i-Ready® Diagnostic
Mathematics

Descriptive Information

Please provide a description of your tool:

Offering a continuum of scale scores from kindergarten through high school, the i-Ready Diagnostic for Mathematics, a web-based adaptive screening assessment, is part of i-Ready’s integrated teaching and learning system. The i-Ready Diagnostic is a valid and reliable tool aligned to rigorous state standards across the following domains: Number and Operations, Algebra and Algebraic Thinking, Measurement and Data, and Geometry, and provides actionable data and reports for each domain. The i-Ready Diagnostic is typically administered three times per academic year, with a recommended 12-18 weeks of instruction between assessments. Each screening takes approximately 45 minutes—which may be broken into multiple sittings—and may be conducted with all students or with specific groups of students who have been identified as at risk of academic failure. i-Ready Diagnostic’s sophisticated adaptive algorithm automatically selects from thousands of technology-enhanced and multiple-choice items to get to the core of each student's strengths and challenges, regardless of the grade level at which he or she is performing. The system automatically analyzes, scores, and provides reports that include student-level and aggregated (e.g., class, school, and district) results. Available as soon as a student completes the assessment, i-Ready Diagnostic’s intuitive reports provide comprehensive information (including developmental analyses) about student performance, group students who struggle with the same concepts, make instructional recommendations to target skill deficiencies, and monitor progress and growth as students follow their individualized instructional paths. Reports include suggested next steps for instruction and PDF Tools for Instruction lesson plans for the teacher to use during individual, small-group, or whole-class instruction. In addition, should educators also purchase the optional i-Ready Personalized Instruction, the system automatically prescribes online lessons that address each student’s identified academic needs.

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):

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):
Measurement & Data

Please describe specific domain, skills or subtests:

The i-Ready Diagnostic for Mathematics assesses four domains (Number and Operations, Algebra and Algebraic Thinking, Measurement and Data, and Geometry). For the domain of Number and Operations, the topics addressed include counting and cardinality; base ten—whole numbers and decimals (place value, compare, add, subtract, multiply, divide); fractions (model, compare, add, subtract, multiply, divide); rational numbers (model, compare, add, subtract, multiply, divide); and real and complex numbers (model, compare, add, subtract, multiply, divide). For the Algebra and Algebraic Thinking domain, the topics addressed include operations and algebraic thinking (fluency, number relationships, properties, solving word problems); expressions and equations (variables, exponents, solving word problems); ratio and proportional relationships (percent, rate, lines, and slope); functions (linear, exponential, quadratic, polynomial, logarithmic, trigonometric, rational interpreting functions); building functions; and systems of equations and inequalities. For the Geometry domain, the topics addressed include two-dimensional shapes; three-dimensional shapes; lines, segments, points, rays, and angles; symmetry and transformations; congruence and similarity; coordinate geometry; Pythagorean theorem; circles; and proofs. For the Measurements and Data domain, the topics addressed include measurement units and tools - customary and metric (time, money, length, capacity, weight, and mass); geometric measurement; area, perimeter, surface area, volume; creating and interpreting graphs; and statistics and probability (randomness, probability distributions, collecting and analyzing data, making inferences and conclusions based on probability and expected values, and correlations).

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

info@cainc.com

Address

153 Rangeway Road, N. Billerica MA 01862

Phone Number

800-225-0248

Website

www.curriculumassociates.com

Initial cost for implementing program:

Cost

$6.00

Unit of cost

student

Replacement cost per unit for subsequent use:

Cost

$6.00

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.

$6.00/student/year for i-Ready Diagnostic for Mathematics; volume and multi-year subscription discounts are available. Annual license fee includes online student access to assessment, plus staff access to management and reporting suite, downloadable lesson plans, and user resources including i-Ready Central support website; account set-up and secure hosting; all program maintenance/ updates/ enhancements during the active license term; unlimited user access to U.S.-based service and support via toll-free phone and email during business hours. Professional development is required and available at an additional cost ($2,000/session up to six hours). If Curriculum Associates' minimum recommended professional development is purchased, the district will receive a 25 percent discount for a net price of $1500/session.

Provide information about special accommodations for students with disabilities.

i-Ready Diagnostic for Mathematics is a web-based, vendor-hosted, Software-as-a-Service application. The per-student or site-based license fee includes account set-up and management; unlimited access to i-Ready Diagnostic, management, and reporting functionality; and unlimited access to U.S.-based customer service/technical support and all program maintenance, updates, and enhancements for as long as the license remains active. The license fee also includes hosting, data storage, and data security. Via the i-Ready Diagnostic teacher and administrator dashboards and i-Ready Central support website, educators can access comprehensive user guides and downloadable lesson plans, as well as implementation tips, best practices, video tutorials, and more to supplement our live (either onsite or remotely-facilitated), fee-based professional development. These resources are self-paced and available 24/7. The i-Ready Diagnostic includes many accommodations and accessibility features, making it accessible by most students. Among those are Universal Accessibility Features that are available to all students and do not require that an educator intervene to enable these features. In addition, there are processes and tools in the i-Ready Diagnostic that are used to support students who require accommodations. Since fall 2019, the i-Ready Diagnostic meets the Level AA standard under the Web Content Accessibility Guidelines (WCAG 2.0), with documented exceptions. Although all students have access to Universal Accessibility Features, some features of the i-Ready Diagnostic are designed to be available only to those students with IEPs or 504 plans that stipulate the use of the accommodations process or tool. The decision as to which accommodations a student receives are generally made by IEP teams and other educators within the school. Although Curriculum Associates provides guidance on how to implement various accommodations, it is up to educators who work with individual students to determine which accommodations are needed and how to correctly implement these accommodations. Universal Accessibility Features include these: • The test is untimed. • Students are also able to view closed captioning for introductory videos. • Students can also navigate through the Diagnostic using a keyboard. • Students can adjust the volume of the audio, as needed. • The i-Ready Diagnostic for Mathematics has universally accessible audio support available for all items in grades K-5. Locally-provided accessibility supports can include additional breaks during testing; use of an English dictionary, thesaurus, or bi-lingual dictionary (depending on domain assessed); noise buffering headphones; magnification devices to make the screen easier to read for students with low vision; and a separate setting for testing. As noted, teachers should follow each student’s IEP to determine needed and appropriate accommodations. Further information about i-Ready accessibility and accommodation is available at https://i-readycentral.com/pdfs/accessibility-and-accommodations-update/.

