Stimulating the Social Brain: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Stimulating the Social Brain (NCT03374631), a randomized na study. The primary outcome is Change in General Paranoid Ideation for Active vs. Sham Simulation.

2. Clinical Question

The trial's central question concerns whether stimulation is associated with a change in how participants process social stimuli, with paranoid ideation as the primary outcome. The outcome is a score on a self-report scale, not a diagnosis or a direct measure of a clinical event. The registry describes the score as assessing sub-clinical paranoid thought, with higher scale scores indicating higher paranoia at a given assessment.

Trustworthiness-task scores and performance on the Penn Emotion Recognition Test are listed as secondary outcomes. These outcomes address related but distinct aspects of social judgment and emotion recognition. Their results can add context, but they do not replace the primary comparison or establish that the underlying question has been answered conclusively.

The participant group is described as healthy adults. The registry record does not report evidence about other populations, longer-term effects, or outcomes beyond the behavioral assessments described. The clinical question should therefore be read as a short-term comparison of active and sham stimulation in this enrolled group, not as a conclusion about treatment for a disorder.

3. Trial Design

The registry record describes a randomized, double-masked crossover trial of active anodal tDCS and sham tDCS. Enrollment was 40, and the listed study status is completed. The record gives a study start date of 2017-12-01 and a primary completion date of 2020-10-01. The phase is listed as not applicable.

In a crossover design, participants receive more than one study condition in sequence, so each participant may contribute observations under both conditions. The two listed sequences were active stimulation followed by sham stimulation, and sham stimulation followed by active stimulation. Behavioral testing followed each stimulation session, and the second session was scheduled one week after the first. The registry describes the trial as double-masked but does not report who was masked or how masking was maintained.

The posted primary outcome summaries list 40 observations for active stimulation and 40 for sham stimulation. Because this is a crossover study, those entries should not be read as evidence of 80 distinct participants. The registry reports overall enrollment as 40 and does not provide further detail about the number of participants with complete paired observations or the analysis population.

The primary outcome was assessed 30 minutes after completion of active or sham stimulation. The secondary outcomes use the same stated assessment timing. The record does not report a washout rationale, whether possible carryover between sessions was evaluated, or the statistical model used to account for sequence and repeated observations. Those details matter when interpreting crossover results and are not established by the design label alone.

The sponsor is The University of Texas at Dallas. Details of the original sample-size justification, planned interim analyses, and full statistical analysis plan are not reported in the registry record. The listed trial design and timing describe how the study was organized, but do not by themselves specify how the comparison was analyzed.

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.

First Intervention (20 Minutes)

Washout (1 Week)

Second Intervention (20 Minutes)

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 General Paranoid Ideation for Active vs. Sham Simulation, measured over Paranoid ideation will be assessed 30 minutes after completion of the active/sham stimulation.

The primary endpoint is the change in General Paranoid Ideation for active versus sham stimulation. It uses the self-report Paranoia Scale, whose scores range from 20-100, with higher scores indicating higher levels of paranoia. The registry describes the endpoint as the score before stimulation minus the score after stimulation. Under that definition, a positive change represents an improvement in paranoia.

Assessments were scheduled 30 minutes after completion of the active or sham stimulation. The measure was selected to capture sub-clinical paranoid thought and to assess whether that self-reported experience changed after stimulation. It is a continuous score: the posted summaries report means and standard deviations rather than counts of participants meeting a threshold.

Comparing the change score between conditions focuses on whether the average pre-to-post movement differs between active and sham stimulation. That is distinct from comparing only post-stimulation scores, because the endpoint incorporates the before-stimulation assessment. The registry record does not report the exact scoring details beyond the stated direction of subtraction and score interpretation, nor does it report a threshold for a change considered important to participants. Consequently, the endpoint supports interpretation of average score differences, but the record does not establish the clinical importance of any particular difference.

