association. Admissions Requirements Recommendations, 2004. Available at: http://www.aptaeducation. org/Admiss_Req.pdf. Accessed March 1, 2006.

(56) Koenig JA, Sireci SG, Wiley A. Evaluating the predictive validity of MCAT scores across diverse applicant groups. Acad Med. 1998;73:1095-1106.

(57) Swanson DB, Case SM, Koenig J, Killian CD. Preliminary study of the accuracies of the old and new medical college admission tests for predicting performance on USMLE Step 1. Acad Med. 1996;71 (1 suppl):S25-S27.

(58) Hojat M, Robeson M, Damjanov I, et al. Students' psychosocial characteristics as predictors of academic performance in medical school. Acad Med. 1993;68: 635-637.

(59) Sedlacek WE. Beyond the Big Test: Noncognitive Assessment in Higher Education. San Francisco, Calif: Jossey-Bass Inc Publishers; 2004.

* SPSS Inc, 233 S Wacker Drive, Chicago, IL 60606.

RR Utzman, PT, MPH, PhD, is Associate Professor and Academic Coordinator of Clinical Education, Division of Physical Therapy, West Virginia University School of Medicine, PO Box 9226, Morgantown, WV 26506-9226 (USA). Address all correspondence to Dr Utzman at: [e-mail].

DL Riddle, PT, PhD, FAPTA, is Otto D Payton Professor, Department of Physical Therapy, Medical College of Virginia Campus, Virginia Commonwealth University, Richmond, Va.

DV Jewell, PT, PhD, CCS, FAACVPR, is Assistant Professor, Department of Physical Therapy, Medical College of Virginia Campus, Virginia Commonwealth University.

[Utzman RR, Riddle DL, Jewell DV. Use of demographic and quantitative admissions data to predict academic difficulty among professional physical therapist students. Phys Ther. 2007;87:1164-1180.]

Table 1.
Population and Target Sample Characteristics

Region              MPT Programs (a)    Transition (b)

                    No.   Proportion   No.   Proportion
All accredited
  programs
  Northeast          40   0.21          13   0.07
  Midwest            43   0.23           8   0.04
  South              50   0.26           9   0.05
  West               17   0.09           8   0.04
Total               150   0.79          38   0.20
Eligible programs
  Northeast           8   0.08          10   0.11
  Midwest            13   0.14           6   0.06
  South              32   0.34           6   0.06
  West               12   0.13           5   0.05
Total                65   0.68          27   0.28
Target sample
  Northeast           2   0.08           3   0.13
  Midwest             3   0.13           1   0.04
  South               7   0.29           1   0.04
  West                3   0.13           1   0.04
  Total              15   0.63           6   0.25

Region              DPT Programs (c)     Total

                    No.   Proportion   No.   Proportion
All accredited
  programs
  Northeast         1     0.01          54   0.28
  Midwest           1     0.01          52   0.27
  South             0     0.00          59   0.31
  West              1     0.01          26   0.14
Total               3     0.02         191
Eligible programs
  Northeast         1     0.01          19   0.20
  Midwest           1     0.01          20   0.21
  South             0     0.00          38   0.40
  West              1     0.01          18   0.19
Total               3     0.03          95
Target sample
  Northeast         1     0.04           6   0.25
  Midwest           1     0.04           5   0.21
  South             0     0.00           8   0.33
  West              1     0.04           5   0.21
  Total             3     0.13          24

(a) Master of Physical Therapy (MPT) programs offered MPT degree
only 2000-2004.

(b) Transition programs began conferring Doctor of Physical Therapy
(DPT) degrees during the period 2000-2004.

(c) DPT programs conferred DPT prior to 2004.