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:

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

45

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?

Curriculum Associates recommends giving the i-Ready Diagnostic three times a year. The i-Ready Diagnostic provides benchmark scores in the form of Grade-Level Placements (Three Grades Below, Two Grades Below, One Grade Below, Early on Grade Level, Mid on Grade Level or Above). The i-Ready Diagnostic also provides intervention tiers associated with the Grade-Level Placements.

If yes, for which months are benchmarks available?

The Grade-Level Placement benchmarks are available at the beginning of the year (typically September), middle of the year (typically January or February), and end of the year (typically April or May).

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:

4-8 hours of training

Please describe the minimum qualifications an administrator must possess.

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:

In-person (either onsite or remotely facilitated) professional development is also required and available for an additional cost.

Can users obtain ongoing professional and technical support?

Yes

If Yes, please describe how users can obtain support:

Curriculum Associates provides a dedicated account manager plus unlimited access to in-house technical support during business hours to every customer.

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:

i-Ready Diagnostic for Mathematics also provides a Quantile score and criterion-referenced Grade-Level Placement scores.

Does your tool include decision rules?

No

If yes, please describe.

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.

i-Ready Diagnostic scale scores are linear transformations of logit values. Logits are measurement units for logarithmic probability models such as the Rasch model. Logits are used to determine both student ability and item difficulty. Within the Rasch model, if the ability matches the item difficulty, then the person has a .50 chance of answering the item correctly. For i-Ready Diagnostic, student ability and item logit values generally range from around -7 to 6. When the i-Ready vertical scale was updated in August 2016, the equipercentile equating method was applied to the updated logit scale. The appropriate scaling constant and slope were applied to the logit value to convert to scale score values between 100 and 800 (Kolen and Brennan, 2014). This scaling is accomplished by converting the estimated logit values with the following equation: Scale Value = 466.41 + 25.42 × Logit Value Once this conversion is made, floor and ceiling values are imposed to keep the scores within the 100–800 scale range. This is achieved by simply recoding all values below 100 up to 100 and all values above 800 down to 800. The scale score range, mean, and standard deviation on the updated scale are either exactly the same as (range), or very similar (mean and standard deviation) to those from the scale prior to the August 2016 scale update, which generally allows year-over-year comparisons of i-Ready scale scores.

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.

i-Ready Diagnostic for Mathematics has intervention screening reports that categorize students into three colors: green identifies students who are eligible for Tier 1 instruction, yellow identifies students in need of Tier 2 intervention, and red identifies students at risk of being identified as in need of Tier 3 intervention. There are three intervention screening report views: beginning-of-year, standard, and end-of-year. Depending on the placement level of the student, he or she is designated into one of the three levels based on chronological grade level. In addition to reporting student performance by tier, i-Ready includes criterion-referenced Grade-Level Placements. Placement levels (cut points) for students’ overall performance and for each domain are presented on the Diagnostic Results for a student report. Placement levels indicate where students should be receiving instruction. i-Ready’s Grade-Level Placements are designed to help educators target instruction for each student. Grade-Level Placements also inform classroom instruction and provide domain-specific insights, allowing for targeted differentiation and remediation. i-Ready Diagnostic also provides national norms (as percentiles) for beginning-of-year, mid-year, and end-of-year testing. Test users who are more familiar with the percentile-based screening approach could also use the national norms for intervention classification. Curriculum Associates is committed to fair and unbiased product development. i-Ready Diagnostic is developmentally, linguistically, and culturally appropriate for a wide range of students at each of grade. For instance, the names, characters, and scenarios used within the programs—as well as the “study buddies” who act as onscreen guides for students—are ethnically and culturally diverse. We developed all items in i-Ready to be accessible for most students regardless of their need for accommodation. In most cases, students who require accommodations (e.g., large print or extra time) will not require additional help to complete an i-Ready Diagnostic. The design of the assessment emphasizes making necessary adjustments to the items, so that a large percentage of students requiring accommodations will be able to take the test in a standard manner and the interpretation or the purpose of the test is not compromised. According to the Standards (AERA, APA, NCME, 2014), “Universal Design processes strive to minimize access challenges by taking into account test characteristics that may impede access to the construct for certain test takers.” i-Ready Diagnostic was developed with the universal principles of design for assessment in mind and followed the seven elements of Universal Design for large-scale assessments recommended by NCEO (2002): 1. Inclusive assessment population 2. Precisely defined constructs 3. Accessible, non-biased items 4. Amenable to accommodations 5. Simple, clear, and intuitive instructions and procedures 6. Maximum readability and comprehensibility 7. Maximum legibility Differential Item Function (DIF) was investigated using WINSTEPS® by comparing the item difficulty measure for two demographics categories in a pairwise comparison. The following demographic categories were compared: Female vs. Male; Black or African American and Latino vs. Caucasian; South, West, and Northeast vs. Midwest; English Learner vs. Non–English Learner; Students with Disabilities vs. General Education Students; Economically disadvantaged vs. Not economically disadvantaged. In each pairwise comparison, estimates of item difficulty for each category in the comparison were calculated. The difference between the two groups was then evaluated using both the Welch’s t-statistics and Mantel-Haenszel method. Items with significant and large differences in difficulty between the comparison groups were flagged for content inspection. In mathematics, of the 3,103 items evaluated, the majority of items (at least 90 percent) showed negligible DIF (level A) and only 3 percent of items showed large DIF (level C). Items with significant, but small, DIF are subjected to extensive content review by a committee, who then determine whether each item should remain in the operational pool, be removed, or be revised and re-piloted.

