Ernest C. Davenport

High School Mathematics Course-Taking by Gender and Ethnicity

The 1990 NAEP transcript data were used to study the number of Carnegie units (CUs) earned by students in seven categories of mathematics courses plus a miscellaneous category. On average, students earned 3.11 CUs, slightly more than the minimum of 3 suggested in A Nation at Risk (National Commission on Excellence in Education, 1983). Fifty-four percent of the CUs were earned in the standard high school sequence (Algebra 1 and 2 and geometry), and 20% were earned in preformal courses (e.g., General Math 1 and 2). Overall, gender and ethnic differences in the total number of mathematics CUs were small, but ethnic differences relative to the type of math course represented by the course categories were large. Gender differences in mathematics course-taking are discussed in light of differences in college attendance patterns and achievement variability. Implications of ethnic differences for school and curriculum reform are discussed.

Phi/Phimax: Review and Synthesis

This paper explores the phimax adjustment to phi. It shows phi/phimax to be a measure of relationship apart from its affiliation with phi. The adjustment when the variables are inversely related, phimin, is also considered. Next is a discussion of the relation between phi/phimax and kappa. The article ends with an analytical look at phi/phimax. Some findings of this exploration are: phi/phimax is an asymmetrical, equal-interval step function with ties to probability. Finally, phi/phimax is shown to be nonrobust in situations where it should be most useful.

Monitoring the Mathematics Achievement of Black Students

Findings from the National Assessment of Educational Progress for 1973 and 1978 are reviewed. They show improvement in levels of mathematics achievement for black students at ages 9 and 13, compared with a decline for white students at those ages. In a special National Assessment of mathematics in 1975 -76 for ages 13 and 17, substantial differences are found between average mathematics achievement scores of white and black youth. Based on a multiple regression analysis at age 17, more than half of the total variance in mathematics achievement scores is accounted for by regression, with schoolto-school differences in background variables and individual background differences within school about equally influential. About half of the white-black mean difference is accounted for by regression and, in this accounting, school differences in background variables play a more prominent role than individual differences within school. A particularly influential predictor of mathematics achievement is the number of high school algebra and geometry courses taken. Marked differences are found between predominantly black and predominantly white high schools in the average numbers of such courses taken. The adoption of policies that reduce those differences would be expected to result in relatively higher levels of mathematics achievement for black students.

A Reexamination of the Bogus Pipeline

A variant of a technique developed to enhance the validity of self-reports, the generalized bogus pipeline (GBP), was investigated in three experiments reported in this paper. Empirical support for both the construct validity and the efficacy of the GBP was generally supportive for that manipulation. An important serendipitous finding, however, was that the GBP may be unnecessary when respondent anonymity is assured. Empirical support for the construct validity and efficacy of anonymity assuring procedures was much stronger. Meta-analyses across all three experiments suggests that the effect size of anonymity in obtaining more valid self-reports of sensitive behavior was larger than the effect size of the GBP and that the GBP did little to improve the veracity of self-reports beyond the effect of anonymity. Implications of the findings are discussed in terms of the relative merits of the bogus pipeline paradigm and anonymity procedures with suggestions to increase the validity of self-reports utilizing anonymity assuring procedures.

Significance Testing of Congruence Coefficients: A Good Idea?

Tuckers congruence coefficient is often used to compare the equality of latent structures on a given test for different subgroups. Initial use of the index was subjective; given the same congruence coefficient, one investigator could decide that a pair of factors was similar, whereas another investigator could decide that they were different. Critical values were subsequently developed for this index to provide an objective basis for decision making. In practice, these values too often suggest congruence between factors known to differ. Results of the present study suggest that significance tests of congruence coefficients are inappropriate as currently performed.

Patterns of SAT Scores, Choice of STEM Major, and Gender

Using Baccalaureate and Beyond 2001 data, we found that STEM major was associated with an SAT pattern less common among females than males, in which the student’s quantitative score exceeded the verbal score. Verbal ability was negatively associated with STEM major. Implications for career theory and test interpretation are discussed.

The Empirical Power and Type I Error Rates of the GBT and ω Indices in Detecting Answer Copying on Multiple-Choice Tests

The generalized binomial test (GBT) and ω indices are the most recent methods suggested in the literature to detect answer copying behavior on multiple-choice tests. The ω index is one of the most studied indices, but there has not yet been a systematic simulation study for the GBT index. In addition, the effect of the ability levels of the examinees in answer copying pairs on the statistical properties of the GBT and ω indices have not been systematically addressed as yet. The current study simulated 500 answer copying pairs for each of 1,440 conditions (12 source ability level × 12 cheater ability level × 10 amount of copying) to study the empirical power and 10,000 pairs of independent response vectors for each of 144 conditions (12 source ability level × 12 cheater ability level) to study the empirical Type I error rates of the GBT and ω indices. Results indicate that neither GBT nor ω inflated the Type I error rates, and they are reliable to use in practice. The difference in statistical power of these two methods was very small, and GBT performs slightly better than does ω. The main effect for the amount of copying and the interaction effect between source ability level and the amount of copying are found to be very strong while all other main and interactions effects are negligible.

Two Studies of Reported Pretraumatic Stressors' Effect on Posttraumatic Stress Disorder Severity

We contrasted in two studies the effects of military trauma on Vietnam veterans who reported high and low premilitary stress. In the first, we administered the Posttraumatic Stress Disorder Interview (PTSD-I), a premilitary modification of the Social Readjustment Rating Scale, and the Military Stress Scale to hospitalized veterans. Premilitary stress appeared to reduce the impact of combat on several trauma-reexperiencing ratings, although the relevant evidence was inconsistent. In the second study, the premilitary stress main effects and the premilitary stress/combat interactions on four PTSD-I factors were nonsignificant. Thus, the severities of most PTSD symptoms increased with trauma intensity, but not with milder premilitary stress. The inconsistent data on the impact of pretraumatic stress on the trauma severity/PTSD relationships suggest further study.

Modeling Configural Patterns in Latent Variable Profiles: Association With an Endogenous Variable

A model is proposed for identifying latent predictor score patterns associated with a latent outcome variable. The model employs 2 new devices: (a) a path coefficient vector of contrast coefficients to describe a configural pattern in a structural model, and (b) a new type of latent variable with values that quantify the match of the persons latent predictor variable profile pattern to a theoretical pattern associated with the factor. The model is illustrated using data on perceptions and evaluations of political candidates during a debate. Findings suggest a pattern of scores on the perceptual variables associated with perceived debate success for female observers but not for male observers.

College-bound high-school graduates of 1972 and 1980 compared by college major

College enrollments are shown to have increased since the 1970s for majors in computer science, engineering, and business, and to have decreased for the biological and social sciences, the humanities, and education. In both the 1970s and the 1980s, high average levels of high-school achievement are observed for declared college majors in science and engineering fields. Education and business majors display records of relatively low average levels of achievement in high school, as do college dropouts, whatever their college major.