RAND tables


Excerpted Tables from the RAND Report



RAND conducted analysis of assessments from five of the six Bridge Project states—California, Georgia, Maryland, Oregon, and Texas. Illinois, which was part of the Bridge Project study, was not used because assessments were in a state of flux at the time of the RAND analysis. The Bridge Project case study sites were chosen for a variety of state-specific reasons (e.g. the use of affirmative action in higher education admission decisions in California and Texas; and specific K-16 reforms in Georgia, Maryland and Oregon).

The following are tables excerpted from the RAND report, "Alignment Among Secondary and Post-Secondary Assessments in Five Case Study States," followed by more detail about the methodology and coding categories.


Technical Characteristics of the Math Assessments Technical Characteristics of the English Assessments











Alignment Among the Technical, Content and Cognitive Demands Categories for Math Assessments Alignment Among Various Categories for Wriitng and Reading Assessments












Additional Information about the Methodology:

Assessments Examined
Purposes of Assessments Examined in this Study

National College Admissions Tests Used in Each Case Study Site
Coding Categories
Evaluating the Extent of Alignment Among Tests

Assessments Examined
Because of the magnitude of tests available, it was necessary to limit the number of tests examined in this study. The analysis were restricted to math and English/Language Arts (ELA) measures administered to high-school and incoming first-year college students; most remediation decisions at the postsecondary level are based on achievement deficiencies in those areas. The assessments were limited to those used by selected institutions in the Bridge Project’s five case study sites. Because the kinds of tests administered may vary by college, it is important to sample exams from a range of institutions. Namely, the minimum skill level required of students entering a highly selective institution may differ from the level required of students entering a less selective college. As a result, the content of remedial college placement tests used to assess entry-level skills can vary by institution. For each of our sites, RAND examined assessments administered by colleges that represented a range from less selective to highly selective. However, the chosen institutions are not a scientific sample.

Purposes of Assessments Examined in this Study

Bridge Project researchers asked RAND to examine four types of assessments in this study: state achievement, college admissions, college placement, and end-of-course exams. The tests and their goals are:

  • State achievement tests provide a broad survey of student proficiency toward state standards in a particular subject like math or reading.
  • College admissions exams sort applicants more qualified for college-level work from those less qualified.
  • College placement tests determine which course is most appropriate for students. Some college placement tests are used to identify students who may require additional remediation, whereas other college placement exams are used more broadly to determine which course students are eligible to enroll in, given their prior academic preparation.
  • End-of-course tests are measures of knowledge of one particular course.

Because of the magnitude of tests available, it was necessary to limit the number of tests examined in this study. RAND focused its analysis on math and English/Language Arts (ELA) measures administered to high-school and incoming first-year college students. Bridge researchers chose math and ELA because most remediation decisions at the postsecondary level are based on achievement deficiencies in these areas. Because the kinds of tests administered may vary by college, it is important to sample exams from a range of institutions. For each of our sites, researchers examined assessments administered by colleges that represented a range from less selective to highly selective. However, the chosen institutions are not a scientific sample.

National College Admissions Tests Used in Each Case Study Site
The first set of tests we examined, which includes the SAT I, SAT II, ACT, and AP exams, are used in five of Bridge’s case study sites, as well nationally, to aid in college admissions decisions. For those students applying to a four-year institution, many are required to take either the SAT I or ACT, and, at more selective schools, several SAT II exams as part of the admissions process. While AP tests are not a requirement, admissions officers are likely to view students with AP experience as better-prepared and more competitive applicants. Also, students with scores of four or five on AP tests are often rewarded with college credit in the subject area.

The SAT I, a three-hour mostly multiple-choice exam, is intended to help admissions officers distinguish applicants more qualified for college-level work from those less qualified. It is not designed to measure knowledge from any specific high school course, but instead measures general mathematical and verbal reasoning.

The SAT II is a series of one-hour, mostly multiple-choice tests that assess in-depth knowledge of a particular subject, and is used by admissions officers as an additional measure with which to evaluate student subject-matter competence. The SAT II is used primarily at the more selective institutions and is taken by far fewer students than is the SAT I. For this study, RAND examined the following SAT II tests: Mathematics Level IC, Mathematics Level IIC, Literature, and Writing. The SAT II Mathematics Level IC test assesses math knowledge commonly taught in three years of college preparatory math courses, whereas the SAT II Mathematics Level IIC test assesses math knowledge in more than three years of college preparatory math courses. The SAT II Literature test assesses students’ proficiency in understanding and interpreting reading passages, and the SAT II Writing test assesses students’ knowledge of standard written English.

