The Effect of Physical Training and the Omega 3 Consumption on Attention Deficit Hyperactivity Disorder in Children: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for The Effect of Physical Training and the Omega 3 Consumption on Attention Deficit Hyperactivity Disorder in Children (NCT01807299), a randomized na study. The primary outcome is Conners Scale.

2. Clinical Question

3. Trial Design

The registry record describes a randomized, triple-masked, parallel-group trial with an enrollment of 68. The study is listed as completed, with a start date of 2011-05 and primary completion in 2013-03. The phase is listed as NA. The sponsor is Federal University of São Paulo.

The four outcome arms are Omega-3 Only, Sedentary (Control), Placebo + Phsycal Training, and Omega 3 + Phsycal Training. Their reported outcome sample sizes are 14.0, 14.0, 12.0, and 13.0, respectively. These are the arm-level sample sizes associated with the reported outcome summaries; the registry record does not explain how they relate to the enrollment figure or whether outcome data were unavailable for other enrolled participants.

The intervention descriptions distinguish fish oil from mineral oil and physical training from the sedentary condition. The omega 3 description specifies 2g per day for 90 days. The training description specifies exercise three times a week for three months; the sedentary group was oriented not to train for three months. The registry record does not detail how randomization was generated or concealed, what masking meant for each role, or whether adherence to the assigned regimens was assessed.

The listed design is parallel, so the reported arms represent separate groups rather than repeated treatment periods. The record does not report a factorial design or specify whether the four groups were intended to estimate separate main effects and an interaction. Those interpretations should therefore not be assumed from the arm labels alone.

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.

Overall Study

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: Conners scale and the child stress scale (ESI)

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.

6. Primary Endpoint

The registry lists the primary outcome as Conners Scale, measured over 3 months.

The primary endpoint is the mean score on the Conners Scale at 3 months, reported in units on a scale. The registry record describes scores above 60 as indicating ADHD and gives the scale range as a minimum of 0 and a maximum of 126. The reported arm summaries are means with standard deviations, so the endpoint is treated as a continuous measure rather than as a count or a time-to-event outcome.

A continuous scale can retain information about different score levels, rather than reducing a participant’s result to a category. In general, comparing group means describes the average level of the measured score in each group. A lower mean represents a lower average score on this scale, but the registry record does not establish a threshold for a clinically important difference or explain how changes in the scale should be interpreted for individual children.

The primary outcome population field also names the child stress scale (ESI), while the primary outcome title and description refer to the Conners Scale. The posted results contain one outcome measure and report Conners Scale summaries. A separate ESI result is not reported in the registry record. The record also does not report a baseline Conners score or a change-from-baseline endpoint, so the displayed summaries describe final values at the stated timeframe rather than a reported change score.

7. Results Posted in the Registry

• Omega-3 Only: mean 36.64 versus 42.31 on control; difference -5.67 (95% CI -14.88 to 3.54), standardized effect d = -0.46; z-test p = 0.227.
• Placebo + Phsycal Training: mean 40.08 versus 42.31 on control; difference -2.23 (95% CI -12.58 to 8.12), standardized effect d = -0.17; z-test p = 0.673.
• Omega 3 + Phsycal Training: mean 36.82 versus 42.31 on control; difference -5.49 (95% CI -13.15 to 2.17), standardized effect d = -0.53; z-test p = 0.160.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary measure is continuous, and the registry record reports a mean and standard deviation for each arm. In general, a mean gives the arithmetic average of the measured scores, while a standard deviation describes how spread out scores are around that average. A standard deviation is not a confidence interval: it reflects participant-level variability, whereas a confidence interval expresses uncertainty about an estimated quantity such as a difference in group means.

What does a mean difference represent?

The unadjusted comparisons use Sedentary (Control) as the reference. Each estimated mean difference is the intervention-arm mean minus the control-arm mean. A negative value therefore indicates a lower mean score in the named intervention arm. For example, the reported estimate for Omega-3 Only is -5.67, and the estimate for Omega 3 + Phsycal Training is -5.49. These estimates are based on final values at 3 months; they are not reported differences in change from baseline.

The comparisons are unadjusted recalculations from the posted summary statistics. They do not represent the sponsor’s reported analysis, which uses a different stated method and is described across all four groups. No adjustment for baseline scores or other covariates is included in these recalculations. The registry record does not report whether the sponsor’s analysis used such adjustments.

How should the confidence intervals be read?

A confidence interval gives a range of estimates compatible with the data and the method used, under the method’s assumptions. A narrower interval indicates greater precision; a wider interval indicates less precision. It is not a range containing a known fixed proportion of individual children’s scores. The recalculated intervals are -14.88 to 3.538 for Omega-3 Only, -12.58 to 8.124 for Placebo + Phsycal Training, and -13.15 to 2.169 for Omega 3 + Phsycal Training. Each spans zero, indicating that the interval includes no mean difference. The registry record does not identify a confidence level for these recalculated intervals.