7. Results Posted in the Registry

• Active Stimulation: mean 1.60 versus 0.73 on control; difference 0.87 (95% CI -0.65 to 2.39), standardized effect d = 0.25; z-test p = 0.262.

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.

Trustworthiness Task Score for Active vs. Sham Stimulation

• 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:
  • Active Anodal tDCS: mean -0.14 versus -0.14 on control; difference 0.00 (95% CI -0.27 to 0.27), standardized effect d = 0.00; z-test p = 1.000.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Active Anodal tDCS and the control. The interval gives the range of effects that remain compatible with the data.

Penn Emotion Recognition Test for Active vs. Sham Stimulation

• 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:
  • Active Anodal tDCS: mean 35.05 versus 35.33 on control; difference -0.28 (95% CI -1.31 to 0.75), standardized effect d = -0.12; z-test p = 0.594.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Active Anodal tDCS and the control. The interval gives the range of effects that remain compatible with the data.

The secondary outcomes cover trustworthiness-task scores and emotion-recognition performance. Across them, the posted comparisons do not supply a consistent, clear separation between active and sham stimulation: one comparison has an estimated mean difference of zero, while the other is small relative to the uncertainty reflected in its interval. This broad pattern does not add strong corroboration for a distinct active-versus-sham effect on the primary measure.

These outcomes are related to the study's interest in social processing, but they measure different tasks from self-reported paranoid ideation. A result on trustworthiness or emotion recognition would not be interchangeable with a change on the Paranoia Scale. Likewise, similarity in the overall pattern does not prove that the measures capture the same underlying process.

The secondary comparisons are unadjusted, and the registry lists no reported analyses for them. When several outcomes are examined, the chance of finding an apparently notable result can increase unless the analysis plan accounts for the number and role of the comparisons. The record does not report whether a multiplicity strategy was planned or used. For that reason, secondary results generally carry less inferential weight than a prespecified primary result, especially when the analysis details and correction approach are not documented.

The appropriate use of the secondary findings is contextual: they show what the posted scores look like across additional behavioral measures, but they should not be treated as independent confirmation of the primary result or as proof of a broader effect on social cognition. The registry does not report a prespecified hierarchy among the secondary endpoints, so their relative priority cannot be determined from the record.

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

• Trustworthiness Task Score for Active vs. Sham Stimulation
• Penn Emotion Recognition Test for Active vs. Sham Stimulation

9. Statistical Interpretation

10. Statistical Methods Explained

The primary measure is continuous, and the registry reports it using a mean and standard deviation. A mean describes the average score change among the observations summarized. A standard deviation describes how dispersed individual scores are around that average. These answer different questions: the mean describes the central tendency, while the standard deviation describes variation among observations.

What does the mean difference represent?

The posted comparison is a mean difference for active stimulation versus sham stimulation. It summarizes the contrast between the two condition means on the pre-to-post change scale. Its direction must be interpreted using the endpoint definition: the score before stimulation minus the score after stimulation, with positive values designated as improvement. The estimate of 0.87 is the registry's reported comparison value. It is not a separate measure of the proportion of participants who improved, and it does not show how many individuals had a positive change.

What does the confidence interval add?

A confidence interval expresses uncertainty around an estimated contrast. In general, it describes a range of values compatible with the data and the statistical procedure used, under the method's assumptions. A narrow interval indicates greater precision than a wide interval. For the primary comparison, the interval crosses zero, meaning that it includes a no-difference value as well as values on either side. The posted interval therefore does not pin down the direction of the underlying contrast with precision.

How should the p-value be read?

The unadjusted p-value of 0.262 is a measure of how unusual data at least this discrepant would be under a specified null model of no difference, assuming the model and analysis are appropriate. It is not the probability that there is no effect, nor does it measure the size or importance of an effect. The record does not report a multiplicity adjustment for this value. A p-value should be interpreted alongside the estimated difference and its interval, not in isolation.

Why does the crossover design matter?