The ACT is an approximately three-hour exam consisting entirely of multiple-choice items. Developed to be an alternative measure to the SAT I in evaluating applicants’ chances of success in college, it does not emphasize general reasoning (as does the SAT I) but is instead a curriculum-based exam that assesses achievement in science, reading, language arts, and math (Wightman & Jaeger, 1988). RAND included only the reading, language arts, and math sections for this study.

AP tests are used to measure college-level achievement in several subjects, and to award academic credit to students who demonstrate college-level proficiency. RAND examined the AP Language and Composition exam for this study.

Analyses are not included here. Rather, this document provides data from RAND’s analysis for use by policymakers and researchers interested in relationships between assessments.

RAND excluded the two AP exams in calculus (i.e., Calculus AB and Calculus BC) because they are markedly different from the other studied math tests. For example, they do not include material from any other mathematical content area except calculus, and are the only measures that require a graphing calculator.

Coding Categories
Two raters examined alignment among the different types of assessments using several coding categories, which are described below.

The coding categories for both math and ELA describe the technical features, cognitive demands, and content of each assessment. The technical features category involves characteristics such as time limit and format. The cognitive demands category captures the kinds of cognitive processes elicited. For reasons that will be explained in another section, the content category is slightly different for math and ELA. In math, the content category captures what is being assessed (i.e., particular content area such as elementary algebra or geometry). In ELA, the content category describes the reading passage.

The cognitive demands category and the content category in math are the focus of this study because discrepancies in these areas can potentially send mixed messages to students about the kinds of skills they should learn in order to be prepared for college-level courses. Although variations in technical features and in the ELA content category are believed to have less direct impact on the kinds of signals students receive, it is nevertheless important to document discrepancies in these areas. Technical features, such as test format, can facilitate or limit the kinds of skills that are measured (Bennet & Ward, 1993). RAND described differences in the ELA content category to characterize fully the range of test content possible.

RAND created the above coding categories by exploring different ways of summarizing test content. RAND examined several sources, including test frameworks, such as those used to develop the National Assessment of Educational Progress (NAEP), as well as coding categories used in previous studies of alignment (Education Trust, 1999; Kenney, Silver, Alacaci, & Zawojewski, 1998; Webb, 1999). RAND then combined and modified the different sources to produce coding categories that addressed the range of topics and formats appearing on the tests included in this study.

Math Coding Categories
The first aspect of the math coding categories concerns technical features. Technical features describe test length, time limit, format, and characteristics that can be described by inspection of test instructions or items. In math, items could be classified as one of four formats: multiple-choice, quantitative comparison, grid-in, or open-ended. Multiple-choice items require students to select their answer from a list of possible options. Quantitative comparison items require students to determine the relative sizes of two quantities. Because quantitative comparison items ask students to select their answer from four possible options, they are considered a subset of the multiple-choice format. However, RAND distinguished between the two types of formats because response options across multiple-choice items vary from one question to the next, whereas response options across quantitative comparison items remain the same. Grid-in items require students to produce their own answer and mark their answer in a corresponding grid. Open-ended items also require students to produce their own answer, but differ from grid-in items in that the former item type can take on negative values. Additionally, many of the open-ended items in our study require students to explain their reasoning.

Technical features also include characteristics that can be described by examining the test instructions or items. These include characteristics such as provisions for the use of tools such as calculators or rulers, the use of diagrams or other graphics, the use of formulas, whether formulas were provided or had to be memorized, and whether each item was contextualized (i.e., a word problem that made reference to a real-life situation). The use of formulas was sometimes difficult to determine because problems can be solved in multiple ways, and in some cases an item could be solved either with or without a formula. Items were coded as requiring a formula only if it was determined that the formula was necessary for solving the problem.
For the content category, RAND listed several math content areas, ranging from basic through advanced math. The content areas included prealgebra, elementary algebra, intermediate algebra, planar geometry, coordinate geometry, statistics and probability, trigonometry, and miscellaneous. Almost all of the tests RAND examined had specifications that included many or all of these content areas. RAND listed subareas as means of making the distinctions among the main content areas clearer, but raters coded using only the main content areas.

To evaluate the cognitive demands of a test, RAND needed a coding scheme that captured different levels of cognitive processes, from routine procedures to complex problem solving. This led researchers to adopt the same criteria as those used for NAEP, namely conceptual understanding, procedural knowledge, and problem solving. The descriptions of each are described in the table below.