What do the p-values describe?

The p-values reported for the recalculated comparisons are unadjusted: 0.227, 0.673, and 0.16 for Omega-3 Only, Placebo + Phsycal Training, and Omega 3 + Phsycal Training, respectively. In general, a p-value describes how unusual data at least as discrepant as those observed would be under a specified null model. It is not the probability that the null hypothesis is true, nor is it a measure of the size or clinical importance of a difference. These p-values do not incorporate a reported correction for considering multiple comparisons.

The sponsor’s analysis is listed as “Chi-squared, Corrected,” with a parameter described as “Mean Difference (Final Values),” a reported value of 5, and p = 0.05. The registry record does not explain the calculation, the meaning of the correction, or how a chi-squared analysis generated a reported mean difference. No confidence interval is reported for that analysis. It cannot be reconstructed as the same set of pairwise mean comparisons from the details recorded.

Why does variation matter?

In general, greater variation among scores makes a group mean less precise when the sample size is unchanged. The arm-level standard deviations differ: the control standard deviation is 12.1, while those for the intervention arms are 12.75, 14.47, and 7.91. The comparisons use pooled standard deviations of 12.43, 13.24, and 10.3, respectively. These quantities help describe the scale of variation used in the recalculations, but do not address possible bias from missing outcomes, departures from the analysis plan, or differences at baseline.

Over-dispersion is a concern in count models when observed counts vary more than the model assumes. This is a general statistical issue, but the reported primary endpoint is a continuous scale score, not a count. The record gives no indication that an over-dispersion model was used or needed for this endpoint. Likewise, the registry record does not report a model specification, an analysis population, a missing-data method, or the assumptions behind the sponsor’s corrected analysis.

Because the sponsor’s reported analysis and the summary-statistic recalculations differ, the recalculated pairwise results should be understood as descriptive, unadjusted estimates rather than a replacement for the sponsor’s analysis. The discrepancy is recorded, and the sponsor’s own analysis takes precedence.

10. Confidence Intervals and Precision

Precision concerns how narrowly the data locate an estimated difference. The recalculated mean differences are accompanied by confidence intervals, and all three intervals are broad and include zero. The intervals are -14.88 to 3.538 for Omega-3 Only, -12.58 to 8.124 for Placebo + Phsycal Training, and -13.15 to 2.169 for Omega 3 + Phsycal Training. Their width means the estimates do not pin down a single value closely. The included zero also means that the recalculated intervals do not rule out no difference between an intervention arm and the sedentary control.

The point estimates are negative, but the intervals extend to positive values as well. Thus, the summary statistics do not establish the direction of the underlying mean difference with precision. The estimate for Placebo + Phsycal Training is closer to zero than the other two estimates, but its interval is also broad. No minimally important difference is reported, so the intervals cannot be judged against a registry-defined threshold for clinical importance.

The arm sample sizes associated with the summaries are 14.0, 14.0, 12.0, and 13.0. The standard deviations also show that score variability differed across arms. These features are relevant to the uncertainty of group comparisons, but the registry record does not provide the analysis details needed to assess every source of uncertainty. In particular, no baseline-adjusted estimate, confidence level, missing-data analysis, or full statistical model is reported.

The sponsor’s reported result has p = 0.05 but no confidence interval. A p-value alone does not show the range of effect sizes compatible with the data, and the registry record does not provide enough detail to translate that reported overall analysis into the precision of the three pairwise comparisons. The unadjusted intervals and the sponsor’s result answer differently described statistical questions; the registry record does not reconcile them.

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. The outcome is a continuous scale score, so the planning illustration is expressed as participants per arm; the total-event convention applies to time-to-event outcomes. The illustration assumes a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. It uses the observed effect as its reference and considers detecting the stated fraction of that observed effect. The original trial’s own design assumptions are not reported in the registry record.

The 80% power column gives an illustrative per-arm sample size for a design that would have 80% power under those assumptions; the 90% column gives the corresponding illustration for 90% power. Power is the probability of detecting an effect of the specified size under the assumed model, if that effect is truly present. These planning calculations are not observed power.

The entries are specific to each comparison. For Omega-3 Only, planning for 100% of the observed effect gives 76 participants per arm for 80% power and 101 for 90% power; planning for 75% gives 135 and 180; planning for 50% gives 302 and 404. For Placebo + Phsycal Training, the corresponding figures are 554 and 741 for 100%, 984 and 1,317 for 75%, and 2,214 and 2,963 for 50%. For Omega 3 + Phsycal Training, they are 56 and 75 for 100%, 99 and 132 for 75%, and 222 and 297 for 50%.