In a crossover study, the same person may contribute observations under active and sham conditions. The two observations from one person can be related. A paired analysis can use that relationship, while an analysis treating condition summaries as unrelated can fail to represent it. General statistical practice also considers order or period effects and possible carryover, since outcomes under a later condition may be influenced by an earlier session. The registry identifies a crossover structure and lists two treatment sequences, but it does not report whether the posted comparison accounts for paired observations, sequence, period, or carryover. Those analysis details are not reported in the registry record.

The comparison includes a pooled standard deviation of 3.472, which is a measure of variability used in the posted standardized comparison information. Standardizing a difference expresses its size relative to a measure of spread, but does not make it clinically meaningful by itself. The registry does not report a threshold for an important change on the Paranoia Scale.

Why can over-dispersion matter?

As a general statistical point, over-dispersion occurs when the observed variability is greater than a model assumes. A model that understates variability can make uncertainty appear too small and can make tests look more decisive than they should. The posted primary outcome is continuous and is summarized with a standard deviation; the registry does not report an over-dispersion assessment or a model diagnostic. This concept is therefore relevant as a general consideration, not a claim that over-dispersion occurred in this trial.

The registry reports no analyses for the posted secondary outcomes. The primary comparison's modeling details, missing-data method, analysis population, and treatment of multiple endpoints are not reported in the registry record. Statistical methods beyond the posted summary statistics and comparison should not be inferred.

11. Confidence Intervals and Precision

The primary mean-difference estimate is 0.87, and its confidence interval crosses zero, extending into both negative and positive values. This means the posted estimate is compatible with a range that includes no average difference and also includes contrasts in either direction. The unadjusted p-value is 0.262. These features indicate that the comparison is not estimated precisely enough to distinguish a clear direction from no difference using the posted interval.

The point estimate alone can look more definite than the interval warrants. It gives one value for the contrast, while the interval communicates uncertainty around that value. The interval does not establish that the true contrast is exactly zero; rather, it shows that zero is among the values compatible with the data and reported method. Nor does the interval identify which values would matter to participants, because the registry record does not report a threshold for a meaningful score change.

The standard deviations of 3.11 and 3.8 describe the observed spread of change scores within the two condition summaries. They are not confidence intervals and should not be used as a substitute for the uncertainty around the difference. In a crossover trial, precision may depend on how strongly a participant's responses under the two conditions are related. The registry record does not report that within-participant correlation or the analysis method used to incorporate it.

Accordingly, the primary result is best read as an uncertain estimate rather than as evidence of a precisely measured benefit or precisely measured absence of a difference. The record does not provide enough analysis detail to assess all assumptions behind the interval.

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 planning figures are participants per arm, not total events. The illustration uses a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. It uses a target effect set to a stated fraction of the observed effect. These are assumptions for the planning illustration; the original trial's design assumptions and sample-size justification are not reported in the registry record.

For the primary comparison, planning for 100% of the observed effect gives 251 participants per arm for 80% power and 335 participants per arm for 90% power. Planning for 75% of the observed effect gives 445 participants per arm for 80% power and 596 participants per arm for 90% power. Planning for 50% of the observed effect gives 1,001 participants per arm for 80% power and 1,339 participants per arm for 90% power.

In plain language, the 80% power column represents an illustrative sample size intended to give the stated chance of detecting the assumed effect under the planning model, if its assumptions hold. The 90% column uses a higher target chance of detection under those same assumptions. The illustration shows that smaller target effects require more participants per arm to achieve those targets.

These are planning illustrations based on the observed estimate, not observed power. They do not show the probability that the trial's result is correct, and they do not establish what sample size the investigators originally planned. Because the study has a crossover design, readers should also distinguish the per-arm planning presentation from the trial's actual enrollment and repeated-condition structure.

