easyCBM
Proficient Math

Descriptive Information

Please provide a description of your tool:

easyCBM® is a web-based district assessment system that includes both benchmarking and progress monitoring assessments combined with a comprehensive array of reports. The assessments in easyCBM are curriculum-based general outcome measures, or CBMs, which are standardized measures that sample from a year’s worth of curriculum to assess the degree to which students have mastered the skills and knowledge deemed critical at each grade level. easyCBM, available for Grades K–8, provides three forms of a screening measure to be used locally for establishing benchmarks and multiple forms (generally 10 per strand in math) to be used to monitor progress. All measures have been developed with reference to specific content in math (Common Core State Standards) and developed using Item Response Theory (IRT).

The tool is intended for use with the following grade(s).

Preschool / Pre - kindergarten
Kindergarten
First grade
Second grade
Third grade
Fourth grade
Fifth grade
Sixth grade
Seventh grade
Eighth grade
Ninth grade
Tenth grade
Eleventh grade
Twelfth grade

The tool is intended for use with the following age(s).

0-4 years old
5 years old
6 years old
7 years old
8 years old
9 years old
10 years old
11 years old
12 years old
13 years old
14 years old
15 years old
16 years old
17 years old
18 years old

The tool is intended for use with the following student populations.

Students in general education
Students with disabilities
English language learners

ACADEMIC ONLY: What skills does the tool screen?

Reading

Phonological processing:

RAN
Memory
Awareness
Letter sound correspondence
Phonics
Structural analysis

Word ID

Accuracy
Speed

Nonword

Accuracy
Speed

Spelling

Accuracy
Speed

Passage

Accuracy
Speed

Reading comprehension:

Multiple choice questions
Cloze
Constructed Response
Retell
Maze
Sentence verification
Other (please describe):

Vocabulary in context

Listening comprehension:

Multiple choice questions
Cloze
Constructed Response
Retell
Maze
Sentence verification
Vocabulary
Expressive
Receptive

Mathematics

Global Indicator of Math Competence

Accuracy
Speed
Multiple Choice
Constructed Response

Early Numeracy

Accuracy
Speed
Multiple Choice
Constructed Response

Mathematics Concepts

Accuracy
Speed
Multiple Choice
Constructed Response

Mathematics Computation

Accuracy
Speed
Multiple Choice
Constructed Response

Mathematic Application

Accuracy
Speed
Multiple Choice
Constructed Response

Fractions/Decimals

Accuracy
Speed
Multiple Choice
Constructed Response

Algebra

Accuracy
Speed
Multiple Choice
Constructed Response

Geometry

Accuracy
Speed
Multiple Choice
Constructed Response

Other (please describe):

Please describe specific domain, skills or subtests:

BEHAVIOR ONLY: Which category of behaviors does your tool target?

Internalizing
Externalizing
Internalizing and Externalizing

BEHAVIOR ONLY: Please identify which broad domain(s)/construct(s) are measured by your tool and define each sub-domain or sub-construct.

Acquisition and Cost Information

Where to obtain:

Email Address

District: inquiry@service.riversideinsights.com; Individual: support@easycbm.com

Address

District Users: Riverside Insights, Attention: Customer Service One Pierce Place, Suite 101C, Itasca, Illinois 60143 Individual Users: BRT, University of Oregon, Eugene, OR 97403

Phone Number

District: 800/323.9540

Website

District accounts: https://riversideinsights.com/k12-assessments/easycbm; Teacher accounts: easyCBM.com

Initial cost for implementing program:

Cost

$7.75

Unit of cost

student

Replacement cost per unit for subsequent use:

Cost

$7.75

Unit of cost

student

Duration of license

year

Additional cost information:

Describe basic pricing plan and structure of the tool. Provide information on what is included in the published tool, as well as what is not included but required for implementation.

easyCBM is available through Riverside Insights on an annual subscription license for districts. Price is $7.75/student/year, which gives teachers access to all measures. The price includes manuals and use of the assessments. Training webinars are provided through the Riverside Training Academy; prices range from $500-$1700 depending on the number of teachers in the district. It is also available directly through the University of Oregon for individual classroom teacher use (limited to one teacher per building, maximum of 200 students). This teacher subscription includes the online training that is part of the system. As easyCBM is computer-administered, students should have access to an Internet-connected computer (Mac or PC). However, they can also take the tests in paper/pencil versions, with responses being manually added to the online system for scoring. Teachers need Internet-connected computers to access the manual, score reports, training videos, etc.

Provide information about special accommodations for students with disabilities.

All measures were developed following Universal Design for Assessment guidelines to reduce the need for accommodations. All mathematics items include a built-in read aloud option for every question and response requiring reading. Districts are directed to follow their standard practices for providing additional accommodations as needed.

Administration

BEHAVIOR ONLY: What type of administrator is your tool designed for?

