Exercise Training to Improve Cognitive Function: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Exercise Training to Improve Cognitive Function (NCT03824639), a randomized na study. The primary outcome is Change in Delayed Recall Score on Wechsler Logical Memory Task From Baseline to 6 Months.

2. Clinical Question

3. Trial Design

The registry record describes a randomized, parallel-group trial with single masking. It lists 60 participants with mild cognitive impairment and identifies the sponsor as the VA Office of Research and Development. The record gives the study status as completed, with a start date of 2019-04-23 and a primary completion date of 2022-05-31. The phase is recorded as NA.

Participants were assigned to one of two behavioral interventions: structured exercise or health education. The registry record does not identify who was masked, so the meaning of single masking cannot be specified further. It also does not report the method used to generate the random allocation sequence, the allocation concealment procedures, or the original statistical design assumptions.

The primary outcome was change in delayed recall on the Wechsler Logical Memory Task from baseline to 6 months. A secondary outcome was change in delayed recall on the Rey-Osterrieth Complex Figure Test over the same timeframe. The record lists two outcome measures and two analyses, and one secondary outcome is posted. The reported group sizes for the primary outcome are 29 in the Exercise Group and 31 in the Control Group. Those outcome counts describe the posted analyses; the registry record does not explain whether all randomized participants were included or how missing outcome measurements were handled.

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

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 Change in Delayed Recall Score on Wechsler Logical Memory Task From Baseline to 6 Months, measured over baseline and 6 months.

The primary endpoint is change in delayed recall score on the Wechsler Logical Memory Task from baseline to 6 months. This task asks participants to recall details from two short stories. Its delayed recall score can range from 0, for no details recalled for either story, to 50, for all details recalled on both stories. The endpoint is expressed in units on a scale, with the posted group summaries reported as means and standard deviations.

Using change rather than a score at one time point focuses the comparison on how the group averages moved between baseline and the 6-month assessment. A positive change indicates an increase in the score over that period, while a negative change indicates a decrease. This interpretation applies to the direction of the scale; it does not establish why a change occurred or what it means for an individual participant.

The trial’s stated project focus is the feasibility of a home-based exercise intervention to improve episodic memory in people with mild cognitive impairment. Delayed recall is the outcome the registry record selected for the primary statistical comparison. The record does not report a minimum change considered important or explain how the endpoint was selected, so the size of a group-average difference cannot be classified as clinically important from this information alone.

7. Results Posted in the Registry

• Exercise Group: mean 0.74 versus -0.87 on control; difference 1.61 (95% CI -0.59 to 3.81), standardized effect d = 0.37; z-test p = 0.152.

8. Secondary Efficacy Endpoints

The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.

Change in Delayed Recall Score on the Rey-Osterrieth Complex Figure Test From Baseline to 6 Months

• Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
• Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
• Result:
  • Exercise Group: mean 1.18 versus 0.46 on control; difference 0.72 (95% CI -1.29 to 2.73), standardized effect d = 0.18; z-test p = 0.482.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Exercise Group and the control. The interval gives the range of effects that remain compatible with the data.

The registry record lists one secondary outcome: change in delayed recall score on the Rey-Osterrieth Complex Figure Test from baseline to 6 months. Its group-level pattern is in the same direction as the primary result: the exercise group’s average change is higher than the control group’s average change. The secondary comparison is also uncertain, with its reported interval including zero and an unadjusted p-value of 0.482. The sponsor analysis reports Cohen’s d of 0.18 for this outcome.

Considering the primary and secondary outcomes together, the posted point estimates both favor a higher average change in the exercise group, but neither comparison precisely distinguishes the group means. Similar direction across outcomes can be informative descriptively, but it does not independently establish a consistent effect. The outcomes use different recall tests, and the registry record does not report how the two measures were related in the analysis or whether one was intended to confirm the other.

Unadjusted secondary results carry less weight when several outcomes or comparisons may be considered, because repeated testing can increase the chance of observing apparently notable results by chance. General statistical explanation: multiplicity procedures address that issue by controlling or otherwise accounting for repeated statistical testing. The registry record does not report whether any such procedure was used, nor does it give the complete original analysis plan. The secondary result should therefore be treated as supporting descriptive context, not as independent confirmation of the primary comparison.