Table 2.
Definitions and Coding for Academic Difficulty

Code            Definition

0=graduate      Progressed through the program with no interruptions;
                graduated on time

1=academic      Student was required to repeat a course or unit or was
  problems      placed on academic probation for failure to meet
                academic or clinical performance standards of the
                program

2=nonacademic   Student delayed graduation (took leave of absence or
  delay         converted to part-time status) for nonacademic reasons
                (eg, illness, finances)

3=dismissal     Student was dismissed from the program for failure to
                meet academic or clinical performance standards

4=academic      Student withdrew from the program for academic
  withdrawal    reasons (eg, upon withdrawal, student had a grade of
                D or F, was in danger of failing a course, or was in
                jeopardy of being dismissed, suspended, or placed on
                probation)

5=nonacademic   Student withdrew from the program for issues
  withdrawal    unrelated to academic performance (eg, illness,
                changed his or her mind about the profession)

Table 3. Independent Variables (a)

Variable                   Source             Type
Student-level variables
  Undergraduate GPA        Program director   Continuous
  GRE scores (verbal,      Program director   Continuous
    quantitative)
  Class/cohort (target     Program director   Categorical
    year of graduation
    when student was
    initially admitted-
    ie, 2000,2001,
    2002, 2003, or
    2004)
  Age (student age         Program director   Continuous
    at the time of
    admission)
  Sex (0=male, 1=female)   Program director   Categorical
  Race/ethnicity           Program director   Categorical
    (1=black/African
    American, 2-Asian/
    Pacific Islander,
    3=Hispanic, 4=Native
    American or Alaskan
    Native, 5=white/
    non-Hispanic,
    6=nonresident
    alien, 7=other)
Program-level variable
  Degree level (degree     Program director   Categorical
    level of the
    program at the
    time the student
    was admitted; 0=DPT,
    1=MPT or MSPT)

(a) GPA=grade point average, GRE=Graduate Record Examination,
DPT=Doctor of Physical Therapy degree, MPT=Master of Physical
Therapy degree, MSPT=Master of Science in Physical Therapy
degree.

Table 4.
Demographic Characteristics of Enrolled Students in All Programs
Compared With Sample

                     Total    1999-2000
                     Sample
                     (%)      Sample                 Accredited
                              (%[+ or -]95% CI (a))  Programs
                                                     (%) (b)

Sex
  Female             65.9       65[+ or -]1.9 (c)     68
Ethnicity
  Native American     0.5      0.6[+ or -]0.31         0.4
  Asian/Pacific       7.0      6.4[+ or -]0.97 (d)     5.1
    Islander
  African American    2.5      1.4[+ or -]0.47 (c)     3.2
  White/non-         81.2     81.6[+ or -]1.54 (c)    86.0
    Hispanic
  Hispanic            2.6      2.8[+ or -]0.66         3.2
  Other               2.2      1.7[+ or -]0.51 (d)     0.9
  Unknown             4.0      5.5[+ or -]0.91 (d)     1.1

                     2001-2002

                     Sample                 Accredited
                     (%[+ or -]95% CI)      Programs
                                            (%) (b)

Sex
  Female               68[+ or -]2.1 (c)    70.7
Ethnicity
  Native American     0.5[+ or -]0.31        0.4
  Asian/Pacific       8.2[+ or -]1.22 (d)    6.9
    Islander
  African American    3.9[+ or -]0.86        4.2
  White/non-         79.8[+ or -]1.78 (c)   83.4
    Hispanic
  Hispanic            2.6[+ or -]0.71 (c)    3.6
  Other               2.7[+ or -]0.72 (d)    1.8
  Unknown             2.3[+ or -]0.67 (d)    0.8

                     2003-2004

                     Sample                 Accredited
                     (%[+ or -]95% CI)      Programs
                                            (%) (b)

Sex
  Female               69[+ or -]4.0        73
Ethnicity
  Native American     0.2[+ or -]0.38        0.5
  Asian/Pacific       9.2[+ or -]2.48 (d)    6.1
    Islander
  African American    5.2[+ or -]1.91        5.2
  White/non-         80.2[+ or -]3.43       80.9
    Hispanic
  Hispanic            2.5[+ or -]1.34 (c)    4.5
  Other               2.1[+ or -]1.23        1.7
  Unknown             0.6[+ or -]0.66        1.1

(a) CI=confidence interval.

(b) Source: Fact Sheet: Physical Therapist Education Programs,
2005. (23)

(c) Sample proportion lower, P=.05.

(d) Sample proportion higher, P=.05.

Table 5.
Quantitative Admissions Data for Students Enrolled in
Sample Programs (a)

          uGPA   vGRE   qGRE

Mean      3.43   469    595
Median    3.45   460    600
Minimum   2.10   240    200
Maximum   4.00   800    800

(a) uGPA=undergraduate grade point average, vGRE=verbal Graduate Record
Examination score, qGRE=quantitative Graduate Record Examination score.