General education teacher
Special education teacher
Parent
Child
External observer
Other

If other, please specify:

What is the administration setting?

Direct observation
Rating scale
Checklist
Performance measure
Questionnaire
Direct: Computerized
One-to-one
Other

If other, please specify:

Does the tool require technology?

Yes

If yes, what technology is required to implement your tool? (Select all that apply)

Computer or tablet
Internet connection
Other technology (please specify)

If your program requires additional technology not listed above, please describe the required technology and the extent to which it is combined with teacher small-group instruction/intervention:

Educators can also use printers to print reports and PDF versions of the measures, if they wish.

What is the administration context?

Individual
Small group   If small group, n=
Large group   If large group, n=
Computer-administered
Other

If other, please specify:

What is the administration time?

Time in minutes

30

per (student/group/other unit)

student

Additional scoring time:

Time in minutes

0

per (student/group/other unit)

student

ACADEMIC ONLY: What are the discontinue rules?

No discontinue rules provided
Basals
Ceilings
Other

If other, please specify:

Are norms available?

Yes

Are benchmarks available?

Yes

If yes, how many benchmarks per year?

3

If yes, for which months are benchmarks available?

August/September, December/January, and May/June

BEHAVIOR ONLY: Can students be rated concurrently by one administrator?

If yes, how many students can be rated concurrently?

Training & Scoring

Training

Is training for the administrator required?

Yes

Describe the time required for administrator training, if applicable:

Less than 1 hour of training

Please describe the minimum qualifications an administrator must possess.

Paraprofessional level

No minimum qualifications

Are training manuals and materials available?

Yes

Are training manuals/materials field-tested?

Yes

Are training manuals/materials included in cost of tools?

Yes

If No, please describe training costs:

Training is provided through the Riverside Training Academy for an annual cost of $500–$1700, depending on the number of educators in the district.

Can users obtain ongoing professional and technical support?

Yes

If Yes, please describe how users can obtain support:

Help Desk via email and phone, as well as through the online FAQ/help page

Scoring

How are scores calculated?

Manually (by hand)
Automatically (computer-scored)
Other

If other, please specify:

Do you provide basis for calculating performance level scores?

Yes

What is the basis for calculating performance level and percentile scores?

Age norms
Grade norms
Classwide norms
Schoolwide norms
Stanines
Normal curve equivalents

What types of performance level scores are available?

Raw score
Standard score
Percentile score
Grade equivalents
IRT-based score
Age equivalents
Stanines
Normal curve equivalents
Developmental benchmarks
Developmental cut points
Equated
Probability
Lexile score
Error analysis
Composite scores
Subscale/subtest scores
Other

If other, please specify:

Does your tool include decision rules?

Yes

If yes, please describe.

Students are identified as “low risk”, “some risk”, or “high risk” based on their performance on the Proficient Mathematics measures relative to grade-level peers in the national norm group. Individual districts set the range of percentile ranks for such classifications following training provided by Riverside Insights on the system and its uses. The benchmark/screener reports provide suggested progress monitoring measures to use as follow-up for students identified as “high risk.” Trainings on the system provide guidance to teachers to log and provide interventions to students identified as “some risk” or “high risk” following their district’s policies.

Can you provide evidence in support of multiple decision rules?

No

If yes, please describe.

Please describe the scoring structure. Provide relevant details such as the scoring format, the number of items overall, the number of items per subscale, what the cluster/composite score comprises, and how raw scores are calculated.

The Proficient Mathematics score is simply the total of all items correct.

Describe the tool’s approach to screening, samples (if applicable), and/or test format, including steps taken to ensure that it is appropriate for use with culturally and linguistically diverse populations and students with disabilities.

The authors have approached screening from two perspectives with respect to (a) goal level sampling from nationally framed standards and (b) scaling. Test format focuses on principles of universal design with either individually administered tasks (for early reading skills and fluency) or computer-based testing for group-administered tests in vocabulary, comprehension, and all mathematics tests. Scoring practices emphasize objectivity with diagnostic information for teachers and immediate feedback for students. a) In mathematics, the authors used the Common Core State Standards (CCSS) to direct item content for the Proficient Mathematics assessments. Grade-level teachers with expertise in Special Education and Mathematics were hired to write the items, with further review by content and assessment experts at the University of Oregon. b) From a scaling perspective, the authors designed alternate forms for the math measures to be comparable using item response theory (IRT). A common-person, common-item equating design was used to scale all items. Within specific skill areas, approximately 250 students responded to multiple item sets, and each test form contains items common across forms. The equated item scale scores and model fit statistics were used to (a) identify items of similar difficulty, (b) estimate student equated scores, and (c) remove/revise items of poor psychometric quality. The authors then placed the items into final alternate forms so that each form included items with similar levels of difficulty. The authors generally placed easier items and interspersed common items near the beginning of the form, as Benchmark screening measures are timed, and students would then be assured of a sensitive measure for estimating their ability. Tasks are grade-level referenced. For all computer-based tests, the student administration is compatible with popular browsers (PC: Firefox and Chrome, Mac: Safari, Firefox, and Chrome). Furthermore, the computer presentation is optimized for a clear presentation of the item, with large-option buttons to facilitate option selection, and “next” buttons to assure easy navigation in moving forward or backward across problems. Test items and test forms underwent bias review to ensure that they are appropriate for diverse populations, with a special emphasis on culturally and linguistically diverse student populations and students with learning disabilities. In addition, the authors conduct DIF analyses to provide evidence that the items function equivalently across different student populations.