Table 2.1 Descriptions of the Math Cognitive Demands Category
Dimension Definition
Conceptual understanding Reflects a student’s ability to reason in settings involving the careful application of concept definitions, relations, or representations of either
Procedural knowledge Includes the various numerical algorithms in mathematics that have been created as tools to meet specific needs efficiently
Problem solving Requires students to connect all of their mathematical knowledge of concepts, procedures, reasoning, and communication/representational skills in confronting new situations
Source: Mathematics Framework for the 1996 and 2000 National Assessment of Educational Progress (NAGB, 2000).


As is typical with studies like these (e.g., Kenney, Silver, Alacaci, & Zawojewski, 1998), the raters found the cognitive demands category to be the most difficult to code, partly because items can often be solved in multiple ways, sometimes as a function of the examinee's proficiency. What might be a problem-solving item for one examinee might require another to apply extensive procedural knowledge. For instance, consider an item asking students for the sum of the first 101 numbers starting with zero. A procedural knowledge approach might involve a computation-intensive method, such as entering all the numbers into a calculator to obtain the resulting sum. However, a problem-solving approach would entail a recognition that all the numbers, except the number 50, can be paired with another number to form a sum of 100 (100+0, 99+1, 98+2, etc.). The total sum is then computed by multiplying the number of pairs (i.e., 50) by 100 and adding 50.

For items that can be solved in multiple ways, raters coded for the cognitive process that was most likely to be elicited. Judgments about the cognitive processes most likely to be evoked were based on raters’ prior experience in which they observed high school students as the students solved math problems.

ELA Coding Categories

Coding categories in ELA cover three types of skills: reading, editing, and writing. Reading skills relate to students’ vocabulary and comprehension of reading passages. Editing skills relate to students’ ability to recognize sentences that violate standard written English conventions. Writing skills pertain to how well students can produce a composition that clearly and logically expresses their ideas. Many of the tests include two or all three of these skills, but some assessments focus on a single type, namely writing. Because many of the tests measuring reading or editing skills include reading passages followed by sets of items, it was necessary to categorize both the reading passage and the individual items.

As with math, the ELA coding categories summarize the technical features, content, and cognitive demands of each assessment. The technical features category in ELA describes time limit, test length, and format. There are only two possible formats for ELA assessments, multiple-choice or open-ended. In ELA, open-ended items require students to produce a writing sample.

The content category is different from that in math because content areas are not as clearly delineated in English. Whereas a math item may be classified into specific content areas such as elementary algebra, geometry, or so forth, there are not analogous English content areas in which to classify reading passages. Instead, the content category in English describes the subject matter of the reading passage (topic), the author’s writing style (voice), and the type of reading passage (genre). In other words, there are three dimensions to the ELA content category: topic, voice, and genre. Topic consists of five levels—fiction, humanities, natural science, social science, and personal accounts. Voice consists of four levels—narrative, descriptive, persuasive, and informative. Genre also contains four levels—letter, essay, poem, and story.

For exams measuring reading or editing skills, raters used all three dimensions of the content category to describe the reading passages. However, all three dimensions are not relevant to writing tests, as such tests do not include reading passages. Instead, writing tests contain a short prompt that introduces a topic that serves as the focus of students’ compositions. Because students are not instructed to use a particular voice or genre for their compositions, only the topic dimension is needed to describe the writing prompts. Table 2.2 provides more details of the content category used for ELA assessments.

Table 2.2
Descriptions of the ELA Content Category
Description or Example
Used for Reading Skills Used for Editing Skills Used for Writing Skills
Topic   yes yes yes


Writing based on imaginary events or people      


e.g., artwork of Vincent Van Gogh      

Natural sciences

e.g., the reproductive process of fish      

Social sciences

e.g., one man, one vote; cost effectiveness of heart transplants

Personal accounts

e.g., diary account of death of a parent      
Voice   yes yes no


Stories, personal accounts, personal anecdotes      


Describes person, place, or thing      


Attempt to influence others to take some action or to influence someone’s attitudes or ideas      


Share knowledge; convey messages, provide information on a topic, instructions for performing a task      
Genre   yes yes no









For measures of reading and editing skills, the cognitive demands category is intended to capture different levels of cognitive processes, ranging from low to high levels. Using similar coding categories as those in previous alignment studies (Education Trust, 1999), RAND distinguished among three levels of cognitive processes: recall, evaluate style, and inference.

