Development of earlyReading and earlyMath Composite Score

An important use of FastBridge screening scores is to identify students who are at-risk and to indicate the intensity of the instructional support needed to meet end-of-year performance expectations. This is done by segmenting the overall score range for each screener into three levels of risk: high risk, some risk, and low risk. The lowest segment of the score range is associated with high risk and the highest segment is associated with low risk. When the screener consists of multiple subtests that are scored separately, as it does for the earlyReading and earlyMath assessments, it is necessary to combine the results from each subtest into a single score. That score is called a composite score.

The FastBridge earlyReading and earlyMath composites were developed to:

1. maximize reliability and validity, especially with respect to decision accuracy;
2. maximize sensitivity to each student’s skill development across the year;
3. to provide a simple indicator of within-grade growth; and
4. to be brief.

To support these objectives, only a subset of the available subtests was chosen for the composite. Selection of the subtests was determined based on developmental appropriateness and empirical analyses of sensitivity to growth and predictive validity. We know from the science of reading and a large corpus of early literacy research that reading skill development follows a predictable sequence for most students: letter recognition → letter-sound correspondence → word recognition and decoding → reading fluency → reading comprehension.  Similarly, mathematics skills develop through a progression that includes: oral counting → numeral identification → cardinality → computation. As students progress through these sequences, the skills that are developing tend to be the most predictive of future success and most sensitive to growth. Once a skill has been mastered, it becomes less predictive and sensitive. By targeting subtests to the time of year when the skills develop most rapidly, the overall testing burden can be minimized while maintaining strong validity and growth sensitivity.

The composite uses a within-grade vertical scale that allows direct comparison of scores across seasons. This enables analysis of growth using weekly rates of improvement (ROIs) and growth norms. Additionally, the composite uses weighting to enhance prediction of end-of-year performance expectations. The following describes the steps in the development of the composite score.

Step 1: Common scale

In the first step, all subtest scores are converted to a common scale within each season. The scale is determined by selecting a subtest with high reliability and sensitivity to growth as the reference test. The reference subtest must be used in all three seasons. By rescaling each subtest to a common reference scale, all subtests contribute equally to the analyses in Step 2.

Within each season, each subtest was rescaled relative to the reference subtest as follows:

(eq 1)

Where R is the reference subtest and F represents the focal subtests.

The subtests comprising the composite for each grade and subject are presented in Tables 13 and 14. The footnote indicates the reference subtest.

Step 2: Weighting and vertical scaling

To determine the optimal weighting strategy and to obtain a vertical scale across seasons, a confirmatory factor analysis (CFA) model was fitted to the rescaled scores (see Figure 1). The CFA model is a correlated factor model in which the latent composite factor scores are correlated across seasons. The regression weights relating the latent composite score to each subtest were constrained to be equal across seasons for a given subtest. For example, the regression weight b1 appears in each season for Focal subtest 1. That means the same regression weight is used in the fall, winter, and spring. Because CFA scales are arbitrary, the scale is defined by fixing the regression weight for one of the subtests, here represented as an R for reference subtest, equal to 1.0. Finally, the random error terms for a given subtest were allowed to correlate across seasons. Allowing correlated errors improved overall model fit.

Table 13.

earlyReading Composite Subtests

Grade	Fall	Winter	Spring
PK	Concepts of Print Onset Sounds Letter Names a	Concepts of Print Onset Sounds Letter Names a	Onset Sounds Letter Names a Letter Sounds
K	Concepts of Print Onset Sounds Letter Names Letter Sounds a	Onset Sounds Letter Sounds a Word Segmenting Nonsense Words	Letter Sounds a Word Segmenting Nonsense Words Sight Words–50
1	Word Segmenting Nonsense Words a Sight Words–150 Sentence Reading	Word Segmenting Nonsense Words a Sight Words–150 CBMreading	Word Segmenting Nonsense Words a Sight Words–150 CBMreading

^a Reference subtest for within-season rescaling.