Classification Accuracy & Cross-Validation Summary

Grade	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Classification Accuracy Fall
Classification Accuracy Winter
Classification Accuracy Spring

Smarter Balanced Mathematics Assessment (SBAS Math)

Classification Accuracy

Select time of year

Fall

Winter

Spring

Describe the criterion (outcome) measure(s) including the degree to which it/they is/are independent from the screening measure.

We used the Smarter Balanced Mathematics Assessment as our criterion measure. This measure is completely independent from the screening measure, although both SBAS and easyCBM are aligned to the Common Core State Standards in Mathematics. SBAS is a large-scale assessment in wide use across the United States as a state accountability measure.

Do the classification accuracy analyses examine concurrent and/or predictive classification?

Concurrent
Predictive

Describe when screening and criterion measures were administered and provide a justification for why the method(s) you chose (concurrent and/or predictive) is/are appropriate for your tool.

Describe how the classification analyses were performed and cut-points determined. Describe how the cut points align with students at-risk. Please indicate which groups were contrasted in your analyses (e.g., low risk students versus high risk students, low risk students versus moderate risk students).

We conducted a receiver operating characteristics (ROC) analysis for each grade, season, and measure to determine the optimal cut score (defined as the score associated with the highest sum of sensitivity and specificity) for each measures to classify students at or below the 20th percentile on the Smarter Balance Assessment System reading/math. The cut point of the score associated with the 20th percentile aligns with prior studies and wide-spread district policy that suggests this is an appropriate cut-point for identifying students with intensive need, contrasting high risk students with students not at high risk. Analyses were conducted and created in the R programming environment (R Core Team, 2024) with the cutpointr R package (Theile & Hirschfeld, 2021).

Were the children in the study/studies involved in an intervention in addition to typical classroom instruction between the screening measure and outcome assessment?

Yes

If yes, please describe the intervention, what children received the intervention, and how they were chosen.

Students who scored below the cut-point 20th percentile were assigned a variety of interventions, depending on specific pattern of need (types of assessment items with which they struggled, success of prior years’ interventions, whether they also had identified literacy needs) and resources available at the schools. Interventions ranged from one-on-one daily instruction on mathematics to small group (2-6 students) twice-weekly supplemental mathematics instruction, to after-school mentoring with a focus on mathematics, to “flex-Friday” one-hour preview/review sessions with cross-grade-level groupings based on identified content need. A number of students concurrently received several of these interventions (typically only those students whose ELA performance did not indicate a need for literacy intervention as well because those students who also needed literacy intervention simply did not have sufficient time in the school day to receive all the instructional interventions they needed). Interventions were delivered by a variety of personnel (depending on school/district resources): Special Education teachers, general education teachers during their “intervention block”, instructional assistants, and student mentors (some adult, some older children).

Cross-Validation

Has a cross-validation study been conducted?

No

If yes,

Select time of year.

Fall

Winter

Spring

Describe the criterion (outcome) measure(s) including the degree to which it/they is/are independent from the screening measure.

Do the cross-validation analyses examine concurrent and/or predictive classification?

Concurrent
Predictive

Describe when screening and criterion measures were administered and provide a justification for why the method(s) you chose (concurrent and/or predictive) is/are appropriate for your tool.

Describe how the cross-validation analyses were performed and cut-points determined. Describe how the cut points align with students at-risk. Please indicate which groups were contrasted in your analyses (e.g., low risk students versus high risk students, low risk students versus moderate risk students).

Were the children in the study/studies involved in an intervention in addition to typical classroom instruction between the screening measure and outcome assessment?

If yes, please describe the intervention, what children received the intervention, and how they were chosen.