Secondary outcomes registered for this trial, for reference (only those above were recalculated):

• Change in Delayed Recall Score on the Rey-Osterrieth Complex Figure Test From Baseline to 6 Months

9. Statistical Interpretation

10. Statistical Methods Explained

The primary outcome is continuous: each participant’s change is represented by a numerical score, and the registry record reports a mean and standard deviation for each group. A mean describes the group’s average observed change. A standard deviation describes how spread out individual changes are around that average. It is not the uncertainty in the mean difference; the latter also depends on the number of observations and is represented in the interval around the comparison.

What does the mean difference represent?

The recalculated comparison subtracts the Control Group mean change from the Exercise Group mean change. The result is 1.61 units. A positive value indicates a higher average change in the exercise group, while a negative value would indicate a higher average change in the control group. The scale-specific units make this result interpretable in relation to the test score, but the registry record does not give a threshold for judging whether a particular difference matters clinically.

What does the interval add?

General statistical explanation: a confidence interval is a range of values compatible with the observed data under the method used to calculate it. It communicates uncertainty around an estimate rather than identifying the one true value. For the primary comparison, the reported interval includes values on both sides of zero. Because zero represents no difference in group means, this interval does not rule out no difference; it also includes positive differences. The interval’s breadth indicates that the estimate is not highly precise. The confidence level and details of the sponsor’s interval method are not reported in the registry record.

How should the p-value be read?

The unadjusted p-value for the primary comparison is 0.152. General statistical explanation: a p-value measures how unusual data at least as incompatible with a specified null model would be if that model were correct. It is not the probability that the null hypothesis is true, and it is not a measure of clinical importance. Because this value is unadjusted, it does not account for testing multiple outcomes or comparisons. The registry record does not state a multiplicity procedure or a threshold used in the original analysis.

What does Cohen’s d describe?

The registry record reports Cohen’s d of 0.37 for the primary comparison. This standardized effect expresses the group difference in relation to variability, rather than in units on the recall test. Standardization can help describe the magnitude of an effect on a common scale, but it removes the direct connection to the test’s units. Its meaning depends on the variability in the population and on the context of the measure. The sponsor analysis does not include an interval or p-value alongside this estimate.

Why might variability matter?

General statistical explanation: greater variation among individual changes makes a group mean less precisely estimated when the number of observations is unchanged. The standard deviations reported for the primary endpoint are 4.0 in the Exercise Group and 4.7 in the Control Group. These values describe dispersion in observed changes, not measurement error or uncertainty in the treatment contrast. The registry record does not report whether the original analysis checked distributional assumptions, used adjustments for baseline values, or accounted for other participant characteristics.

The recalculated comparison is an unadjusted calculation from the posted group summaries. It does not incorporate individual-level data, covariate adjustment, or any other model details that may have been used in the sponsor’s analysis. The registry record identifies the sponsor’s reported statistic as Cohen’s d but does not specify the analysis method. No claim about the original model can therefore be made from the posted record.

11. Confidence Intervals and Precision

The primary mean difference is 1.61 units, with an interval extending from a negative value to a positive value. Since zero lies inside the interval, the posted results do not rule out no difference in mean change. The interval also permits positive differences, so the data do not pinpoint the size of any group separation. Its width signals limited precision in this estimate.

Precision depends on both the observed variation and the amount of information available. The primary analysis includes 29 participants in the Exercise Group and 31 in the Control Group, with standard deviations of 4.0 and 4.7 units, respectively. These group sizes and spreads help explain why an estimate can remain uncertain even when its point estimate is positive. The registry record does not provide individual-level data or a confidence level for the posted interval, so the interval’s construction cannot be independently evaluated from the record.

Statistical uncertainty and importance are separate considerations. An interval crossing zero does not prove that the groups are identical; it means the estimate is not precise enough to exclude a range that includes no difference under the stated interval method. Conversely, a positive point estimate does not by itself establish a meaningful effect. The registry record does not report a threshold for an important difference on the Wechsler Logical Memory Task, so clinical importance cannot be judged from the estimate alone.

The sponsor’s posted analysis gives Cohen’s d of 0.37 but does not report an interval for that standardized estimate. Consequently, the precision of the sponsor’s standardized effect is not described in its own analysis entry. The mean-difference interval offers uncertainty on the original score scale, while the standardized statistic supplies a scale-relative summary.

12. 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 sample-size figures are planning illustrations expressed as participants per arm, not total events. They are based on a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each row plans for a stated fraction of the observed effect: the full observed effect, 75% of the observed effect, or 50% of the observed effect. These calculations are illustrations based on the observed result, not the trial’s original design justification. The original design assumptions are not reported in the registry record.