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 Assessment

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.

TThe criterion measure is the Smarter Balanced Assessment (SBA) Mathematics test for grades 3-8. The SBA is an end-of-year state summative assessment administered in the spring in various states. The percentile scores defined in the Smarter Balanced 2017–18 Summative Technical Report are used to classify students. Students who scored below the score corresponding to the 20th percentile on the SBA for the given grade were classified as at-risk and students who scored at or above the score corresponding to the 20th percentile were classified as not-at-risk.

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).

Cut points on the criterion measure (SBA) were determined as the scale score corresponding to the 20th percentile defined in the Smarter Balanced 2017–18 Summative Technical Report for the given subject and grade. This cut point follows the definition of students in need of intensive intervention provided by NCII’s Technical Review Committee. Students who scored below the score corresponding to the 20th percentile on the SBA for the given grade were classified as at-risk and students who scored at or above the score corresponding to the 20th percentile were classified as not-at-risk. Cut points on the screening measure (i-Ready Diagnostic) were empirically identified as scores that best align with SBA’s 20th percentile scores for each subject, grade and testing window. Using these cut scores, students were classified as at-risk if they scored below the cut score in the i-Ready Diagnostic for the given testing window, or not-at-risk if they scored at or above the cut. Classification indices between at-risk/not-at-risk on i-Ready and at-risk/not-at-risk on the SBA assessment are calculated per the formulas in the classification worksheet.

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.

We did not collect information on whether students who were included in this analysis received an intervention in addition to typical classroom instruction between the screening measure and outcome assessment. With that said, based on the criteria for inclusion in this analysis (i.e., students scoring below the 20th percentile in spring) it is likely that students received some form of intervention.

Cross-Validation

Has a cross-validation study been conducted?

Yes

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.

The criterion measure is the Mathematics Smarter Balanced Assessment (SBA) for grades 3-8, an end-of-year state summative assessment administered in the spring. The percentile scores defined in the Smarter Balanced 2017–18 Summative Technical Report are used to classify students. Students who scored below the score corresponding to the 20th percentile on the SBA test for the given grade were classified as at-risk and students who scored at or above the score corresponding to the 20th percentile were classified as not-at-risk.

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).

For the cross-validation study, we used data from five school districts not included in the main Classification Accuracy study. In order to validate our results, we used the same cut points as the main Classification Accuracy study for both the criterion measure (SBA) and screening measure (i-Ready Diagnostic) when performing the classification analyses. Cut points on the criterion measure (SBA) were determined as the scale score corresponding to the 20th percentile defined in the Smarter Balanced 2017–18 Summative Technical Report for the given subject and grade. This cut point follows the definition of students in need of intensive intervention provided by NCII’s Technical Review Committee. Students who scored below the score corresponding to the 20th percentile on the SBA test for the given grade were classified as at-risk and students who scored at or above the score corresponding to the 20th percentile were classified as no-risk. Cut points on the screening measure (i-Ready Diagnostic) were the same scores identified as cut-points in the main Classification Accuracy study. Using these cut scores, students were classified as at-risk if they scored below the cut score in the i-Ready Diagnostic for the given testing window, or not-at-risk if they scored at or above the cut. Classification indices between at-risk/not-at-risk on i-Ready Diagnostic and at-risk/not-at-risk on the SBA are calculated per the formulas in the classification worksheet.

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.

We did not collect information on whether students who were included in this analysis received an intervention in addition to typical classroom instruction between the screening measure and outcome assessment. With that said, based on the criteria for inclusion in this analysis (i.e., students scoring below the 20th percentile in spring) it is likely that students received some form of intervention.

---

Classification Accuracy - Fall

Evidence	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Criterion measure	Smarter Balanced Assessment	Smarter Balanced Assessment	Smarter Balanced Assessment	Smarter Balanced Assessment	Smarter Balanced Assessment	Smarter Balanced Assessment
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	411	429	446	459	468	479
Classification Data - True Positive (a)	1918	2078	1969	2294	2248	1929
Classification Data - False Positive (b)	1569	1275	1499	1294	1182	1352
Classification Data - False Negative (c)	472	514	457	556	515	475
Classification Data - True Negative (d)	8907	9791	9605	10571	10206	9245
Area Under the Curve (AUC)	0.91	0.93	0.92	0.93	0.94	0.93
AUC Estimate’s 95% Confidence Interval: Lower Bound	0.91	0.93	0.92	0.93	0.93	0.92
AUC Estimate’s 95% Confidence Interval: Upper Bound	0.92	0.93	0.93	0.94	0.94	0.93