---

Classification Accuracy - Fall

Evidence	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Criterion measure	Smarter Balanced Mathematics Assessment (SBAS Math)	Smarter Balanced Mathematics Assessment (SBAS Math)	Smarter Balanced Mathematics Assessment (SBAS Math)	Smarter Balanced Mathematics Assessment (SBAS Math)	Smarter Balanced Mathematics Assessment (SBAS Math)	Smarter Balanced Mathematics Assessment (SBAS Math)
Cut Points - Percentile rank on criterion measure	20	20	20	20	20	20
Cut Points - Performance score on criterion measure	2362	2397	2410	2423	2427	2434
Cut Points - Corresponding performance score (numeric) on screener measure	21	23	23	21	21	21
Classification Data - True Positive (a)	743	739	716	573	511	560
Classification Data - False Positive (b)	45	13	13	42	29	19
Classification Data - False Negative (c)	247	228	303	169	298	270
Classification Data - True Negative (d)	168	154	164	183	195	154
Area Under the Curve (AUC)	0.84	0.92	0.89	0.86	0.81	0.84
AUC Estimate’s 95% Confidence Interval: Lower Bound	0.84	0.91	0.89	0.86	0.81	0.84
AUC Estimate’s 95% Confidence Interval: Upper Bound	0.85	0.92	0.89	0.86	0.81	0.84

Statistics	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Base Rate	0.82	0.85	0.85	0.77	0.78	0.83
Overall Classification Rate	0.76	0.79	0.74	0.78	0.68	0.71
Sensitivity	0.75	0.76	0.70	0.77	0.63	0.67
Specificity	0.79	0.92	0.93	0.81	0.87	0.89
False Positive Rate	0.21	0.08	0.07	0.19	0.13	0.11
False Negative Rate	0.25	0.24	0.30	0.23	0.37	0.33
Positive Predictive Power	0.94	0.98	0.98	0.93	0.95	0.97
Negative Predictive Power	0.40	0.40	0.35	0.52	0.40	0.36

Sample	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Date	Fall 2023	Fall 2023	Fall 2023	Fall 2023	Fall 2023	Fall 2023
Sample Size	1203	1134	1196	967	1033	1003
Geographic Representation	New England (CT) Pacific (OR, WA)	New England (CT) Pacific (OR, WA)	New England (CT) Pacific (OR, WA)	New England (CT) Pacific (OR, WA)	New England (CT) Pacific (OR, WA)	New England (CT) Pacific (OR, WA)
Male	52.4%	52.2%	51.4%	50.1%	51.9%	52.1%
Female	47.6%	47.8%	48.3%	49.8%	47.9%	46.9%
Other
Gender Unknown			0.3%	0.1%	0.2%	1.0%
White, Non-Hispanic	60.7%	58.8%	59.7%	61.4%	60.2%	59.1%
Black, Non-Hispanic	8.4%	8.9%	10.2%	9.0%	9.7%	8.3%
Hispanic	21.6%	22.6%	22.8%	22.4%	22.6%	20.9%
Asian/Pacific Islander	10.6%	8.7%	10.4%	9.7%	10.1%	11.9%
American Indian/Alaska Native	1.3%	2.5%	1.1%	0.7%	1.5%	1.3%
Other	19.0%	21.1%	18.6%	19.1%	18.6%	19.4%
Race / Ethnicity Unknown
Low SES
IEP or diagnosed disability	19.7%	17.1%	16.2%	15.1%	15.3%	14.6%
English Language Learner	8.7%	6.8%	5.4%	6.3%	5.3%	3.6%

Classification Accuracy - Winter

Evidence	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Criterion measure	Smarter Balanced Mathematics Assessment (SBAS Math)	Smarter Balanced Mathematics Assessment (SBAS Math)	Smarter Balanced Mathematics Assessment (SBAS Math)	Smarter Balanced Mathematics Assessment (SBAS Math)	Smarter Balanced Mathematics Assessment (SBAS Math)	Smarter Balanced Mathematics Assessment (SBAS Math)
Cut Points - Percentile rank on criterion measure	20	20	20	20	20	20
Cut Points - Performance score on criterion measure	2362	2397	2410	2423	2427	2434
Cut Points - Corresponding performance score (numeric) on screener measure	27	25	24	23	22	24
Classification Data - True Positive (a)	816	796	851	574	615	661
Classification Data - False Positive (b)	21	26	23	36	24	26
Classification Data - False Negative (c)	199	200	195	134	195	193
Classification Data - True Negative (d)	203	151	165	177	205	152
Area Under the Curve (AUC)	0.92	0.91	0.92	0.88	0.88	0.88
AUC Estimate’s 95% Confidence Interval: Lower Bound	0.91	0.91	0.92	0.89	0.88	0.88
AUC Estimate’s 95% Confidence Interval: Upper Bound	0.92	0.92	0.93	0.89	0.88	0.88

