Improving the Academic Performance of First-Grade Students With Reading and Math Difficulty: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Improving the Academic Performance of First-Grade Students With Reading and Math Difficulty (NCT03991234), a randomized na study. The primary outcome is Word Reading Fluency-2 (Zumeta et al., 2012).

2. Clinical Question

The study addresses a practical comparison: whether researcher-delivered instruction coordinated across reading and math is associated with a different post-intervention reading-fluency result than the school’s usual program. Random assignment placed eligible students into coordinated instruction, reading intervention, math intervention, or business-as-usual control. All four conditions were assessed before the researcher-delivered intervention began and after it ended. The posted endpoint result concerns word-reading fluency. It should not be treated as a complete account of every planned academic outcome: the registry summary names arithmetic fluency too, while no secondary outcome results are posted. The record does not report the eligibility thresholds, participant characteristics beyond the stated learning difficulties, or whether results differed across subgroups.

3. Trial Design

This was a randomized, parallel-group trial with single masking. The registry lists 385 enrolled participants and records the study as completed. It began on 2019-11-11, with primary completion on 2025-05-20. The record does not identify who was masked, so the masking label alone does not establish whether students, instructors, assessors, or another party were unaware of assignments. The phase is listed as NA.

Students who met entry criteria were randomly assigned to one of four conditions: coordinated reading and math intervention, reading intervention, math intervention, or business-as-usual control. The three researcher-delivered interventions lasted 15 weeks, with 3 30-minute sessions per week. The coordinated condition combined explicit instruction addressing skills similar to those in the two separate intervention arms. Reading intervention emphasized letter-sound associations, decoding, sight words, and contextualized reading. Math intervention addressed number knowledge, counting strategies, and arithmetic skill. The control condition consisted of typical school reading and math instruction, with a supplemental program if designated by the school.

Students in all four conditions were tested before the researcher-delivered intervention and after it ended. The primary word-reading fluency timeframe is described as an average of 25 weeks. The posted arm results give endpoint means and standard deviations for the four groups. A separate registry analysis compares coordinated intervention with business-as-usual using a multilevel model. The record does not report the randomization procedure, allocation concealment, the exact analysis population, or the details of the multilevel model. It also does not report the trial’s original sample-size assumptions or justification.

4. Participant Flow and Accounting

The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.

Before assignment: Students who met the eligibility criteria were pretested. After pretesting, the number of students needed for enrollment were randomly selected from the group of students with complete pretest data. Those students were subsequently randomly assigned to the four treatment groups.

Overall Study

Reasons for not completing this period:

5. Baseline Characteristics

The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.

Population: The 93 students who were lost to follow-up were not included in the analysis because they did not have follow-up data.

6. Primary Endpoint

The registry lists the primary outcome as Word Reading Fluency-2 (Zumeta et al., 2012), measured over an average of 25 weeks.

The primary endpoint is Word Reading Fluency-2, measured in words read correctly. Students have 1 min to read 60 words, presented in bands of 5 words beginning with the most frequent words and then moving to the next-most frequent words. Two forms are given, and the final score is the average score on those forms. The registry describes the reported quantity as a mean and the spread as a standard deviation. The endpoint timeframe is an average of 25 weeks.

Fluency captures both accurate word reading and the ability to read words within a limited time. In general, a continuous score such as words read correctly retains more information about differences between students than a result reduced to a simple pass-or-fail category. Comparing group means can therefore describe whether average measured performance differs between assigned conditions. The standard deviation describes variation in scores within each group; it is not a measure of uncertainty in the group mean.

The endpoint is relevant to the stated reading difficulty and to the intervention content, which includes instruction in decoding and contextualized reading. However, the score is one defined measure at a specified assessment point. It does not by itself describe performance in every reading skill, longer-term progress, or arithmetic fluency. The registry summary identifies arithmetic fluency as another primary endpoint, but its results are not reported in the registry record. The record also does not provide outcome results for the other listed measures.

7. Results Posted in the Registry

• Coordinated Reading and Math Intervention: mean 10.22 versus 7.38 on control; difference 2.83 (95% CI 0.03 to 5.63), standardized effect d = 0.33; z-test p = 0.048.
• Math Intervention: mean 7.07 versus 7.38 on control; difference -0.32 (95% CI -2.86 to 2.22), standardized effect d = -0.04; z-test p = 0.807.
• Reading Intervention: mean 12.35 versus 7.38 on control; difference 4.96 (95% CI 2.01 to 7.92), standardized effect d = 0.54; z-test p = <0.001.