Statistics	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Base Rate	0.19	0.19	0.18	0.19	0.20	0.18
Overall Classification Rate	0.84	0.87	0.86	0.87	0.88	0.86
Sensitivity	0.80	0.80	0.81	0.80	0.81	0.80
Specificity	0.85	0.88	0.87	0.89	0.90	0.87
False Positive Rate	0.15	0.12	0.13	0.11	0.10	0.13
False Negative Rate	0.20	0.20	0.19	0.20	0.19	0.20
Positive Predictive Power	0.55	0.62	0.57	0.64	0.66	0.59
Negative Predictive Power	0.95	0.95	0.95	0.95	0.95	0.95

Sample	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Date	Spring 2018	Spring 2018	Spring 2018	Spring 2018	Spring 2018	Spring 2018
Sample Size	12866	13658	13530	14715	14151	13001
Geographic Representation	New England (CT) Pacific (CA, OR, WA) South Atlantic (DE)	New England (CT) Pacific (CA, OR, WA) South Atlantic (DE)	New England (CT) Pacific (CA, OR, WA) South Atlantic (DE)	New England (CT) Pacific (CA, OR, WA) South Atlantic (DE)	New England (CT) Pacific (CA, OR, WA) South Atlantic (DE)	New England (CT) Pacific (CA, OR, WA) South Atlantic (DE)
Male	44.1%	44.5%	44.1%	44.3%	44.7%	49.4%
Female	43.0%	42.2%	42.8%	42.7%	42.7%	46.7%
Other
Gender Unknown	12.9%	13.3%	13.1%	13.0%	12.5%	3.9%
White, Non-Hispanic	19.4%	19.5%	20.7%	19.4%	18.4%	22.6%
Black, Non-Hispanic	3.0%	3.3%	3.8%	3.1%	3.2%	3.9%
Hispanic	38.0%	38.9%	38.0%	42.1%	41.7%	44.5%
Asian/Pacific Islander
American Indian/Alaska Native	0.3%	0.3%	0.4%	0.3%	0.3%	0.3%
Other	1.7%	1.7%	1.6%	1.4%	1.3%	1.5%
Race / Ethnicity Unknown	31.4%	30.2%	28.4%	26.7%	28.1%	18.8%
Low SES
IEP or diagnosed disability
English Language Learner

Classification Accuracy - Winter

Evidence	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Criterion measure	Smarter Balanced Assessment	Smarter Balanced Assessment	Smarter Balanced Assessment	Smarter Balanced Assessment	Smarter Balanced Assessment	Smarter Balanced Assessment
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	424	440	455	465	472	481
Classification Data - True Positive (a)	1978	2147	2039	2308	2053	1762
Classification Data - False Positive (b)	1129	1033	1340	1096	989	1065
Classification Data - False Negative (c)	474	500	508	523	500	415
Classification Data - True Negative (d)	9478	10173	10070	10711	9949	9094
Area Under the Curve (AUC)	0.94	0.94	0.93	0.94	0.94	0.94
AUC Estimate’s 95% Confidence Interval: Lower Bound	0.93	0.94	0.93	0.94	0.94	0.93
AUC Estimate’s 95% Confidence Interval: Upper Bound	0.94	0.95	0.94	0.95	0.95	0.94

Statistics	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Base Rate	0.19	0.19	0.18	0.19	0.19	0.18
Overall Classification Rate	0.88	0.89	0.87	0.89	0.89	0.88
Sensitivity	0.81	0.81	0.80	0.82	0.80	0.81
Specificity	0.89	0.91	0.88	0.91	0.91	0.90
False Positive Rate	0.11	0.09	0.12	0.09	0.09	0.10
False Negative Rate	0.19	0.19	0.20	0.18	0.20	0.19
Positive Predictive Power	0.64	0.68	0.60	0.68	0.67	0.62
Negative Predictive Power	0.95	0.95	0.95	0.95	0.95	0.96

Sample	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Date	Spring 2018	Spring 2018	Spring 2018	Spring 2018	Spring 2018	Spring 2018
Sample Size	13059	13853	13957	14638	13491	12336
Geographic Representation	New England (CT) Pacific (CA, OR, WA) South Atlantic (DE)	New England (CT) Pacific (CA, OR, WA) South Atlantic (DE)	New England (CT) Pacific (CA, OR, WA) South Atlantic (DE)	New England (CT) Pacific (CA, OR, WA) South Atlantic (DE)	New England (CT) Pacific (CA, OR, WA) South Atlantic (DE)	New England (CT) Pacific (CA, OR, WA) South Atlantic (DE)
Male	44.4%	44.2%	44.0%	44.1%	44.4%	49.4%
Female	42.8%	42.3%	43.3%	43.0%	42.5%	46.5%
Other
Gender Unknown	12.9%	13.4%	12.7%	12.9%	13.1%	4.1%
White, Non-Hispanic	19.4%	19.5%	20.1%	19.4%	19.1%	23.7%
Black, Non-Hispanic	2.9%	3.3%	3.8%	3.1%	3.2%	3.8%
Hispanic	37.9%	39.0%	38.8%	42.1%	40.0%	42.5%
Asian/Pacific Islander
American Indian/Alaska Native	0.3%	0.3%	0.4%	0.3%	0.3%	0.3%
Other	1.7%	1.6%	1.6%	1.4%	1.3%	1.5%
Race / Ethnicity Unknown	31.6%	30.2%	28.3%	26.9%	28.7%	19.4%
Low SES
IEP or diagnosed disability
English Language Learner