Table 14.

earlyMath Composite Subtests

Grade	Fall	Winter	Spring
PK	Subitizing Counting Objects Numeral Identification a	Subitizing Counting Objects Numeral Identification a	Counting Objects Numeral Identification a Number Sequence
K	Match Quantity Number Sequence–K Numeral Identification–K a	Decomposing–K Number Sequence–K Numeral Identification–K a	Decomposing–K Number Sequence–K Numeral Identification–K a
1	Decomposing–1 Number Sequence–1 Numeral Identification–1 b	Decomposing–1 Number Sequence–1 Place Value	Decomposing–1 Place Value Story Problems

^a Reference subtest for within-season rescaling.

^b Original data included means and SDs in all three seasons.

Figure 5.

Confirmatory Factor Analysis Model

Step 3: Sum weighted subtest scores

Using the regression weights from the CFA model, subtest scores within each season are summed. For example, for the PK earlyReading fall composite, the weighted summed score is defined as:

(eq 2)

Where i represents a student and each subtest score is the rescaled value for that season using
equation 1. 

Tables 15 and 16 list the CFA weights by subject and season.

Table 15.

earlyReading Composite Subtest CFA weights

Grade	Subtest	Fall	Winter	Spring
PK	Concepts of Print Letter Names Onset Sounds Letter Sounds	0.69 1.00 0.88 –	0.69 1.00 0.88	– 1.00 0.88 0.96
K	Concepts of Print Onset Sounds Letter Names Letter Sounds Word Segmenting Nonsense Words Sight Words	0.61 0.64 0.89 1.00	– 0.64 – 1.00 1.00 1.24	– – – 1.00 1.00 1.24 1.38
1	Word Segmenting Nonsense Words Sight Words–150 Sentence Reading CBMreading	0.10 0.87 1.00 1.09 –	0.10 0.87 1.00 – 1.09	0.10 0.87 1.00 – 1.09

Table 16. 

earlyMath Composite Subtest CFA weights

Grade	Subtest	Fall	Winter	Spring
PK	Counting Objects Number Identification (KG) Subitizing Number Sequence (KG)	1.15 1.00 1.11 –	1.15 1.00 1.11 –	1.15 1.00 – 1.18
0	Number Identification (KG) Number Sequence (KG) Match Quantity Decomposing (KG)	1.00 1.01 0.70 –	1.00 1.01 – 0.73	1.00 1.01 – 0.73
1	Number Identification (1) Number Sequence (1) Decomposing (1) Place Value Story Problems	1.02   1.02 1.00	– 1.02 1.00 0.75	– – 1.00 0.75 0.85

Step 4: (Rescale Composite)

In the final step, the mean of the three weighted seasonal sums (computed across all students) is calculated. It is used to define the mean and SD for the rescaled composite sum.

(eq 3)

This step centers the vertical scale score roughly equivalent to the winter mean and defines the scale (i.e., SD). In the final part of Step 4, the vertical composite score is rescaled to have a mean of 50 and SD = 10.

(eq 4)

Where  is the fall composite score for student, i;  is the weighted sum of the rescaled subtest scores, Mean is defined in eq 3, and 15 and 50 are the rescaling constants.

Composite Score Range

As described above, the composite score for earlyReading and earlyMath is the collective raw scores of multiple subtests transformed by a combination of statistical and psychometric methods designed to maximize predictive validity and provide comparability of scores across seasons. Consequently, these raw score transformations lead to minimum scores larger than zero in most cases. Minimum values for earlyReading and earlyMath are shown in the table below. Although this transformed scale does not have a defined maximum score, scores above 100 are rare and a score of 150 is used as the maximum score in the development of norms.

Table 17.

Minimum Composite Scores

	earlyReading			earlyMath
	Fall	Winter	Spring	Fall	Winter	Spring
Preschool	32	39	45	21	17	19
Kindergarten	24	26	37	6	9	6
Grade 1	19	17	11	0	1	4