8. Statistical Interpretation

9. Statistical Methods Explained

The results include continuous group summaries and an inferential analysis. For a continuous endpoint, a mean gives the average score in a group. The standard deviation describes the spread of individual scores around that mean. In general, a larger standard deviation indicates more variability among observed scores; it does not mean the group mean is less accurate by that same amount. The posted outcome means and standard deviations allow readers to see both the average score and the amount of within-group variation, but they do not show the score distribution or individual-level changes.

The registry’s reported comparison for coordinated intervention against business-as-usual is a multilevel model. It reports a net mean difference of .330, a 95% confidence interval from 0.021 to 0.64, and p = .018. In general, a multilevel model can account for data structured at more than one level, such as observations grouped within a larger unit, when that structure is represented in the model. The registry does not report which levels were included, what covariates were used, how the model was specified, or how the net difference was adjusted. Those details should not be inferred from the method label alone.

The registry also includes simple recalculations based on the posted group summary statistics. These are unadjusted comparisons of each intervention arm with the business-as-usual group. For coordinated intervention, the recalculated mean difference is 2.831, with an interval from 0.029 to 5.633 and p = 0.048. For math intervention, the recalculated mean difference is -0.317, with an interval from -2.857 to 2.223 and p = 0.807. For reading intervention, the recalculated mean difference is 4.964, with an interval from 2.01 to 7.918 and p < 0.001. The recalculation for each comparison uses the displayed arm summaries; it is not the trial’s full multilevel analysis.

The standardized effect-size values accompanying these recalculations are d = 0.332 for coordinated intervention, d = -0.040 for math intervention, and d = 0.540 for reading intervention. In general, a standardized effect expresses a mean difference relative to a measure of score variability, making it less dependent on the endpoint’s original units. It does not remove uncertainty or make comparisons between different populations automatically valid. The registry does not report a standardized effect from its multilevel model.

A p-value is a measure of how unusual a result at least as extreme as the observed result would be under a specified null hypothesis and analysis model. It is not the probability that an intervention had no effect, and it does not measure the size or importance of a difference. A p-value just below a conventional threshold should not be read as a sharp boundary between important and unimportant evidence. The reported p = .018 belongs to the registry’s multilevel comparison; p = 0.048 is from the unadjusted recalculation. The calculations are based on different analysis approaches, and the discrepancy flag means the registry’s own analysis takes precedence.

A confidence interval describes uncertainty around an estimate under the analysis assumptions. A narrow interval indicates greater precision than a wide interval, all else equal. The multilevel model’s 95% interval is tied to that model’s estimate. The intervals accompanying the simple recalculations are presented as intervals, but a confidence level for those recalculated intervals is not separately stated in the record. In general, an interval that includes values on both sides of zero is compatible with both a negative and a positive difference under the calculation, while an interval that stays on one side of zero does not establish the practical importance of its estimates.

The registry lists six outcome measures and six analyses, but no secondary outcome results are posted. The record does not report whether the analyses were prespecified in the same form as posted, whether any multiplicity adjustment was made, or how missing observations were handled. It also does not state the original trial design assumptions for sample size, the analysis population, or the exact model diagnostics. These omissions limit assessment of the inferential results beyond the reported estimates and their stated methods.

What does the unadjusted label mean?

In general, an unadjusted comparison uses the available group summaries without incorporating the additional modeling or adjustment represented by a more complex analysis. It can be useful as a transparent descriptive check, but it may not reproduce the estimate from a model that accounts for features of the design or analysis. The registry’s coordinated-intervention result is explicitly from a multilevel model, while the posted recalculation uses the group means and pooled standard deviation. Given the discrepancy, the recalculation should be treated as a complementary summary rather than the primary inferential result.

What does randomization contribute?

In general, random assignment is intended to make groups comparable on average at the point of assignment, including on factors not measured in the study. It does not guarantee that every group is identical, nor does it resolve missing data, outcome measurement issues, deviations from assigned conditions, or limitations in the model. The record identifies the allocation as randomized but does not provide the procedure, concealment details, adherence information, or analysis population needed to evaluate those aspects closely.

10. Confidence Intervals and Precision

The registry’s multilevel estimate for coordinated intervention versus business-as-usual is .330 words read correctly, with a 95% confidence interval from 0.021 to 0.64. The interval lies on the positive side of zero, while its endpoints are separated enough that the estimate does not identify one precise difference. The p-value is .018. Taken together, these figures describe the registry analysis as reporting a positive net mean difference, with uncertainty around its size under the multilevel model.

