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 tables 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.
earlyReading Minimum Composite Scores
|
Fall |
Winter |
Spring |
|
|
Grade KG |
23.7 |
26.4 |
37.1 |
|
Grade 1 |
18.6 |
17.5 |
11.3 |
earlyMath Minimum Composite Scores
|
Fall |
Winter |
Spring |
|
|
Grade KG |
6.3 |
9.5 |
6.2 |
|
Grade 1 |
0.0 |
1.1 |
4.3 |
Two issues arise from the use of raw scores for earlyReading and earlyMath. First, some subtests predict student attainment of the composite better than others (e.g., Onset Sounds are a better predictor of early reading than Letter Sounds for Kindergarten). Therefore, if the raw scores of each subtest are combined without consideration for these differences, the predictive power of the composite score will be weakened.
Second, because the combination of subtests comprising the composite changes across seasons a simple weighted sum would not be comparable across seasons. The reason is two-fold. First, subtests have very different scales. For example, the maximum score on Concepts of Print is 12; whereas, on Letter Sounds it is greater than 100. Second, the skills each subtest measures develop at different rates. To account for these differences the total composite score is transformed to a common scale that has been statistically linked across seasons.
Fastbridge researchers implemented two weighting techniques that remedy these problems. The first weight uses a vertical scale score to adjust the raw score so that all subtests have equivalent predictive estimates of the underlying skill (i.e., reading and math). The second weight uses a factor loading from a factor analysis for each subtest to estimate growth across screening periods. Thus, the total composite score for a screening period combines these weights such that:
Total Composite Score = Raw Scorest1 * (Vertical Scale Score st1) * (Factor Loading st1) +
Raw Score st2 * (Vertical Scale Score st2) * (Factor Loading st2) + … +
Raw Score stn * (Vertical Scale Score stn) * (Factor Loading stn)
Next, the total composite score in each season is transformed to a scale with a mean of 50 and a standard deviation of 15. This linear transformation results in the final composite score.
Final composite score = Total Composite Score * 15/SDsample + [50 - 15/SDsample + Msample]
The combined weights and linear transformation on the raw score provide a more accurate picture for educators to estimate students’ strengths in early reading and math competencies and growth across screening periods.
On the final composite score scale, a score of 0 is equivalent to 3.33 standard deviation units below the mean, and scores this far from the mean are very rare. Due to floor effects on some subtests (i.e., in which a subtest score of 0 is not rare), the lowest possible score on the final composite is generally not 3.33 SD below the mean, but a value closer to the mean. As a result, the minimum composite score is greater than 0 in all but one instance. Furthermore, because the magnitude of the floor effects differs by subtest and by season, and due to the effects of growth on the vertical scale, the minimum composite score also differs.