Table 2.3 provides descriptions of each of these levels.
In reading, questions that could be answered via direct reference to the passage are recall items, whereas questions that require examinees to interpret the material are inference items. Questions that pertain to the development of ideas or improve upon the presentation of the reading passages are coded as evaluating style. For editing measures, items that entail application of grammatical rules are recall items. Typically, most of these questions concern mechanics or usage errors. Inference items are those that require examinees to identify cause-and-effect relationships, and evaluating style items relate to rhetoric skills, such as sentence organization or clarity.

Table 2.3
Descriptions of the ELA Cognitive Demands Category for Tests
Measuring Reading or Editing Skills
Cognitive Process Description or Example
Recall Answer can be found directly in the text, or by using the definitions of words or literary devices, or by applying grammatical rules
Infer Interpret what is already written
Evaluate style Improve the way the material is written

The above cognitive demands category is not applicable to writing measures because students do not respond to items, but instead write their own compositions. For writing tests, the cognitive demands category focuses on the scoring criteria, particularly the emphasis given to mechanics, word choice, organization, style, and insight.

Table 2.4
Description of the ELA Cognitive Demands Category for Tests
Measuring Writing Skills

Scoring Criteria
Description or Example
Grammar, punctuation, capitalization
Word choice
Use of language, vocabulary, sentence structure
Logical presentation, development of ideas, use of appropriate supporting examples
Style Voice, attention to audience
Insight Analytic proficiency, accurate understanding of stimulus passage, thoughtful perceptions about its ramifications


Rater Agreement in Applying the Coding Categories
Two raters, who had expertise in the relevant subject area, judged alignment by applying the coding categories to each item. One rater coded the math assessments, and the other rater coded the English assessments. An additional rater coded eight tests, 4 each in math and English. All discrepancies were resolved through discussion. Consensus was fairly high, as kappa statistics ranged from .80 to 1.0 (i.e., perfect agreement) for all but two categories. (For specific percent agreement for each coding category, see Appendix B). One of the exceptions was the content category in math, where items often assessed skills in more than one area. Agreement in this category was .76. The final exception was the cognitive demands category in math, where kappa values ranged from .42 to .63, with an average of .56.

Evaluating the Extent of Alignment Among Tests
In interpreting the results, an important issue concerns the standard with which to evaluate the extent of alignment. Specifically, how large should the discrepancies be before we consider two tests to be poorly aligned? To guide its decisions, RAND analyzed data from an alignment study conducted by Education Trust (1999). They found the average discrepancy across coding categories to be approximately 24 percent, with a standard deviation of 19 percent. That is, differences between any two tests were typically within the range of 5 percent-43 percent. Using these results as a guideline, RAND decided that differences of 25 percent or less are considered “small,” (i.e., the tests are well-aligned), differences between 25 percent and 50 percent are “moderate,” (i.e., the tests are moderately aligned), and differences greater than 50 percent are “large” (i.e., the tests are not well-aligned). Thus, in order to be a misalignment, discrepancies between tests must be greater than 50 percent and cannot be attributed to differences in intended test use.

As there is currently no consensus among researchers regarding the standards for judging the extent of alignment among assessments, the above criteria should not be interpreted as a definitive standard. Additionally, because there has been no research to date that has established how large discrepancies among tests must be before they send students received mixed signals regarding the skills needed to be prepared for college-level work, differences that are considered “small” can nevertheless have important implications. Thus, categorizations of discrepancies as “small,” “moderate,” or “large” should be interpreted cautiously, and the study’s focus should be viewed as mainly descriptive and comparative.

Although the use of expert judgments is a fairly common approach to studying alignment (e.g., Kenney, Silver, Alacaci, Zawojewski, 1998; Webb, 1999), this study does not provide a complete picture of these assessments. RAND has not, for example, systematically examined differences in content standards or test specifications, which may account for some of the discrepancies among exams. Furthermore, an analysis of scores might reveal that seemingly different instruments rank order or classify students roughly equivalently. Similarly, observations and interviews with students as they take the tests, an approach that is sometimes used during the test development process, could result in somewhat different interpretations of a test’s reasoning requirements.

Finally, increasing the number of forms studied for each assessment may enhance the generalizability of the findings. Although researchers attempted to examine all available forms, this was not always possible. Namely, college admissions measures and some commercially-available college placement exams have multiple, parallel versions. Despite the fact that parallel forms are intended to have similar content and structure, tests represent a sample of skills from a single testing occasion, so forms from other occasions will vary to some extent. This is especially true when RAND analyze alignment among English Language Arts (ELA) topics, where any given test form provides a limited sample (e.g., there may be only one reading passage).


For additional information on these and other Bridge Project activities, please contact Terry Alter.