The unadjusted recalculation is less similar in magnitude: its estimate is 2.831, with an interval from 0.029 to 5.633 and p = 0.048. The discrepancy between this result and the model result is material for interpretation, but the reason is not reported in the registry record. The model result takes precedence for the trial’s reported analysis. The record does not state the confidence level for the interval produced by this recalculation, so it is best described simply as the posted interval estimate.

For math intervention, the recalculated interval runs from -2.857 to 2.223, spanning zero, and the p-value is 0.807. For reading intervention, the interval runs from 2.01 to 7.918 and p < 0.001. These intervals communicate different degrees of compatibility with a zero mean difference under the simple calculation. They do not account for multiplicity, and no adjusted analyses for these comparisons are reported.

In general, a confidence interval is not a guarantee that the true value lies within its endpoints. Its interpretation depends on the method and assumptions used to construct it. Precision is also distinct from practical importance: a precise estimate can be small, and an imprecise estimate can include a range of magnitudes. Here, the registry’s own model estimate and interval should be the focus for the coordinated-intervention comparison, while the unadjusted recalculations should be read as separate summary-based analyses.

11. Planning a Similar Trial: Sample Size

This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.

The planning figures are participants per arm, not total events. They apply to the three comparisons with business-as-usual for which recalculations are posted. Each set of figures asks how many participants per arm would be needed under the stated planning assumptions to detect a specified fraction of the observed effect. For example, the coordinated-intervention planning values use 100%, 75%, and 50% of the observed effect; the reading and math comparisons use the same fractions.

The planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is the stated fraction of the observed effect. These are planning illustrations computed from the observed effect, not the trial’s own original design assumptions; the original assumptions are not reported in the registry record.

The 80% power column means the planned sample size under those assumptions for a design with an 80% chance of detecting the specified effect if that effect is the true one. The 90% power column uses a higher target chance of detection under the same planning framework. In general, smaller effects are harder to detect, so they require more participants per arm to reach a given power target. This is not observed power; it is a forward-looking illustration based on the recalculated effect and stated assumptions.

The estimates are highly sensitive to the effect used. The coordinated-intervention planning values are 143 participants per arm for 80% power and 191 for 90% power when using 100% of the observed effect; for 75%, the values are 254 and 339; for 50%, they are 570 and 763. For reading intervention, the corresponding values are 54 and 72, then 96 and 128, then 216 and 288. The math-intervention estimates are much larger: 9,988 and 13,370, then 17,755 and 23,769, then 39,949 and 53,480. The trial’s original sample-size rationale is not reported in the registry record.

12. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z_1−α/2 = 1.960) and the desired power (z_1−β = 0.842 for 80% and 1.282 for 90%).

Formula

n is the number of participants in each arm, Δ is the difference in means to detect and σ is the common standard deviation.

Worked calculation for this trial

1. Observed difference Δ = 2.831; pooled standard deviation σ = 8.527.
2. n = 2 × (1.96 + 0.842)² × 8.527² / 2.831² = 142.4, rounded up to 143 participants per arm for 80% power.

The smaller-effect rows in the table above repeat the same calculation with the effect multiplied by 0.75 and 0.5 (for ratios, applied to the logarithm of the ratio).

R code

alpha <- 0.05
z_a   <- qnorm(1 - alpha / 2)          # two-sided
delta <- 2.831                      # observed difference in means
sigma <- 8.52655636142842                     # pooled standard deviation
n_per_arm <- function(power, frac = 1) {
  ceiling(round(2 * (z_a + qnorm(power))^2 * sigma^2 / (delta * frac)^2, 6))
}
for (f in c(1, 0.75, 0.5))
  cat(sprintf("%3.0f%% of observed effect: n per arm = %s (80%% power), %s (90%% power)\n", 100 * f,
              format(n_per_arm(0.80, f), big.mark = ","), format(n_per_arm(0.90, f), big.mark = ",")))

# Check against R's built-in function (t-based, so very slightly larger)
cat("power.t.test:", round(power.t.test(delta = delta, sd = sigma, power = 0.80)$n, 1), "\n")

# Simulation: exact two-sample t-test using simulated means and variances
set.seed(3991234)
n    <- n_per_arm(0.80)
reps <- 20000
m_diff <- rnorm(reps, delta, sigma * sqrt(2 / n))             # difference in sample means
s2     <- sigma^2 * rchisq(reps, 2 * (n - 1)) / (2 * (n - 1))   # pooled sample variance
tstat  <- m_diff / sqrt(s2 * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(tstat) > qt(0.975, 2 * (n - 1))), reps))

Output from running the code

100% of observed effect: n per arm = 143 (80% power), 191 (90% power)
 75% of observed effect: n per arm = 254 (80% power), 339 (90% power)
 50% of observed effect: n per arm = 570 (80% power), 763 (90% power)
power.t.test: 143.4 
Simulated power at n = 143 per arm: 0.798 (20000 replicates)

The simulation draws many sets of group means and variances at the planned sample size and counts how often the two-sample t-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.