Statistics	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Base Rate	0.82	0.85	0.85	0.77	0.78	0.83
Overall Classification Rate	0.82	0.81	0.82	0.82	0.79	0.79
Sensitivity	0.80	0.80	0.81	0.81	0.76	0.77
Specificity	0.91	0.85	0.88	0.83	0.90	0.85
False Positive Rate	0.09	0.15	0.12	0.17	0.10	0.15
False Negative Rate	0.20	0.20	0.19	0.19	0.24	0.23
Positive Predictive Power	0.97	0.97	0.97	0.94	0.96	0.96
Negative Predictive Power	0.50	0.43	0.46	0.57	0.51	0.44

Sample	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Date	Winter 2024	Winter 2024	Winter 2024	Winter 2024	Winter 2024	Winter 2024
Sample Size	1239	1173	1234	921	1039	1032
Geographic Representation	New England (CT) Pacific (OR, WA)	New England (CT) Pacific (OR, WA)	New England (CT) Pacific (OR, WA)	New England (CT) Pacific (OR, WA)	New England (CT) Pacific (OR, WA)	New England (CT) Pacific (OR, WA)
Male	52.1%	51.9%	51.3%	50.9%	51.0%	52.5%
Female	47.9%	48.1%	48.5%	49.0%	48.7%	46.6%
Other
Gender Unknown			0.2%	0.1%	0.3%	0.9%
White, Non-Hispanic	60.1%	58.1%	59.2%	62.1%	59.6%	59.3%
Black, Non-Hispanic	8.6%	9.5%	10.5%	8.9%	10.2%	8.2%
Hispanic	22.1%	22.8%	23.5%	22.0%	22.0%	21.5%
Asian/Pacific Islander	10.6%	8.8%	10.3%	9.0%	9.7%	11.5%
American Indian/Alaska Native	1.5%	2.6%	1.1%	0.7%	1.5%	1.6%
Other	19.3%	21.1%	19.0%	19.3%	19.0%	19.4%
Race / Ethnicity Unknown
Low SES
IEP or diagnosed disability	19.3%	17.1%	16.4%	14.9%	15.4%	15.0%
English Language Learner	8.6%	6.7%	5.4%	5.0%	5.2%	3.4%

Classification Accuracy - Spring

Evidence	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Criterion measure	Smarter Balanced Mathematics Assessment (SBAS Math)	Smarter Balanced Mathematics Assessment (SBAS Math)	Smarter Balanced Mathematics Assessment (SBAS Math)	Smarter Balanced Mathematics Assessment (SBAS Math)	Smarter Balanced Mathematics Assessment (SBAS Math)	Smarter Balanced Mathematics Assessment (SBAS Math)
Cut Points - Percentile rank on criterion measure	20	20	20	20	20	20
Cut Points - Performance score on criterion measure	2362	2397	2410	2423	2427	2434
Cut Points - Corresponding performance score (numeric) on screener measure	30	28	22	23	24	25
Classification Data - True Positive (a)	892	815	953	659	580	667
Classification Data - False Positive (b)	42	13	37	38	16	18
Classification Data - False Negative (c)	141	201	99	106	234	135
Classification Data - True Negative (d)	194	169	161	208	207	129
Area Under the Curve (AUC)	0.92	0.94	0.94	0.92	0.88	0.92
AUC Estimate’s 95% Confidence Interval: Lower Bound	0.92	0.94	0.94	0.91	0.87	0.92
AUC Estimate’s 95% Confidence Interval: Upper Bound	0.92	0.94	0.94	0.92	0.88	0.92

Statistics	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Base Rate	0.81	0.85	0.84	0.76	0.78	0.85
Overall Classification Rate	0.86	0.82	0.89	0.86	0.76	0.84
Sensitivity	0.86	0.80	0.91	0.86	0.71	0.83
Specificity	0.82	0.93	0.81	0.85	0.93	0.88
False Positive Rate	0.18	0.07	0.19	0.15	0.07	0.12
False Negative Rate	0.14	0.20	0.09	0.14	0.29	0.17
Positive Predictive Power	0.96	0.98	0.96	0.95	0.97	0.97
Negative Predictive Power	0.58	0.46	0.62	0.66	0.47	0.49

Sample	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Date	Spring 2024	Spring 2024	Spring 2024	Spring 2024	Spring 2024	Spring 2024
Sample Size	1269	1198	1250	1011	1037	949
Geographic Representation	New England (CT) Pacific (OR, WA)	New England (CT) Pacific (OR, WA)	New England (CT) Pacific (OR, WA)	New England (CT) Pacific (OR, WA)	New England (CT) Pacific (OR, WA)	New England (CT) Pacific (OR, WA)
Male	52.3%	51.8%	51.0%	51.1%	52.1%	52.8%
Female	47.6%	48.2%	48.8%	48.8%	47.5%	46.2%
Other
Gender Unknown	0.1%		0.2%	0.1%	0.4%	1.1%
White, Non-Hispanic	59.7%	58.2%	59.0%	61.1%	59.2%	60.8%
Black, Non-Hispanic	8.7%	9.7%	10.8%	9.9%	10.2%	8.2%
Hispanic	22.4%	22.5%	23.8%	23.4%	22.7%	21.0%
Asian/Pacific Islander	10.8%	8.7%	10.1%	9.3%	9.9%	11.4%
American Indian/Alaska Native	1.5%	1.1%	1.0%	1.0%	1.7%	1.3%
Other	19.2%	20.9%	19.0%	18.7%	18.9%	18.3%
Race / Ethnicity Unknown
Low SES
IEP or diagnosed disability	19.5%	17.4%	15.9%	14.8%	14.2%	15.3%
English Language Learner	8.9%	6.7%	5.9%	6.3%	5.2%	3.1%