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 = 0.870; pooled standard deviation σ = 3.472.
2. n = 2 × (1.96 + 0.842)² × 3.472² / 0.870² = 250.0, rounded up to 251 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 <- 0.87                      # observed difference in means
sigma <- 3.47218231088173                     # 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(3374631)
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 = 251 (80% power), 335 (90% power)
 75% of observed effect: n per arm = 445 (80% power), 596 (90% power)
 50% of observed effect: n per arm = 1,001 (80% power), 1,339 (90% power)
power.t.test: 251 
Simulated power at n = 251 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. Multiplicity, Missing Data and Analysis Populations

The registry lists four outcome measures and posts results for the primary paranoid-ideation measure and two secondary outcomes. It does not identify the remaining outcome measure in the available outcome descriptions. The record does not report a familywise error strategy, a false-discovery approach, or another multiplicity adjustment. The secondary comparisons are identified as unadjusted, and no secondary analyses are listed.

Multiplicity matters because examining several outcomes can increase the chance that at least one result appears statistically notable by chance, even if each individual comparison is interpreted using its own test. This does not invalidate a result, but it affects how much weight to place on unadjusted findings. The registry does not report the planned testing hierarchy or whether any outcomes were designated as exploratory.

Missing-data handling is also not reported in the registry record. The record does not say how incomplete outcome assessments were treated, whether an imputation method was used, or whether participants with missing observations were excluded from particular analyses. It does not report the number of participants contributing complete paired measurements under both stimulation conditions.

The analysis population is not reported in detail. The record does not specify whether the primary comparison used all enrolled participants, participants who completed both sessions, or another defined group. It also does not describe protocol deviations or exclusions from analysis. These omissions limit assessment of whether the reported summaries represent all randomized participants and whether missingness could affect the comparison.

Interim analyses and the full statistical analysis plan are not reported in the registry record. No assumptions about stopping rules, endpoint selection after looking at results, or adjustments for repeated testing can be made from the available information.

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 0% reporting threshold.

The registry reports zero serious adverse events among 40 participants at risk in the active anodal tDCS group and zero among 40 at risk in the sham tDCS group. It reports zero other adverse events in each group and zero deaths in each group. No serious adverse-event terms are listed.

These figures describe the events recorded for the groups and the risk sets shown in the registry. They do not establish that no unrecorded events occurred, and they do not precisely characterize uncommon or delayed events. The registry does not provide event definitions, severity detail beyond the serious-versus-other categories, or further timing information for adverse events. The crossover structure also means that group labels should be interpreted in light of the treatment sequences rather than assumed to represent separate groups of distinct participants.

The posted safety summary is therefore a record of no reported serious events, other events, or deaths in the listed risk sets. It should not be taken as a comprehensive estimate of safety outside the study's reported observations.

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

The results describe a randomized comparison of active anodal tDCS and sham stimulation in healthy adults. For the primary score-change endpoint, the active-condition mean was 1.6 and the sham-condition mean was 0.73, with a posted mean-difference estimate of 0.87. The interval crosses zero, and the unadjusted p-value is 0.262. The estimate points toward a larger positive change under active stimulation according to the endpoint's scoring direction, but its uncertainty includes no difference and contrasts in either direction.

That combination does not establish that active stimulation caused a meaningful change in paranoid ideation. It also does not establish that the conditions are equivalent. An uncertain estimate can reflect limited precision, and the record does not report a threshold for a clinically or personally important difference on the scale. The posted data should therefore be described in terms of the estimate and its uncertainty, not as a definitive positive or negative conclusion.

The secondary outcomes address trustworthiness and emotion recognition. They provide additional behavioral context, but they are not substitutes for the primary measure. Their unadjusted status and the absence of reported analysis details make them less suitable as confirmatory evidence.

The study enrolled healthy adults and assessed outcomes 30 minutes after stimulation. The record does not establish effects in people with a mental-health condition, effects lasting beyond the reported assessment timing, or effects on outcomes not measured in the trial. It also does not report enough information to evaluate paired-analysis choices, carryover, or missing observations. These limits shape what can be inferred from the posted results.