Classification Accuracy - Spring

Evidence	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Criterion measure	Smarter Balanced Assessment	Smarter Balanced Assessment	Smarter Balanced Assessment	Smarter Balanced Assessment	Smarter Balanced Assessment	Smarter Balanced Assessment
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	432	446	459	467	473	481
Classification Data - True Positive (a)	1881	2044	1865	1903	1592	1293
Classification Data - False Positive (b)	785	800	1057	743	712	700
Classification Data - False Negative (c)	423	469	453	438	382	317
Classification Data - True Negative (d)	8773	9194	9066	8949	6701	5413
Area Under the Curve (AUC)	0.95	0.95	0.94	0.95	0.94	0.93
AUC Estimate’s 95% Confidence Interval: Lower Bound	0.95	0.95	0.93	0.95	0.94	0.93
AUC Estimate’s 95% Confidence Interval: Upper Bound	0.95	0.96	0.94	0.96	0.95	0.94

Statistics	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Base Rate	0.19	0.20	0.19	0.19	0.21	0.21
Overall Classification Rate	0.90	0.90	0.88	0.90	0.88	0.87
Sensitivity	0.82	0.81	0.80	0.81	0.81	0.80
Specificity	0.92	0.92	0.90	0.92	0.90	0.89
False Positive Rate	0.08	0.08	0.10	0.08	0.10	0.11
False Negative Rate	0.18	0.19	0.20	0.19	0.19	0.20
Positive Predictive Power	0.71	0.72	0.64	0.72	0.69	0.65
Negative Predictive Power	0.95	0.95	0.95	0.95	0.95	0.94

Sample	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Date	Spring 2018	Spring 2018	Spring 2018	Spring 2018	Spring 2018	Spring 2018
Sample Size	11862	12507	12441	12033	9387	7723
Geographic Representation	New England (CT) Pacific (CA, OR, WA) South Atlantic (DE)	New England (CT) Pacific (CA, OR, WA) South Atlantic (DE)	New England (CT) Pacific (CA, OR, WA) South Atlantic (DE)	New England (CT) Pacific (CA, OR, WA) South Atlantic (DE)	New England (CT) Pacific (CA, OR, WA) South Atlantic (DE)	New England (CT) Pacific (CA, OR, WA) South Atlantic (DE)
Male	45.7%	46.0%	45.4%	43.7%	45.1%	48.5%
Female	43.6%	43.7%	44.1%	42.9%	43.8%	46.3%
Other
Gender Unknown	10.7%	10.3%	10.6%	13.4%	11.2%	5.2%
White, Non-Hispanic	20.2%	20.8%	21.4%	17.4%	13.6%	15.3%
Black, Non-Hispanic	3.2%	3.6%	4.0%	3.2%	3.7%	4.5%
Hispanic	41.0%	42.6%	41.9%	44.0%	47.9%	51.3%
Asian/Pacific Islander
American Indian/Alaska Native	0.3%	0.3%	0.4%	0.3%	0.3%	0.3%
Other	1.7%	1.7%	1.6%	0.9%	1.0%	0.7%
Race / Ethnicity Unknown	26.9%	24.2%	23.0%	28.0%	29.3%	23.0%
Low SES
IEP or diagnosed disability
English Language Learner

Cross-Validation - Fall

Evidence	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Criterion measure	Smarter Balanced Assessment	Smarter Balanced Assessment	Smarter Balanced Assessment	Smarter Balanced Assessment	Smarter Balanced Assessment	Smarter Balanced Assessment
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	411	429	446	459	468	479
Classification Data - True Positive (a)	950	1073	1106	1150	1066	1010
Classification Data - False Positive (b)	895	695	780	834	627	778
Classification Data - False Negative (c)	196	242	246	191	195	216
Classification Data - True Negative (d)	4077	4686	4775	4763	4579	4744
Area Under the Curve (AUC)	0.90	0.92	0.92	0.93	0.95	0.92
AUC Estimate’s 95% Confidence Interval: Lower Bound	0.90	0.92	0.92	0.92	0.94	0.92
AUC Estimate’s 95% Confidence Interval: Upper Bound	0.91	0.93	0.93	0.94	0.95	0.93

Statistics	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Base Rate	0.19	0.20	0.20	0.19	0.19	0.18
Overall Classification Rate	0.82	0.86	0.85	0.85	0.87	0.85
Sensitivity	0.83	0.82	0.82	0.86	0.85	0.82
Specificity	0.82	0.87	0.86	0.85	0.88	0.86
False Positive Rate	0.18	0.13	0.14	0.15	0.12	0.14
False Negative Rate	0.17	0.18	0.18	0.14	0.15	0.18
Positive Predictive Power	0.51	0.61	0.59	0.58	0.63	0.56
Negative Predictive Power	0.95	0.95	0.95	0.96	0.96	0.96

Sample	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Date	Spring 2018	Spring 2018	Spring 2018	Spring 2018	Spring 2018	Spring 2018
Sample Size	6118	6696	6907	6938	6467	6748
Geographic Representation	Mountain (ID) Pacific (CA)	Mountain (ID) Pacific (CA)	Mountain (ID) Pacific (CA)	Mountain (ID) Pacific (CA)	Mountain (ID) Pacific (CA)	Mountain (ID) Pacific (CA)
Male	50.7%	50.5%	50.5%	50.4%	51.0%	51.6%
Female	49.3%	49.5%	49.5%	49.6%	49.0%	48.4%
Other
Gender Unknown
White, Non-Hispanic	22.8%	21.1%	21.8%	22.7%	22.8%	23.2%
Black, Non-Hispanic	7.5%	7.2%	7.3%	7.3%	7.2%	7.5%
Hispanic	54.3%	56.6%	55.2%	54.2%	52.0%	51.9%
Asian/Pacific Islander
American Indian/Alaska Native	0.5%	0.4%	0.4%	0.5%	0.5%	0.4%
Other	0.3%	0.3%	0.3%	0.2%	0.1%	0.1%
Race / Ethnicity Unknown	0.9%	0.6%	0.7%	0.8%	1.5%	0.8%
Low SES
IEP or diagnosed disability
English Language Learner