The 80% power column gives the participants per arm estimated to be needed for an 80% chance of detecting the chosen effect under those planning assumptions, if that effect were the true one. The 90% power column gives the corresponding estimate for a 90% chance. Power describes a design’s long-run detection probability under specified assumptions; it does not say whether the observed trial result is correct or whether an effect is present.

The planning figures increase as the effect used for planning gets smaller. This reflects a general statistical principle: a smaller difference is harder to distinguish from variation, so more participants are needed under otherwise unchanged assumptions. The illustrations should not be read as observed power, nor as evidence that the completed trial was designed to detect these specific effects. The registry record does not report the assumptions behind the trial’s original enrollment target.

13. 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 = 1.610; pooled standard deviation σ = 4.376.
2. n = 2 × (1.96 + 0.842)² × 4.376² / 1.610² = 116.0, rounded up to 116 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 <- 1.61                      # observed difference in means
sigma <- 4.37607129740821                     # 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(3824639)
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 = 116 (80% power), 156 (90% power)
 75% of observed effect: n per arm = 207 (80% power), 277 (90% power)
 50% of observed effect: n per arm = 464 (80% power), 622 (90% power)
power.t.test: 116.9 
Simulated power at n = 116 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.

14. Analyses Reported by the Sponsor

The sponsor’s posted primary analysis reports Cohen’s d of 0.37 for the comparison between the Exercise Group and Control Group. It does not include a p-value or an interval for that statistic. The recalculated unadjusted analysis instead expresses the comparison as a mean difference of 1.61 units on the Wechsler Logical Memory Task scale, with an interval that crosses zero and an unadjusted p-value of 0.152.

These are related but not identical summaries: Cohen’s d is standardized, while the mean difference retains the original test units. The registry record marks no discrepancy between the posted and recalculated results. The sponsor’s analysis takes precedence when a discrepancy is identified; no such discrepancy is identified for this comparison. Because the sponsor entry omits uncertainty measures and its method is not specified, the recalculation adds a descriptive estimate of uncertainty from the posted group summaries but cannot establish what method the sponsor used.

Neither statistic should be interpreted in isolation. The standardized estimate describes relative magnitude, and the original-scale estimate describes the score-unit contrast. The interval and p-value help characterize uncertainty in the recalculated comparison, but do not turn the result into a definitive conclusion about the intervention.

15. Multiplicity, Missing Data and Analysis Populations

The registry record lists two outcome measures and two analyses, with one secondary outcome posted in addition to the primary outcome. It does not report whether the analyses were prespecified in a statistical analysis plan, how outcomes were prioritized, or whether a multiplicity adjustment was applied. The posted p-values are described as unadjusted. Without those details, the record does not establish how the possibility of repeated testing was handled in the original analysis.

General statistical explanation: when multiple outcomes or comparisons are tested, the chance of at least one apparently unusual result can rise if each test is interpreted separately. A prespecified hierarchy, correction, or other approach may be used to address this. The appropriate method depends on the trial’s aims and analysis plan, neither of which is fully described in the registry record. The secondary comparison should therefore not be treated as if it were a separate confirmatory test with no multiplicity concerns.

Missing-data handling is also not reported in the registry record. The primary outcome summaries include 29 participants in the Exercise Group and 31 in the Control Group, but those counts alone do not explain whether these were all randomized participants with available data, whether any measurements were missing, or how any missing outcomes were treated. The record does not identify an analysis population such as all randomized participants or participants with complete measurements.

The registry record also does not report whether the analysis adjusted for baseline score, other participant characteristics, or adherence. It does not give details about model assumptions, sensitivity analyses, or methods for handling deviations from assigned intervention. These omissions limit the ability to evaluate the analysis beyond the posted group summaries and recalculated unadjusted comparisons.

16. 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 record reports zero serious adverse events among 29 participants at risk in the Exercise Group and zero among 31 participants at risk in the Control Group. It also reports zero other adverse events in each group, with the same group counts at risk, and zero deaths in both groups. No serious adverse event terms are listed.

These figures describe the events recorded in the registry entry; they do not show that no events occurred outside the categories or collection procedures represented in that record. The registry record does not provide event definitions, monitoring procedures, or further detail on adverse-event ascertainment. With no reported events in either arm, a comparative estimate of event rates is not available from these counts alone. The figures should be read as reported safety information for this trial, not as a general estimate of risk.

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

The results describe average changes in delayed recall in two randomized groups over baseline to 6 months. The primary point estimate is positive for the exercise-versus-control comparison, but its interval crosses zero and the unadjusted p-value is 0.152. The evidence in the registry record therefore does not precisely determine whether the group averages differed or how large any difference might be.