13. Analyses Reported by the Sponsor

The registry’s reported analysis compares coordinated reading and math intervention with business-as-usual using a multilevel model. It gives a net mean difference of .330, a 95% confidence interval from 0.021 to 0.64, and p = .018. This is the trial’s own posted analysis and is the result to prioritize for that comparison.

The simple recalculation based on the posted group summaries gives a mean difference of 2.831, an interval from 0.029 to 5.633, and p = 0.048. The record flags a discrepancy between this recalculation and the reported analysis. These are not interchangeable estimates: the registry result comes from a multilevel model, while the recalculation is unadjusted from summary statistics. The model details needed to explain the difference are not reported in the registry record.

The recalculation can still serve as a transparent check on the direction and scale of the posted group summaries, but it should not replace the registry’s model estimate. The registry does not report why the estimates differ or provide enough model specification to reproduce the multilevel result. Accordingly, conclusions about the coordinated-intervention comparison should be anchored in .330 and its reported confidence interval and p-value, with the recalculation noted as a distinct analysis rather than a competing trial result.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists six outcome measures and six analyses. The trial summary identifies word-reading fluency and arithmetic fluency as primary endpoints, but only the word-reading fluency results are posted in the record. The number and results of secondary outcomes are not reported in the registry record; the record lists zero secondary results posted. This limits the ability to understand the full pattern of measured outcomes.

Several comparisons with the business-as-usual group are displayed through the simple recalculations: coordinated intervention, math intervention, and reading intervention. The registry’s reported multilevel result is available for coordinated intervention versus control. No corresponding model-based results for the other two comparisons are reported. The record does not state whether adjustment for multiple outcomes or multiple comparisons was planned or performed. Without that information, the unadjusted p-values should be interpreted as comparison-specific results rather than as evidence adjusted for the full set of tests.

Missing-data handling is not reported in the registry record. The arm summaries give outcome sample sizes of 67.0 for coordinated intervention, 74.0 for math intervention, 73.0 for reading intervention, and 78.0 for business-as-usual. These figures do not explain whether any participants lacked endpoint data, how missing observations were handled, or whether the analysis included every randomized participant. The record does not state whether the analysis was intention-to-treat, per-protocol, or another population definition.

The adverse-event record uses separate at-risk denominators, but it does not explain their relationship to the endpoint analysis groups. The distinction between enrollment, arm-level outcome summaries, and safety denominators therefore cannot be resolved from the posted information. In general, missingness can affect estimates if the availability of outcome data is related to observed or unobserved outcomes. Without the missing-data procedures and analysis population, readers cannot determine how much that issue may affect the results.

15. Safety Results

The registry reports serious adverse events as affected participants divided by participants at risk.

Deaths

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 5% reporting threshold.

The registry reports zero serious adverse events and zero other adverse events for each of the four conditions. For the coordinated reading and math intervention, the serious-event and other-event at-risk counts are each 96, with 0 affected. For reading intervention, both at-risk counts are 96, with 0 affected. For math intervention, both at-risk counts are 96, with 0 affected. For business-as-usual control, both at-risk counts are 97, with 0 affected. Deaths are reported as 0 in every condition.

These entries mean that no events were recorded in the listed categories for the reported at-risk groups. They do not establish that no event of any kind occurred, because the record reports the serious and other adverse-event categories separately and does not list event terms. The registry’s serious-event term list is empty. The record does not explain how events were collected, the observation window for safety reporting, or how the at-risk groups were defined. The figures should therefore be read as the safety counts posted in the registry, not as a complete characterization of all possible harms.

16. What the Result Does, and Does Not, Mean

The posted endpoint summaries show different average word-reading fluency scores across the four assigned conditions. Reading intervention had a mean of 12.35 words read correctly, coordinated intervention 10.22, math intervention 7.068, and business-as-usual control 7.385. These are observed group means at the endpoint; they do not establish how individual students changed or why groups differed.

For coordinated intervention versus business-as-usual, the registry’s multilevel model reports a net mean difference of .330, with a 95% confidence interval from 0.021 to 0.64 and p = .018. The simple unadjusted recalculation gives a substantially different estimate of 2.831 and is flagged as discrepant. The registry’s reported analysis takes precedence. The discrepancy also cautions against relying on summary-based recalculations as if they were the trial’s full analysis.