Reliability

Grade	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Rating

*Offer a justification for each type of reliability reported, given the type and purpose of the tool.

Rasch marginal reliability reflects the average precision of the latent trait (θ) estimates for the specific sample. If marginal reliability is 0.80, a useful interpretation is that most of the variability in θ across students represents real differences rather than estimation error—on average, given the fitted Rasch model and the sample’s score distribution. Because IRT provides conditional precision, marginal reliability summarizes (averages) information that varies across the score scale. Precision tends to be highest where test information is greatest (often around the middle of the distribution) and lower at extreme high/low performance. Marginal reliability is therefore especially informative when the tool is used for growth monitoring or when multiple forms are intended to be comparable. Cronbach’s Alpha is an estimate of the internal consistency of the measures. Because the measures are often administered for a set period of time (typically 15 minutes), not all students will complete all items. Having an internally-consistent measure provides some reassurance that scores obtained when students complete only some of the items (for instance, when they “time out” after responding to only half of the possible items on the assessment) reflect the distribution of scores that would be obtained were the entire test completed. Alpha can be interpreted as the expected correlation between two parallel forms of the test (under strict assumptions), or as the degree to which the items hang together as a scale. An alpha of 0.80 suggests that about 80% of the observed total-score variance is attributable to true-score variance and 20% to random error, within the tested sample.

*Describe the sample(s), including size and characteristics, for each reliability analysis conducted.

Demographic information for the sample used for the study are described here. Records from individual students who had taken the easyCBM Proficient Math measure were drawn from districts who allowed research to be conducted on their district data. The data draw included the following fields: Site, Student ID, Grade, disability, English language learner, Ethnicity, Race, Gender, Form (an internal check), Start, Finish, Test Grade, Use (Benchmark only), Benchmark Grade, and Academic Year. The Fall sample included 8,032 Grade 3 students, 9,600 Grade 4 students, 9,449 Grade 5 students, 8,760 Grade 6 students, 8,473 Grade 7 students, and 8,969 Grade 8 students. The Winter sample included 5,767 Grade 3 students, 7,121 Grade 4 students, 6,941 Grade 5 students, 5.157 Grade 6 students, 3,942 Grade 7 students, and 4,734 Grade 8 students. Students with disabilities made up 17.84 percent of the Fall sample and 14.55 percent of the Winter sample; English Learners made up 18.96 percent of the Fall sample and 13.61 percent of the Winter sample; 50.21 of the students in the Fall sample were male and 36.37 percent of the Winter sample was male; 47.56 percent of the Fall sample was female and 33.93 percent of the Winter sample was female. The racial composition of the sample was White - 51.3 percent in the Fall and 36.68 in the Winter; Black/African American - 10.84 percent in the Fall and 10.54 percent in the Winter; Two or More Races - 5.2 percent in the Fall and 3.92 percent in the Winter; Asian - 1.98 percent in the Fall and 1.33 percent in the Winter; American Indian/Native Alaskan - 1.02 percent in the Fall and 0.51 percent in the Winter; Native Hawaiian/Pacific Islander - 0.33 percent in the Fall and 0.22 in the Winter.

*Describe the analysis procedures for each reported type of reliability.