Cross-Validation - Winter

Evidence	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Criterion measure	Smarter Balanced Assessment	Smarter Balanced Assessment	Smarter Balanced Assessment	Smarter Balanced Assessment	Smarter Balanced Assessment	Smarter Balanced Assessment
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	424	440	455	465	472	481
Classification Data - True Positive (a)	950	1115	1096	1186	1089	1026
Classification Data - False Positive (b)	629	623	626	619	576	694
Classification Data - False Negative (c)	216	219	264	193	190	228
Classification Data - True Negative (d)	4286	4654	4755	5000	4610	4796
Area Under the Curve (AUC)	0.93	0.94	0.93	0.95	0.95	0.93
AUC Estimate’s 95% Confidence Interval: Lower Bound	0.92	0.93	0.93	0.94	0.94	0.92
AUC Estimate’s 95% Confidence Interval: Upper Bound	0.94	0.95	0.94	0.95	0.95	0.94

Statistics	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Base Rate	0.19	0.20	0.20	0.20	0.20	0.19
Overall Classification Rate	0.86	0.87	0.87	0.88	0.88	0.86
Sensitivity	0.81	0.84	0.81	0.86	0.85	0.82
Specificity	0.87	0.88	0.88	0.89	0.89	0.87
False Positive Rate	0.13	0.12	0.12	0.11	0.11	0.13
False Negative Rate	0.19	0.16	0.19	0.14	0.15	0.18
Positive Predictive Power	0.60	0.64	0.64	0.66	0.65	0.60
Negative Predictive Power	0.95	0.96	0.95	0.96	0.96	0.95

Sample	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Date	Spring 2018	Spring 2018	Spring 2018	Spring 2018	Spring 2018	Spring 2018
Sample Size	6081	6611	6741	6998	6465	6744
Geographic Representation	Mountain (ID) Pacific (CA)	Mountain (ID) Pacific (CA)	Mountain (ID) Pacific (CA)	Mountain (ID) Pacific (CA)	Mountain (ID) Pacific (CA)	Mountain (ID) Pacific (CA)
Male	49.9%	50.0%	50.2%	50.3%	50.9%	51.2%
Female	50.1%	50.0%	49.8%	49.7%	49.1%	48.8%
Other
Gender Unknown
White, Non-Hispanic	21.9%	20.1%	21.1%	22.3%	22.5%	22.5%
Black, Non-Hispanic	7.7%	7.9%	7.8%	7.5%	7.5%	7.8%
Hispanic	54.5%	56.9%	55.0%	54.1%	52.3%	52.2%
Asian/Pacific Islander
American Indian/Alaska Native	0.4%	0.5%	0.4%	0.4%	0.5%	0.4%
Other	0.4%	0.3%	0.3%	0.2%	0.1%	0.1%
Race / Ethnicity Unknown	1.0%	0.7%	0.7%	0.8%	1.6%	0.8%
Low SES
IEP or diagnosed disability
English Language Learner

Cross-Validation - Spring

Evidence	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Criterion measure	Smarter Balanced Assessment	Smarter Balanced Assessment	Smarter Balanced Assessment	Smarter Balanced Assessment	Smarter Balanced Assessment	Smarter Balanced Assessment
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	432	446	459	467	473	481
Classification Data - True Positive (a)	780	834	801	824	785	720
Classification Data - False Positive (b)	385	382	436	367	385	410
Classification Data - False Negative (c)	190	181	180	180	136	149
Classification Data - True Negative (d)	3495	3937	3564	3410	2691	2591
Area Under the Curve (AUC)	0.94	0.95	0.94	0.95	0.94	0.93
AUC Estimate’s 95% Confidence Interval: Lower Bound	0.94	0.95	0.93	0.94	0.93	0.92
AUC Estimate’s 95% Confidence Interval: Upper Bound	0.95	0.96	0.94	0.96	0.95	0.94

Statistics	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Base Rate	0.20	0.19	0.20	0.21	0.23	0.22
Overall Classification Rate	0.88	0.89	0.88	0.89	0.87	0.86
Sensitivity	0.80	0.82	0.82	0.82	0.85	0.83
Specificity	0.90	0.91	0.89	0.90	0.87	0.86
False Positive Rate	0.10	0.09	0.11	0.10	0.13	0.14
False Negative Rate	0.20	0.18	0.18	0.18	0.15	0.17
Positive Predictive Power	0.67	0.69	0.65	0.69	0.67	0.64
Negative Predictive Power	0.95	0.96	0.95	0.95	0.95	0.95