Smaller effects require more participants to detect under the same assumptions. These numbers are planning illustrations based on the observed estimates, not evidence about the original design or a recommended sample size for a future study. Because the observed effects are estimated from small arm-level samples, planning directly from them may not represent the effect a later study should expect.

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 = -5.670; pooled standard deviation σ = 12.429.
2. n = 2 × (1.96 + 0.842)² × 12.429² / -5.670² = 75.4, rounded up to 76 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 <- -5.67                      # observed difference in means
sigma <- 12.4292497762335                     # 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(1807299)
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 = 76 (80% power), 101 (90% power)
 75% of observed effect: n per arm = 135 (80% power), 180 (90% power)
 50% of observed effect: n per arm = 302 (80% power), 404 (90% power)
power.t.test: 76.4 
Simulated power at n = 76 per arm: 0.796 (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 record reports the sponsor’s own analysis as “Chi-squared, Corrected,” with the parameter “Mean Difference (Final Values),” a value of 5, and p = 0.05 across the four groups. No confidence interval is reported. The record does not explain the calculation, the correction, or whether the reported value of 5 is an estimate on the Conners scale or how it relates to the pairwise estimates.

The unadjusted recalculations use the posted arm means and standard deviations to compare each intervention arm with Sedentary (Control). They produce estimates of -5.67, -2.23, and -5.49, each with its own confidence interval and unadjusted p-value. Those are not the same analysis as the sponsor’s reported four-group result. The methods and comparison structure are not sufficiently described to reconcile them.

The discrepancy is important: the sponsor’s own analysis takes precedence over the recalculated comparisons. The recalculations can still describe what follows from the posted summary statistics, but they should not be presented as if they reproduce or supersede the sponsor’s analysis. The registry record does not report further details that would clarify the difference.

14. Multiplicity, Missing Data and Analysis Populations

The registry record reports one primary outcome measure and no posted secondary outcomes. The primary outcome description names the Conners Scale and also refers to the child stress scale (ESI) in its population field; a separate ESI result is not reported in the registry record. There is one sponsor-reported analysis and three unadjusted recalculated comparisons against the sedentary control. The record does not report a multiplicity strategy or explain whether the sponsor’s analysis was intended as an overall test followed by any pairwise comparisons.

Multiplicity matters in general when several statistical comparisons are made: considering more comparisons can increase the chance of finding an apparently unusual result by chance. The recalculated p-values are explicitly unadjusted. They should therefore be read as individual comparison summaries, not as results corrected for all comparisons or outcomes. No correction should be inferred for the sponsor analysis simply from its label “Corrected”; the registry record does not say what was corrected.

The reported results give final values at 3 months, but do not report baseline scores or a change-from-baseline analysis. The record does not state whether all randomized participants were included in the analyses, whether analyses followed assignment regardless of adherence, or how missing outcomes were handled. Although enrollment is listed as 68, the arm-specific outcome sample sizes are 14.0, 14.0, 12.0, and 13.0. The registry record does not explain the relationship between enrollment and these analysis counts. It would therefore be inappropriate to infer the reason for any difference or to label it as a particular kind of attrition.

The statistical analysis plan, prespecified model, handling of protocol deviations, and analysis populations are not reported in the registry record. The record also does not report interim analyses. Without these details, it is not possible to assess whether the reported analysis fully followed a prespecified plan, whether the missing-data approach could affect the estimates, or whether the reported comparisons were selected from a broader set of analyses.

15. Safety Results

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

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 1% reporting threshold.

The adverse-event record reports zero serious adverse events and zero other adverse events in each of the four groups. The serious-event at-risk counts are 14 for Omega-3 Only, 14 for Sedentary (Control), 12 for Placebo + Phsycal Training, and 13 for Omega 3 + Phsycal Training. The other-event at-risk counts are the same for the corresponding groups.

These entries describe what was recorded in the registry, not proof that no adverse events occurred outside the recorded monitoring or reporting process. The record does not describe how events were collected, how long safety follow-up continued, or what definitions were used. Death counts are not reported in the registry record. The zero counts should be read alongside the limited information about ascertainment and the arm-level counts, rather than as a complete assessment of safety.

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

The posted outcome summaries describe average Conners Scale scores at 3 months in four randomized groups. The mean scores were 36.64 for Omega-3 Only, 42.31 for Sedentary (Control), 40.08 for Placebo + Phsycal Training, and 36.82 for Omega 3 + Phsycal Training. The unadjusted recalculated comparisons have negative point estimates for each intervention arm relative to control, but their confidence intervals include zero and extend in both directions.

These results do not establish a precise pairwise difference. The confidence intervals permit values consistent with lower or higher average scores relative to control, as well as no mean difference. The reported unadjusted p-values are 0.227, 0.673, and 0.16. They do not provide a measure of clinical importance, and the registry record does not state what size of score difference would matter clinically.