Table 6.
Academic Difficulty by Cohort

Cohort   No Difficulty                  Difficulty

         Graduated   Nonacademic        Academic   Academic
         on Time     Delay/Withdrawal   Problems   Withdrawal

2000       740        32                 47         1
2001       710        30                 50         5
2002       716        22                 69         4
2003       510        19                 66         5
2004       436        22                 41         6
Total    3,112       125                273        21

Cohort               Total

         Academic
         Dismissal

2000      8            828
2001      8            803
2002      8            819
2003     12            612
2004     15            520
Total    51          3,582

Table 7.
Logistic Regression for Prediction of Academic Difficulty Using
Continuous Data for Undergraduate Grade Point Average and
Graduate Record Examination Scores (a)

                                        Wald
Predictor          [beta]   SE [beta]   [chi square]   df    P

Program
  1                 0.844   0.534         2.496         1    .114
  2                 1.040   0.384         7.347         1    .007
  3                 1.402   0.452         9.627         1    .002
  4                 0.169   0.461         0.134         1    .714
  5                -0.120   0.553         0.047         1    .828
  6                 0.682   0.409         2.779         1    .096
  7                -0.791   0.536         2.178         1    .140

  8                 1.003   0.505         3.948         1    .047
  9                 0.214   0.477         0.201         1    .654
  10                1.951   0.480        16.496         1   <.001
  11                0.022   0.383         0.003         1    .954
  12                0.250   0.365         0.468         1    .494
  13                0.506   0.405         1.565         1    .211
  14                0.148   0.416         0.126         1    .723
  15                0.235   0.405         0.337         1    .561
  16               -1.543   0.701         4.848         1    .028
  17                0.072   0.533         0.018         1    .892
  18               -0.054   0.345         0.025         1    .875
  19                0.909   0.359         6.415         1    .011
  20                                     49.132        19   <.001
Cohort
  2000             -0.525   0.244         4.628         1    .031
  2001             -0.181   0.234         0.599         1    .439
  2002             -0.164   0.215         0.585         1    .444
  2003              0.194   0.210         0.837         1    .360
  2004                                   11.093         4    .026
DPT degree         -0.308   0.326         0.889         1    .346
Ethnicity
  Other             1.608   0.274        34.420         1   <.001
  Black             0.970   0.290        11.151         1    .001
  Asian/Pacific     0.700   0.221        10.002         1    .002
    Islander
  Hispanic          0.824   0.314         6.900         1    .009
  White/non-                             49.479         4   <.001
    Hispanic
Age                 0.098   0.014        45.763         1   <.001
Male sex            0.203   0.135         2.264         1    .132

uGPA               -0.160   0.021        57.225         1   <.001
vGRE               -0.030   0.010         9.388         1    .002
gGRE               -0.040   0.009        20.757         1   <.001
Constant            3.280   1.019        10.365         1   <.001

Test                                    [chi square]   df   P
  Overall model
      fit
    Likelihood                          403.239        33   <.001
      ratio test
  Goodness-of-
      fit tests
    Hosmer and                            8.307         8    .404
      Lemeshow
    Nagelkerke      0.237
      [r.sup.2]

Predictor          Odds Ratio (95% CI)

Program
  1                 2.327 (0.816-6.632)
  2                 2.830 (1.334-6.005)
  3                 4.063 (1.676-9.851)
  4                 1.184 (0.480-2.919)
  5                 0.866 (0.300-2.622)
  6                 1.978 (0.887-4.409)
  7                 0.454 (0.159-0.296)
  8                 2.726 (1.014-7.328)
  9                 1.239 (0.486-3.156)
  10                7.035 (2.744-18.035)
  11                1.022 (0.483-2.164)
  12                1.284 (0.628-2.624)
  13                1.659 (0.751-3.667)
  14                1.159 (0.513-2.620)
  15                1.265 (0.672-2.769)
  16                0.214 (0.054-0.844)
  17                0.930 (0.327-2.646)
  18                0.947 (0.482-1.863)
  19                2.482 (1.228-5.016)
  20                1.00 (referent)
Cohort
  2000              0.591 (0.366-0.954)
  2001              0.834 (0.528-1.320)
  2002              0.848 (0.557-1.293)
  2003              1.212 (0.803-1.831)
  2004              1.000 (referent)
DPT degree          0.735 (0.388-1.394)
Ethnicity
  Other             4.991 (2.917-8.541)
  Black             2.637 (1.493-4.660)
  Asian/Pacific     2.013 (1.305-3107)
    Islander
  Hispanic          2.279 (1.233-4.214)
  White/non-        1.000 (referent)
    Hispanic
Age                 1.105 (1.072-1.134)
Male sex            1.225 (0.940-1.596)