This is not equivalent to showing that the groups were identical. A broad interval that includes zero can reflect uncertainty, and it also includes positive differences. At the same time, a positive estimate does not establish that structured exercise caused a difference or that any observed difference was important to participants. The record does not report a threshold for meaningful change on the primary scale, individual response patterns, or the original analysis plan.

The project summary describes an assessment of feasibility, but the posted results emphasized are cognitive outcome summaries. The registry record does not report enough information to draw conclusions about adherence, implementation, or feasibility. It also does not establish whether any findings persist beyond the 6-month assessment.

The randomized parallel-group design is relevant to the comparison, but interpretation remains dependent on details not reported in the registry record, including masking procedures, missing-data handling, and the sponsor’s analysis method. The results apply to the participants and interventions represented in this trial record; they do not by themselves establish what would occur in other populations or settings.

18. Why This Trial Matters Statistically

This trial illustrates why a group difference should be read together with its uncertainty. The primary estimate is positive, but the interval spans zero and the unadjusted p-value does not provide a precise separation between the groups. Looking only at the direction of the point estimate would conceal that uncertainty; looking only at a thresholded p-value would also discard information about the estimated difference and its range.

The trial also shows the value of retaining the original outcome scale alongside a standardized statistic. The mean difference is expressed in units on the Wechsler Logical Memory Task, while Cohen’s d describes the difference relative to variability. Each has a different interpretive role. Neither alone establishes clinical importance, particularly when the registry record does not report a meaningful-change threshold.

Planning illustrations based on observed effects can help readers understand how assumptions about the target difference affect required sample size. Smaller target effects require larger planned groups under the stated assumptions. Such illustrations are not a substitute for the trial’s original design rationale, which is not reported in the registry record, and they do not describe observed power.

Finally, the record highlights how incomplete reporting constrains statistical interpretation. Information about the original analysis plan, multiplicity, missing outcomes, analysis populations, and masking details would help readers understand the context and robustness of the posted estimates. Without those details, the most defensible reading stays close to the group summaries and their stated uncertainty.

19. 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.

The registry record provides aggregate group means and standard deviations, not individual participant data. This prevents independent assessment of the distributions of changes, participant-level patterns, or alternative analyses. The analysis method used by the sponsor is not specified, and the sponsor’s primary analysis entry gives a standardized effect without an interval or p-value.

The record does not report how missing outcome measurements were handled, whether all randomized participants were analyzed, or what analysis population was used. The reported group counts therefore cannot, on their own, establish the extent or consequences of missing data. Masking is listed as single, but the record does not identify who was masked or how masking was maintained for these behavioral interventions.

The registry record does not report the original sample-size justification, the statistical analysis plan, or whether the primary endpoint and analysis were specified before outcomes were examined. It also does not report a multiplicity strategy, a threshold for clinically important change, or methods for checking analysis assumptions. These gaps limit evaluation of selection and analysis decisions and of the clinical meaning of the score differences.

The posted outcomes cover baseline to 6 months. The registry record does not provide evidence about longer-term results, adherence, intervention delivery, or feasibility measures beyond the brief project summary. The safety entry reports no adverse events, but gives limited information about definitions and ascertainment. These limitations do not negate the reported summaries; they define what can and cannot be concluded from the registry record.

20. Related Tutorials

21. Related Statistical Calculators

22. Sources

• ClinicalTrials.gov: Exercise Training to Improve Cognitive Function — NCT03824639.
• Registry record last updated 2024-02-14; status last verified 2023-06.
• Results first posted 2024-02-14.
• 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.

23. Record Summary

NCT03824639 is a completed randomized, single-masked, parallel-group trial comparing structured exercise with health education in people with mild cognitive impairment. The registry record lists enrollment of 60 and a primary endpoint of change in delayed recall on the Wechsler Logical Memory Task from baseline to 6 months.

The primary group comparison has a positive mean-difference estimate, but its reported interval crosses zero and its unadjusted p-value is 0.152. The sponsor reports Cohen’s d of 0.37. One secondary delayed-recall outcome is also posted, with an uncertain group comparison. The record reports zero serious adverse events, zero other adverse events, and zero deaths in both groups.

Important details—including the original sample-size rationale, missing-data handling, analysis populations, multiplicity procedures, and sponsor analysis method—are not reported in the registry record. The posted results therefore support a cautious description of the group summaries and their uncertainty, rather than a definitive claim about the intervention.