The sponsor’s analysis reports p = 0.05 for a four-group analysis, but its method and reported value are not reconciled with the unadjusted pairwise recalculations. The sponsor’s own analysis takes precedence. The available record does not explain whether the reported analysis was prespecified, whether it involved a different model, or how its result should be related to specific treatment contrasts.

The group means being below the stated score threshold of 60 does not indicate how many individual children were above that threshold. The reported final values also do not reveal whether participants’ scores improved or worsened from baseline, because baseline values and changes are not reported. No conclusion about an individual child follows from a group average.

Overall, the registry record permits a cautious statistical description of the posted arm means, variability, pairwise recalculations, and sponsor result. It does not resolve the discrepancy between analyses or provide the methodological detail needed to assess missing data, clinical importance, or the precise meaning of the sponsor’s overall test. These results alone should not be presented as definitive evidence that a treatment does or does not work.

17. Why This Trial Matters Statistically

This trial illustrates how a randomized design and a continuous endpoint can produce several distinct ways to summarize results. Arm means describe average scores, standard deviations describe within-arm variation, and mean differences describe contrasts between groups. Confidence intervals add information about precision that a point estimate alone cannot provide. Here, the recalculated intervals include zero and are broad, so the estimates are not precise enough to settle the direction of each pairwise difference.

The record also demonstrates why the named statistical analysis matters. The sponsor reports a corrected chi-squared analysis across all four groups, while the unadjusted recalculations compare each intervention arm with the sedentary control. An overall four-group analysis and pairwise comparisons are not interchangeable questions. The registry does not explain the difference, and the sponsor’s own analysis takes precedence. This is a reason to avoid reporting only whichever result seems easiest to interpret.

The planning illustration connects observed effects with the sample sizes that would be needed under stated assumptions. It also makes clear that planning around smaller effects requires more participants. Those calculations are not the trial’s original design rationale, which is not reported in the registry record, and are not evidence of observed power.

Finally, the endpoint and analysis population require careful reading. A mean final score does not show individual threshold status or change from baseline, and the record does not explain the relationship between enrollment and the arm-level outcome counts. Statistical interpretation depends not only on a p-value, but also on the estimand, analysis population, missing-data handling, multiplicity approach, and precision. Several of those details are not reported in the registry record.

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 limitations affect interpretation of the posted results. The reported endpoint summaries are final Conners Scale values at 3 months; baseline scores and change-from-baseline results are not reported. It is therefore not possible to describe change over time from these summaries. The registry record also gives no threshold for a clinically important mean difference, so statistical estimates cannot be translated into a registry-defined judgment of clinical importance.

The enrollment figure is 68, while arm-level outcome sample sizes are reported as 14.0, 14.0, 12.0, and 13.0. The registry record does not explain this relationship, report an analysis population, or describe missing outcome handling. No reason for the difference should be assumed. Details of randomization, allocation concealment, masking roles, adherence, and protocol deviations are also not reported.

The sponsor’s four-group analysis is described with a corrected chi-squared method and a mean difference in final values, but its calculation is not explained and it has no confidence interval. Its result is not reconciled with the three unadjusted pairwise recalculations. The record does not report an adjustment for multiplicity for the recalculated comparisons, nor does it state whether the sponsor’s analysis was prespecified.

The primary outcome field mentions both the Conners Scale and the child stress scale (ESI), but only Conners Scale results are posted. Safety entries report zero serious and other adverse events, but event collection procedures and safety follow-up are not described; death counts are not reported in the registry record. These limitations do not invalidate the posted summaries, but they constrain how much can be inferred from them.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: The Effect of Physical Training and the Omega 3 Consumption on Attention Deficit Hyperactivity Disorder in Children — NCT01807299.
• Registry record last updated 2020-02-28; status last verified 2020-02.
• Results first posted 2020-02-28.
• 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

The completed registry record describes a randomized, triple-masked, parallel-group trial sponsored by Federal University of São Paulo, with enrollment of 68 and a primary completion date of 2013-03. The primary outcome was the mean Conners Scale score at 3 months among children with attention deficit hyperactivity disorder.

Four arms are reported: Omega-3 Only, Sedentary (Control), Placebo + Phsycal Training, and Omega 3 + Phsycal Training. The posted summaries include arm means and standard deviations, plus unadjusted recalculated comparisons against the sedentary control. Their confidence intervals include zero. A separate sponsor-reported four-group analysis gives p = 0.05, but its method and result are not reconciled with those recalculations; the sponsor’s analysis takes precedence.

The registry record does not report baseline scores, missing-data methods, analysis populations, multiplicity handling, or the original sample-size assumptions. Safety entries record zero serious and other adverse events in each group, while death counts are not reported.