Sample	Grade 3	Grade 4	Grade 5	Grade 6	Grade 7	Grade 8
Date	Spring 2018	Spring 2018	Spring 2018	Spring 2018	Spring 2018	Spring 2018
Sample Size	4850	5334	4981	4781	3997	3870
Geographic Representation	Mountain (ID) Pacific (CA)	Mountain (ID) Pacific (CA)	Mountain (ID) Pacific (CA)	Mountain (ID) Pacific (CA)	Mountain (ID) Pacific (CA)	Mountain (ID) Pacific (CA)
Male	50.9%	50.3%	50.8%	51.2%	51.1%	51.5%
Female	49.1%	49.7%	49.2%	48.8%	48.9%	48.5%
Other
Gender Unknown
White, Non-Hispanic	25.5%	23.6%	25.2%	20.9%	19.9%	19.5%
Black, Non-Hispanic	6.5%	6.2%	6.9%	7.2%	8.3%	8.8%
Hispanic	50.1%	52.6%	50.0%	53.2%	59.9%	61.3%
Asian/Pacific Islander
American Indian/Alaska Native	0.5%	0.5%	0.4%	0.5%	0.5%	0.4%
Other	0.4%	0.2%	0.3%	0.3%	0.1%	0.1%
Race / Ethnicity Unknown	1.0%	0.7%	0.6%	0.7%	1.3%	0.8%
Low SES
IEP or diagnosed disability
English Language Learner

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.

The i-Ready Diagnostic for Mathematics provides two types of reliability estimates: • IRT-based reliability measures such as the marginal reliability estimate and standard error of measurement. • Test-retest reliability coefficients. Marginal Reliability: Given that the i-Ready Diagnostic is a computer-adaptive assessment that does not have a fixed form, some traditional reliability estimates such as Cronbach’s alpha are not an appropriate index for quantifying consistency or inconsistency in student performance. The IRT analogue to classical reliability is called marginal reliability, and operates on the variance of the theta scores and the average of the expected error variance. The marginal reliability uses the classical definition of reliability as proportion of variance in the total observed score due to true score under an IRT model (the i-Ready Diagnostic uses a Rasch model to be specific). Standard Error of Measurement (SEM): In an IRT model, SEMs are affected by factors such as how well the data fit the underlying model, student response consistency, student location on the ability continuum, match of items to student ability, and test length. Given the adaptive nature of i-Ready and the wide difficulty range in the item bank, standard errors are expected to be low and very close to the theoretical minimum for the test of the given length. The theoretical minimum would be reached if each interim estimate of student ability is assessed by an item with difficulty matching perfectly to the student’s ability estimated from previous items. Theoretical minimums are restricted by the number of items served in the assessment—the more items that are served up, the lower the SEM could potentially be. For mathematics, the minimum SEM for overall scores is 6.0. Test-retest Reliability: The i-Ready Diagnostic is often used as an interim assessment, and students can take the assessment multiple times a year. Therefore, the test-retest reliability estimate is appropriate to provide stability estimates for the same students who took two Diagnostic tests.

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

Data for obtaining the marginal reliability and SEM was from the August and September administrations of the i-Ready Diagnostic from 2016 (reported in the 2016 i-Ready Diagnostic technical report). All students tested within the time-frame were included. Evidence of test-retest stability was assessed based on a sub-sample of students who, during the 2016–2017 school year, took i-Ready Diagnostic twice within the recommended 12–18-week testing window. The average testing interval is 106 days (15 weeks). Sample sizes by grade are presented in the table below.

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

This marginal reliability uses the classical definition of reliability as proportion of variance in the total observed score due to true score. The true score variance is computed as the observed score variance minus the error variance (see equation below). ρ_θ=(σ_(θ-)^2 σ ̅_E^2)/(σ_θ^2 ) where ρθ is the marginal reliability estimate, σ2θ is the observed error variance of the ability estimate, σ ̅_E^2is the observed average conditional error variance. Similar to a classical reliability coefficient, the marginal reliability estimate increases as the standard error decreases; it approaches 1 when the standard error approaches 0. The observed score variance, the error variance, and SEM (the square root of the error variance) are obtained through WINSTEPS calibrations. One separate calibration was conducted for each grade. For test-retest reliability, Pearson correlation coefficients were obtained between scores for the two Diagnostic tests. Correlations between the two Diagnostic tests were calculated. In lower grades where growth and variability are expected to be higher, test-retest correlations are expected to be relatively lower.

*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.

The internal structure of the i-Ready Diagnostic for Mathematics is supported by the construct maps and the ordering of the skills addressed at different stages on the map. We recognize that coverage of skills and difficulty of items will overlap a fair amount across grades, as much material is reviewed from year to year. However, what should be apparent from the estimated item difficulties is that, generally, items measuring skills targeting lower levels of the map should be easier, and items measuring skills targeting higher levels of the map should be more difficult.

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

Active items in the current item pool for the 2016–2017 school year are included in the analysis for interval validity. The number of items per grade is listed in the table below. For K-2: Quantile grade-banded results are featured, rather than grade-specific results. The i-Ready Diagnostic mathematics scale scores are created on a vertical scale which makes the scale scores comparable across grades. Thus, for efficiency purposes, the linking sample for the Quantile study includes only students from every other grade (i.e., grades 1, 3, 5, and 7), but results are generalized across grades in various grade bands (e.g., K-2). Additional information on the Quantile study, which was conducted in concert with MetaMetrics, is available upon request. While the Quantile to i-Ready Diagnostic correlation is lower than 0.60, it was not unexpected given the differences in administration between the two assessments (i-Ready Diagnostic Math Assessment provided audio support while the Quantile Linking Test only provided a read-aloud accommodation for all students). Another difference between the i-Ready Diagnostic Math Assessment and the Quantile Linking Test is the number of answer choices, where i-Ready Diagnostic Math Assessment had three answer choices and the Quantile Linking Test had four answer choices.