uGPA                0.852 (0.818-0.888)
vGRE                0.970 (0.951-0.989)
gGRE                0.961 (0.945-0.978)
Constant           26.579
Test
  Overall model
      fit
    Likelihood
      ratio test
  Goodness-of-
      fit tests
    Hosmer and
      Lemeshow
    Nagelkerke
      [r.sup.2]

(a) Data from all programs (N=3,390). SE=standard error, CI=confidence
interval, DPT=Doctor of Physical Therapy degree, uGPA=undergraduate
grade point average, vGRE=verbal Graduate Record Examination score,
gGRE=quantitative Graduate Record Examination score.

Table 8.
Receiver Operating Characteristic Curve Areas (a)

       Area Under the Curve   SE
       (95% CI)

uGPA   0.706 (0.681-0.730)    0.013
vGRE   0.587 (0.558-0.616)    0.015
gGRE   0.639 (0.612-0.666)    0.014
Age    0.633 (0.601-0.666)    0.017

(a) CI=confidence interval, SE=standard error, uGPA=undergraduate grade
point average, vGRE=verbal Graduate Record Examination score,
gGRE=quantitative Graduate Record Examination score.

Table 9.
Logistic Regression for Prediction of Academic Difficulty Using
ROC Curve Cut-points and Data From All Programs (a)

                                             Wald
Predictor                [beta]   SE [beta]   [chi square]   df   P

Program
  1                       0.384   0.422         0.826        1     .363
  2                       0.892   0.353         6.394        1     .011
  3                       0.880   0.361         5.962        1     .015
  4                      -0.287   0.446         0.414        1      .52
  5                      -0.489   0.446         1.205        1     .272
  6                       0.164   0.385         0.181        1      .67
  7                      -0.791   0.519         2.322        1     .128
  8                       0.700   0.497         1.984        1     .159
  9                      -0.081   0.465         0.030        1     .862
  10                      1.471   0.343        18.3336       1    <.001
  11                     -0.203   0.369         0.305        1     .581
  12                      0.107   0.351         0.093        1     .761
  13                      0.318   0.393         0.653        1     .419
  14                     -0.146   0.399         0.134        1     .714
  15                     -0.008   0.390         0.000        1     .981
  16                     -1.423   0.654         4.735        1      .03
  17                     -0.499   0.410         1.476        1     .224
  18                     -0.252   0.334         0.567        1     .452
  19                      0.613   0.347         3.119        1     .077
  20                                           85.560   1    9    <.001
Cohort
  2000                   -0.469   0.225         4.367        1     .037
  2001                   -0.156   0.218         0.511        1     .475
  2002                   -0.157   0.206         0.586        1     .444
  2003                    0.207   0.206         1.013        1     .314
  2004                                         11.288        4     .024
Not white/non-Hispanic    1.017   0.151        45.316        1    <.001
Age 27 y or older         0.456   0.230         3.941        1     .047
uGPA
  3.15 or lower           0.357   0.179         3.986        1     .046
  3.50 or higher         -1.113   0.203        30.074        1    <.001
  3.16-3.49                                    46.006        2    <.001
vGRE
  400 or lower            0.466   0.152         9.333        1     .002
gGRE
  530 or lower            0.735   0.140        27.735        1    <.001
Interactions
  uGPA 3.15 or            0.679   0.309         4.823        1     .028
    lower and age
    27 y or older
  uGPA 3.50 or            0.839   0.381         4.854        1     .028
    higher and age
    27 y or older
Constant                 -2.855   0.340        70.430        1
Test                                          [chi square]   df   P
  Overall model fit
    Likelihood                                381.87         8    <.001
      ratio test
  Goodness-of-
      fit tests
    Hosmer and                                  2.536        8     .960
      Lemeshow
    Nagelkerke            0.225
      [r.sup.2]