The master file drawn from easyCBM server contained all records for fall and winter benchmarks. This file was then separated into two separate files for Fall and Winter Benchmarks. The analyses conducted for this study incorporated marginal reliability and Cronbach’s alpha as indices of score consistency. Within an item response theory (IRT) framework, marginal reliability evaluates how reliably the tests measure student ability across the population. Marginal reliability is calculated using IRT-based ability estimates and their associated standard errors to produce an overall reliability value (Samajima 1994). By weighting reliability by the distribution of student ability, marginal reliability provides a stable, interpretable index of overall score consistency. Conceptually, marginal reliability reflects the proportion of observed variance in estimated latent ability that is attributable to true differences in ability rather than measurement error, defined as the variance of the ability estimates divided by the total of that variance plus the average error variance. In an IRT framework, error varies as a function of the latent ability, and the error variance can be integrated such that the marginal reliability for IRT scores is the ratio of the variance of the estimated latent abilities relative to the sum of the variance of the latent ability and the expected error variance. Marginal reliability coefficients were estimated for each grade and season combination. We used the TAM (Robitzsch, Kiefer, & Wu, 2025) package in the R (R Core Team, 2025) environment to fit a Rasch model using marginal maximum likelihood, where the expected a posteriori (EAP) reliability estimate is defined as v/(s+v) where v is the variance of theta estimates and s is the average of the squared error (Adams, 2005). To compute confidence intervals, a bootstrapping approach was applied with 500 bootstraps. We also estimated Cronbach’s alpha (Cronbach, 1951) as a measure of internal consistency, which estimates the proportion of observed score variance attributable to a common latent construct, under a tau-equivalence model. Alpha is estimated from the inter-item covariance structure and reflects the degree to which scale items measure a common underlying construct. We used the psych (Revelle, 2025) package to estimate Cronbach’s alpha. In addition to TAM (Robitzsch, Kiefer, & Wu, 2025) and psych (Revelle, 2025), he following R packages were also used in the creation of this report: data.table (Barrett et al., 2025), flextable (Gohel & Skintzos, 2025), here (Müller, 2025), janitor (Firke, 2024), tidymodels (Kuhn & Wickham, 2020), and tidyverse (Wickham et al., 2019).

*In the table(s) below, report the results of the reliability analyses described above (e.g., internal consistency or inter-rater reliability coefficients).

Type of	Subgroup	Informant	Age / Grade	Test or Criterion	n	Median Coefficient	95% Confidence Interval Lower Bound	95% Confidence Interval Upper Bound

Results from other forms of reliability analysis not compatible with above table format:

Manual cites other published reliability studies:

No

Provide citations for additional published studies.

Do you have reliability data that are disaggregated by gender, race/ethnicity, or other subgroups (e.g., English language learners, students with disabilities)?

No

If yes, fill in data for each subgroup with disaggregated reliability data.

Type of	Subgroup	Informant	Age / Grade	Test or Criterion	n	Median Coefficient	95% Confidence Interval Lower Bound	95% Confidence Interval Upper Bound

Results from other forms of reliability analysis not compatible with above table format:

Manual cites other published reliability studies:

No

Provide citations for additional published studies.

Validity

Grade	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Rating

*Describe each criterion measure used and explain why each measure is appropriate, given the type and purpose of the tool.

Three separate studies are described here. STUDY 1: We analyzed the relation between the easyCBM Proficient Mathematics assessment (Grades 3-8) and the Mathematics section of the Smarter Balanced Assessment System (SBAS). The widespread use of SBAS across the United States makes it an appropriate measure to use for analyzing criterion validity (both predictive and concurrent). It is external to the easyCBM system and is considered a high-stakes assessment, as it is the measure many states are using for their statewide large-scale assessment system. STUDY 2: We analyzed the relation between the easyCBM Proficient Mathematics Winter Benchmark Assessment (Grades 6-8) and the Stanford Achievement Test, 10th Edition (SAT-10), given one week later. We selected the SAT-10 based on its documented validity evidence (Pearson, 2004) and because both tests were designed to measure a similar construct (mathematics). STUDY 3: We analyzed the relation between the easyCBM Proficient Mathematics measures and the Mathematics section of the Smarter Balanced Assessment.

*Describe the sample(s), including size and characteristics, for each validity analysis conducted.