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

Distributions of indicator difficulties by grade level provide further evidence of internal structure. The difficulty of an indicator corresponds to a 67% probability of passing on the indicator characteristic curve aggregated across all items aligned to the indicator. The table below shows the average and standard deviation of indicator difficulties. Indicator difficulty (as shown in the figures and tables) is used in conjunction with the student’s placement level on the i-Ready Diagnostic to help to determine what students can do, and what they should work on next to continue along the proficiency continuum. These “can dos” and “next steps” are part of the feedback provided in i-Ready reports. Student domain placement levels are compared to indicator difficulties and this provides personalized feedback for each student. To provide further information to educators, a State Standards Performance Report is provided for each state. For each standard, the student’s domain scale score (which is at a finer grain than the placement level) is used to determine whether students have mastered all of the standard, part but not all of the standard, or none of the standard. This determination is again made by comparing the student’s scale score to the indicator difficulty of the skill or skills mapped to each state standard.

*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:

*For K-2: Quantile grade-banded results are featured rather than grade-specific results. The i-Ready Diagnostic for Mathematics scale scores are created on a vertical scale, which makes the scale scores comparable across grades. Thus, for efficiency purposes, the linking sample for the Quantile study includes only students from every other grade (i.e., grades 1, 3, 5, and 7), but results are generalized across grades in various grade bands (e.g., K-2). Additional information on the Quantile study, which was conducted in concert with MetaMetrics, is available upon request. While the Quantile to i-Ready Diagnostic correlation is lower than 0.60, it was not unexpected given the differences in administration between the two assessments (i-Ready Diagnostic provided audio support while the Quantile Linking Test only provided a read-aloud accommodation for all students). Another difference between the i-Ready Diagnostic and the Quantile Linking Test is the number of answer choices, where i-Ready Diagnostic had three answer choices and the Quantile Linking Test had four answer choices. The table below shows validity evidence based on internal structure, represented by indicator difficulty. The mean and standard deviation, as well as the number of items are presented by grade. Results show that items targeting progressively higher grade levels are progressively more difficult, as indicated by the aggregate difficulty of the indicator. Differences in item difficulties between the upper grades are less dramatic than such differences between the lower grades, which reflects the reality of student performance in the classroom. Type of Validity Age or Grade Indicator Difficulty (Mean) Indicator Difficulty (SD) Number of Items Internal Structure K 371.97 21.38 241 Internal Structure 1 398.10 19.15 245 Internal Structure 2 431.24 22.00 324 Internal Structure 3 463.80 20.28 306 Internal Structure 4 483.96 24.28 354 Internal Structure 5 508.11 19.15 270 Internal Structure 6 521.85 23.29 374 Internal Structure 7 546.38 15.59 261 Internal Structure 8 548.85 19.72 223 Indicator difficulty (as shown in the figures and tables) is used in conjunction with the student’s placement level on the i-Ready Diagnostic to help to determine what students can do, and what they should work on next to continue along the proficiency continuum. These “can dos” and “next steps” are part of the feedback provided in i-Ready reports. Student domain placement levels are compared to indicator difficulties and this provides personalized feedback for each student. To provide further information to educators, a State Standards Performance Report is provided for each state. For each standard, the student’s domain scale score (which is at a finer grain than the placement level) is used to determine whether students have mastered all of the standard, part but not all of the standard, or none of the standard. This determination is again made by comparing the student’s scale score to the indicator difficulty of the skill or skills mapped to each state standard.

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.

The internal structure of the i-Ready Diagnostic for Mathematics is supported by the construct maps and the ordering of the skills addressed at different stages on the map. Skills representing the lower levels on the construct map are those generally associated with items targeted at lower grade levels, and skills representing the higher levels on the map are ones generally associated with items targeted at higher grade levels.

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	Yes	Yes	Yes	Yes	Yes	Yes

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:

Differential Item Function (DIF) was investigated using WINSTEPS® by comparing the item difficulty measure for two demographic categories in a pairwise comparison through a combined calibration analysis. The essence of this methodology is to investigate the interaction of the person-groups with each item, while fixing all other item and person measures to those from the combined calibration. The method used to detect DIF is based on the Mantel-Haenszel procedure (MH), and the work of Linacre & Wright (1989) and Linacre (2012). Typically, the group representing test takers in a specific demographic group is referred to as the focal group. The group made up of test takers from outside this group is referred to as the reference group. For example, for gender, Female is the focal group, and Male is the reference group.

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

The latest large-scale DIF analysis included a random sample (10%) of students from the 2015–2016 i-Ready operational data. Given the large size of the 2015–2016 i-Ready student population, it is practical to carry out the calibration analysis with a random sample. The following demographic categories were compared: Female vs. Male; Black or African American and Latino vs. Caucasian; English Learner vs. non–English Learner; Students with Disabilities vs. General Education students; Economically Disadvantaged vs. Not Economically Disadvantaged. In each pairwise comparison, estimates of item difficulty for each category in the comparison were calculated.

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.

Active items in the current item pool for the 2016–2017 school year are included in the DIF analysis. The total numbers of items are 3103 for Mathematics. WINSTEPS (Version 3.92) was used to conduct the calibration for DIF analysis by grade. To help interpret the results, the Educational Testing Service (ETS) criteria using the delta method was used to categorize DIF (Zwick, Thayer, & Lewis, 1999) and is presented. The number and percentage of items exhibiting DIF for each of the demographic categories are reported in the table below. It should be noted that not all students have individual demographic information and the total number of items for two exclusive groups in the categories does not necessarily equal to the total number of items. It is clear that the majority of ELA items show negligible DIF (mostly more than 90 percent), and very few items (less than 6 percent) are showing large DIF (level C) by grade.