Predictor                Odds Ratio(95% CI)

Program

  1                      1.467 (0.642-3.355)
  2                      2.439 (1.222-4.868)
  3                      2.412 (1.190-4.889)
  4                      0.750 (0.313-1.799)
  5                      0.613 (0.256-1.469)
  6                      1.178 (0.554-2.506)
  7                      0.453 (0.164-1.254)
  8                      2.014 (0.760-5.335)
  9                      0.922 (0.371-2.295)
  10                     4.384 (2.219-8.520)
  11                     0.816 (0.396-1.681)
  12                     1.113 (0.559-2.215)
  13                     1.374 (0.636-2.968)
  14                     0.864 (0.395-1.889)
  15                     0.992 (0.462-2.132)
  16                     0.241 (0.067-0.868)
  17                     0.607 (0.272-1.358)
  18                     0.778 (0.404-1.497)
  19                     1.846 (0.935-3.647)
  20                     Referent
Cohort
  2000                   0.626 (0.403-0.971)
  2001                   0.856 (0.558-1.312)
  2002                   0.854 (0.571-1.278)
  2003                   1.230 (0.822-1.840)
  2004                   Referent
Not white/non-Hispanic   2.766 (2.057-3.719)
Age 27 y or older        1.578 (1.006-2.476)
uGPA
  3.15 or lower          1.429 (1.007-2.029)
  3.50 or higher         0.329 (0.221-0.489)
  3.16-3.49              Referent
vGRE
  400 or lower           1.593 (1.182-2.148)
gGRE
  530 or lower           2.086 (1.587-2.742)
Interactions
  uGPA 3.15 or           1.971 (1.076-3.613)
    lower and age
    27 y or older
  uGPA 3.50 or           2.314 (1.097-4.881)
    higher and age
    27 y or older
Constant
Test
  Overall model fit
    Likelihood
      ratio test
  Goodness-of-
      fit tests
    Hosmer and
      Lemeshow
    Nagelkerke
      [r.sup.2]

(a) SE=standard error, CI=confidence interval, uGPA=undergraduate
grade point average, vGRE=verbal Graduate Record Examination score,
gGRE=quantitative Graduate Record Examination score.

Table 10.
Prediction Rule for Academic Difficulty (a)

  Predictor                 Prediction   Proportion of Students
                            Rule         With Difficulty (95% CI)
                            Score (b)

Race/ethnicity other than   +1.0         114/531=0.215 (0.180-0.250)
  white/non-Hispanic
uGPA 3.15 or lower
  Age 26 y or younger       +0.5          79/509=0.155 (0.124-0.186)
  Age 27 y or older         +1.5 (c)      67/228=0.294 (0.235-0.353)
uGPA 3.51 or higher
  Age 26 y or younger       -1.0          40/1,357=0.029 (0.020-0.038)
  Age 27 y or older         +0.5 (d)      20/198=0.101 (0.059-0.143)
vGRE 400 or lower           +0.5         108/695=0.155 (0.128-0.182)
gGRE 530 or lower           +0.5         141/788=0.179 (0.152-0.206)

(a) CI=confidence interval, uGPA=undergraduate grade point average,
vGRE=verbal Graduate Record Examination score, gGRE=quantitative
Graduate Record Examination score.

(b) Based on [beta] coefficients from logistic regression model in
Table 9; the model adjusts for program and cohort.

(c) Includes +0.5 for low uGPA, +0.5 for age 27 y or older, and
+0.5 for interaction between age and uGPA.

(d) Includes -1.0 for high uGPA, +0.5 for age 27 y or older, and
+1.0 for interaction between age and uGPA.

Table 11.
Decision Rule Score by Academic Difficulty

                No Difficulty              Difficulty

                No.     Percentage         No.   Percentage
                        (95% CI (a))             (95% CI (a))

-1.0 or -0.5    1,073   98.1 (97.3-98.9)    21    1.9 (1.1-2.7)
0 or 0.5        1,253   92.1 (90.7-93-5)   107    7.9 (6.5-9.3)
1.0 or 1.5        594   83.5 (80.8-86.2)   117   16.5 (13.8-19.2)
2.0 or higher     138   61.3 (54.9-67.7)    87   38.7 (32.3-45.1)

(a) CI=confidence interval.