The most defensible reading is that the registry reports an uncertain average difference on the primary measure, with no clearly resolved contrast between active and sham conditions. The data do not by themselves answer broader questions about clinical benefit, duration, or use in other populations.

17. Why This Trial Matters Statistically

This trial is statistically informative because it combines a crossover design with a continuous, self-reported primary outcome. The design can allow within-person comparisons, but interpreting such comparisons depends on how the analysis accounts for repeated measurements, order, and possible carryover. The registry describes the sequences and timing, while leaving those analysis choices unreported. That distinction illustrates why a design label alone is not a complete account of the statistical method.

The primary result also illustrates why an estimate, confidence interval, and p-value should be read together. The point estimate is positive under the endpoint's definition, but the interval includes zero and the unadjusted p-value is 0.262. Reporting the estimate without its uncertainty would overstate what the data resolve; reporting only the p-value would conceal the direction and scale of the estimate.

The planning illustration adds a separate lesson. Sample-size calculations based on an observed effect can show how planning needs change when the target effect is made smaller, but they do not reveal the original design rationale and are not a measure of the trial's observed power. Keeping those concepts distinct prevents retrospective planning values from being mistaken for evidence about the study's design or outcome.

Finally, the registry's limited reporting of multiplicity, missing-data handling, and analysis populations demonstrates how reporting completeness affects statistical interpretation. The posted summaries remain useful descriptions, but readers need analysis details to assess all assumptions and potential sources of bias. The trial matters as a case in careful reading: design, endpoint definition, uncertainty, and reporting gaps all influence the conclusions that can responsibly be drawn.

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.

The record describes a small enrolled group of 40 healthy adults and a crossover comparison. It does not report demographic characteristics, detailed eligibility criteria, or whether the analyzed participants were representative of any broader population. Generalization beyond the stated participant group is therefore not established.

The primary outcome is self-reported paranoid ideation, and the registry describes assessment 30 minutes after stimulation. The record does not report longer-term follow-up or an important-difference threshold for the scale. The result speaks to the recorded score change at the stated assessment timing, not necessarily to durable change or a participant-level benefit.

Although the registry identifies randomization, double masking, and a crossover structure, it does not report the masking procedures, the statistical model, or whether within-participant correlation and treatment sequence were addressed. It also does not report whether carryover was assessed, how missing observations were handled, or which analysis population was used. These gaps make it difficult to evaluate the assumptions underlying the posted comparison.

The record lists four outcome measures but posts results for two secondary outcomes, and it does not report a multiplicity strategy. Secondary comparisons are unadjusted, which limits their confirmatory value. The registry also does not report the original sample-size justification or interim-analysis plan. Finally, the safety summary records no events in the listed risk sets but does not provide detailed event definitions or follow-up beyond the reported study context. These reporting limits should be kept in view alongside the numerical findings.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Stimulating the Social Brain — NCT03374631.
• Registry record last updated 2023-03-22; status last verified 2023-03.
• Results first posted 2022-08-01.
• 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

Stimulating the Social Brain (NCT03374631) is a completed randomized, double-masked crossover study sponsored by The University of Texas at Dallas. The registry reports enrollment of 40 healthy adults and compares active anodal tDCS with sham tDCS in two treatment sequences, with the second session scheduled one week after the first.

The primary outcome is pre-to-post change in self-reported paranoid ideation, assessed 30 minutes after stimulation. The posted mean-difference estimate for active versus sham is 0.87, with a confidence interval crossing zero and an unadjusted p-value of 0.262. Trustworthiness-task and Penn Emotion Recognition Test results are posted as secondary outcomes.

The record reports no serious adverse events, other adverse events, or deaths in either listed risk set. Details of the statistical model, missing-data handling, analysis population, multiplicity strategy, and original sample-size rationale are not reported in the registry record.