STUDY 1: Data for this study came from a convenience sample provided by two school districts in the Pacific Northwest. All students enrolled in school and present during the three-week easyCBM benchmark assessment windows in the fall (September 2014), winter (January 2015) and spring (May 2015) were administered the easyCBM assessments. All enrolled students were likewise administered the Smarter Balanced assessments during the testing window provided by the state in the spring of 2015. The data set provided by the districts included easyCBM Proficient Math, Passage Reading Fluency, Vocabulary, and Proficient Reading as well as Smarter Balanced Math and English Language Arts total scores for students enrolled in Grades 3-8. District 1 provided data for Grades 3-8, while District 2 provided data for Grades 4-8. In addition, District 1 provided demographic information, while District 2 (approximately ¼ the size of the first district) did not. Demographics of the sample are provided in Table 1. Because of the missing demographics from a large proportion of the sample, the percentages for each of the demographic variables are calculated based on the students in the sample whose data included full-resolution demographic information. During data cleaning, data from students who were administered the Alternate Assessment rather than the General Education assessment were removed from the dataset prior to further analyses. In all, six students each from Grades 4, 6, and 7 and three students from Grade 5 were removed from the dataset in this step. Data from all additional students were retained. STUDY 2: This convenience sample came from a random sample of students per grade (Grades 6, 7, and 8) within one school in the Pacific Northwest. The 6th grade sample (n = 67) included 33 girls, 8 students receiving special education services (SPED classification included: 1 identified as having an intellectual disability, 1 communication disorder, 1 other health impairment, and 6 learning disability). Of the 67 students, 6 were identified as English Language Learners, and 42 received free (n=36) or reduced-price (n=6) meals. In all, 56 students in this sample were identified as white, 7 as Hispanic, 1 as Asian, and 3 as “other”. The 7th grade sample (n = 63) included 24 girls, 7 students receiving special education services (SPED classification included: 3 identified as having an intellectual disability, 1 other health impairment, and 3 learning disability). Of the 63 students, 3 were identified as English Language Learners, and 36 received free (n=31) or reduced-price (n=5) meals. In all, 49 students in this sample were identified as white, 7 as Hispanic, 2 as Black/African American, and 5 as “other”. The 8th grade sample (n = 64) included 38 girls, 6 students receiving special education services (SPED classification included: 1 Autism spectrum disorder, 1 other health impairment, and 4 learning disability). Of the 64 students, 0 were identified as English Language Learners, and 29 received free (n=22) or reduced-price (n=7) meals. In all, 51 students in this sample were identified as white, 10 as Hispanic, and 2 as “other.” STUDY 3: Data came from a sample of students in four districts who took the Smarter Balanced Assessment in the spring of 2023 and who were also assessed with an easyCBM fall, winter, or spring benchmark measure for Proficient Math, Passage Reading Fluency, Vocabulary, and Proficient Reading in the 2022-2023 school year. The Smarter Balanced Math and English Language Arts total scores for students enrolled in Grades 3-8 were used for comparison. One of the four districts provided data for Grades 3-5 for Smarter Balanced ELA only. Demographics of the sample are provided in the Technical Report 2401 (available from the Center upon request).

*Describe the analysis procedures for each reported type of validity.

In STUDY 1 and STUDY 2, we analyzed the data using bivariate correlations and linear regression using the SPSS software. In STUDY 3, we used Pearson bivariate correlations using the rstatix package (Kassambara, 2023) in the R programming environment (R Core Team, 2024). Kassambara, A. (2023). rstatix: Pipe-Friendly Framework for Basic Statistical Tests. R package version 0.7.2.

*In the table below, report the results of the validity analyses described above (e.g., concurrent or predictive validity, evidence based on response processes, evidence based on internal structure, evidence based on relations to other variables, and/or evidence based on consequences of testing), and the criterion measures.

Type of	Subgroup	Informant	Age / Grade	Test or Criterion	n	Median Coefficient	95% Confidence Interval Lower Bound	95% Confidence Interval Upper Bound

Results from other forms of validity analysis not compatible with above table format:

Manual cites other published reliability studies:

No

Provide citations for additional published studies.

Describe the degree to which the provided data support the validity of the tool.

Data from all three studies support the concurrent and predictive validity of the tool. Correlations between the easyCBM Proficient Mathematics measures and two very different external measures of mathematics suggest that the easyCBM Proficient Math assessments are, indeed, capturing important information about students’ knowledge of mathematics. The easyCBM Proficient Mathematics measures consistently predict student performance on other measures of mathematics

Do you have validity data that are disaggregated by gender, race/ethnicity, or other subgroups (e.g., English language learners, students with disabilities)?

No

If yes, fill in data for each subgroup with disaggregated validity data.

Type of	Subgroup	Informant	Age / Grade	Test or Criterion	n	Median Coefficient	95% Confidence Interval Lower Bound	95% Confidence Interval Upper Bound

Results from other forms of validity analysis not compatible with above table format:

Manual cites other published reliability studies:

No

Provide citations for additional published studies.

Bias Analysis

Grade	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Rating	Provided	Provided	Provided	Provided	Provided	Provided

Have you conducted additional analyses related to the extent to which your tool is or is not biased against subgroups (e.g., race/ethnicity, gender, socioeconomic status, students with disabilities, English language learners)? Examples might include Differential Item Functioning (DIF) or invariance testing in multiple-group confirmatory factor models.

Yes

If yes,

a. Describe the method used to determine the presence or absence of bias:

We ran DIF analyses for all our Proficient Math measures using the Mantel-Haenszel (MH) procedure with an iterative purification process. Items were evaluated by the delta MH statistic, and assigned letter grades (A, B, or C) based on the recommendation of Holland and Thayer (1988).

b. Describe the subgroups for which bias analyses were conducted:

We conducted DIF analyses for the following sub-groups: gender, disability status, and race/ethnicity.

c. Describe the results of the bias analyses conducted, including data and interpretative statements. Include magnitude of effect (if available) if bias has been identified.

Results indicated the Proficient Math measures are not biased against gender, disability status, or race/ethnicity. At all grade levels, and all seasons, the Proficient Math measures received a grade of “A” in the DIF analyses in all three of the groupings examined.