The results do not establish that an intervention works or does not work. They describe a measured endpoint under the analyses posted in the registry. A group mean difference alone does not reveal whether any difference is educationally important, whether it persists beyond the assessed timeframe, or whether it applies to students outside the studied population. The registry does not report the participant characteristics needed to assess how broadly the findings may apply.

The trial summary identifies arithmetic fluency as a primary endpoint alongside word-reading fluency, but arithmetic results are not posted. The record also lists six outcome measures and six analyses without posting secondary outcome results. Consequently, the word-reading result should not be treated as a complete account of the trial’s intended outcomes. The safety record reports zero serious and zero other adverse events in the listed groups, but does not provide event-collection details. Overall, the registry offers a specific result for word-reading fluency alongside important gaps in outcome reporting, analysis details, and precision about the discrepancy.

17. Why This Trial Matters Statistically

This trial is statistically notable because its registry record contains both a reported model-based result and a simple recalculation from arm summaries for the same coordinated-intervention comparison. The reported multilevel estimate is .330, with a 95% confidence interval from 0.021 to 0.64 and p = .018; the unadjusted recalculation is 2.831, with an interval from 0.029 to 5.633 and p = 0.048. A reader needs to distinguish the estimate from the trial’s own model from a summary-based check. The record flags the discrepancy, and the model result takes precedence.

The design also includes four conditions rather than a single intervention-control comparison. The reading-only and math-only arms help frame the coordinated program within a broader set of instruction conditions. However, the posted multilevel analysis is limited to coordinated intervention versus control, while the other arm comparisons are available as unadjusted recalculations. This makes it important not to describe all contrasts as if they shared the same analysis method.

The sample-size illustrations further demonstrate how strongly planning requirements depend on the assumed effect. A smaller target effect produces larger estimated participants-per-arm requirements. Those figures are planning illustrations based on the observed recalculations, not evidence about the design choices made before the trial. The original sample-size assumptions are not reported in the registry record.

Finally, the study assesses a specific continuous reading-fluency measure after a school-based intervention period. Its results are not a substitute for the unreported arithmetic endpoint or the secondary outcomes. Understanding that scope—along with the model discrepancy, missing analysis details, and uncertainty around estimates—is central to responsible statistical interpretation.

18. Limitations

• The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
• Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.

Several trial-specific details needed to assess the findings are not reported in the registry record. The participant description is limited to students beginning first grade with delays in word reading and calculations. Eligibility thresholds, demographic characteristics, school settings, and the number or type of participating schools are not reported. The masking label is single, but the identity of the masked party is not stated.

The intervention and control descriptions show that the school’s usual program could include a supplemental program if designated by the school. The record does not describe variation in usual instruction across schools or provide adherence and implementation results. The researcher-delivered programs are described as 15 weeks with 3 30-minute sessions per week, but the record does not report whether participants received all planned sessions or how fidelity was assessed.

The primary word-reading result is available, but the arithmetic-fluency result named in the study summary is not posted. No secondary outcome results are posted despite the record listing six outcome measures and six analyses. Missing-data procedures and the analysis population are not reported. The record also lacks details of the multilevel model, including its levels and adjustments, and does not explain the discrepancy between the registry analysis and the unadjusted recalculation.

The posted outcome group sizes differ across arms, but the record does not explain the reasons or state how the analysis addressed any unavailable endpoint data. The trial’s original sample-size assumptions and justification are not reported. Finally, the safety figures list zero events in the reported categories but do not describe event collection or monitoring. These limits make it difficult to assess the full analysis strategy, completeness of outcome reporting, and generalizability from the registry record alone.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Improving the Academic Performance of First-Grade Students With Reading and Math Difficulty — NCT03991234.
• Registry record last updated 2026-03-23; status last verified 2026-03.
• Results first posted 2026-03-23.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

22. Record Summary

NCT03991234 is a completed randomized, parallel-group, single-masked study sponsored by Vanderbilt University. It enrolled 385 participants and evaluated coordinated reading and math intervention, reading intervention, math intervention, and business-as-usual school instruction for first-grade students with reading and math difficulties. The researcher-delivered interventions lasted 15 weeks, with 3 30-minute sessions per week.

The primary endpoint discussed is Word Reading Fluency-2, measured as words read correctly. The registry’s multilevel comparison of coordinated intervention with business-as-usual reports a net mean difference of .330, a 95% confidence interval from 0.021 to 0.64, and p = .018. A simple unadjusted recalculation differs; the registry’s own analysis takes precedence. Arithmetic-fluency results and secondary outcome results are not posted. The record reports zero serious and zero other adverse events in each condition, and does not report the original sample-size assumptions, missing-data procedures, or full model specification.