The Effects of Intensity on Exercise-Induced Hypoalgesia During a Knee Extension Exercise: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for The Effects of Intensity on Exercise-Induced Hypoalgesia During a Knee Extension Exercise (NCT05561582), a randomized na study. The primary outcome is Pressure Pain Threshold.

2. Clinical Question

The clinical question is about immediate measurements after a single study session, rather than longer-term outcomes. The session included pain sensitivity testing and pain-related psychological questionnaires, followed by random assignment to an intervention. The registry lists conditioned pain modulation as a secondary outcome. The posted record therefore permits a description of the group-level measurements and comparisons, but it does not establish how those immediate measurements relate to later functioning or health.

3. Trial Design

This was a randomized, parallel-group study with no masking reported. The registry lists 60 participants as enrolled and the study status as completed. The start date was 2022-10-31, and primary completion was 2023-03-27. The registry describes one session for each participant. A participant was assigned to high-intensity knee extension exercise, low-intensity knee extension exercise, or quiet rest.

The exercise groups differed in the load prescribed relative to each participant’s 1-repetition maximum; each exercise intervention involved 3 sets of 10 repetitions. The quiet-rest group sat quietly for two minutes, three times. The registered intervention name is “Seated knee extension exercise,” with intervention type listed as “OTHER.” These details describe the assigned activities, but the registry does not report additional information about adherence, supervision, or the actual exercise loads completed.

There were 20 participants in each group in the posted primary outcome results. The primary outcome was pressure pain threshold, measured in kilopascals, with a timeframe of 1 day. The registry describes pressure testing at the quadriceps and upper trapezius, and gives conditioned pain modulation as a secondary outcome. It does not report the original sample-size justification or the trial’s prespecified analysis methods. The posted record also lists no reported analyses, so the methods used for the sponsor’s analysis cannot be characterized beyond what the registry states.

Random allocation can support fair comparisons by distributing participant characteristics across groups on average, but the record does not give details about sequence generation or allocation concealment. With no masking reported, participants and study personnel were not described as masked. The record does not say whether outcome assessors were masked. These missing details limit assessment of how allocation and measurement procedures were implemented.

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 Pressure Pain Threshold, measured over 1 day.

Pressure pain threshold is the pressure at which a sensation first changes from pressure to pain. The registry describes applying a digital pressure algometer to the quadriceps and upper trapezius for two trials each. Participants were instructed to say “stop” or “pain” when that transition occurred, so the stimulus could be terminated. The measure is reported in kilopascals, with the summary parameter listed as the mean and dispersion as the standard deviation.

This type of measurement is used to quantify sensitivity to a pressure stimulus. Testing the quadriceps examines the exercising muscle, while testing the upper trapezius examines a non-exercising muscle. Considering both locations can help distinguish a local change from a change measured away from the exercising muscle. That is a general rationale for measuring at both sites; it does not establish that any particular pattern occurred in this trial.

The registry also says participants rated pain during threshold testing on a 101-point numeric pain rate scale, anchored from 0 for no pain to 100 for the most intense pain sensation imaginable. The posted primary outcome summary is expressed as pressure pain threshold, not as a separate pain-rating result. The registry record does not clarify which testing location, or whether a combined measure, corresponds to the arm means and comparisons. That makes the precise interpretation of the posted summary less specific than the measurement description.

7. Results Posted in the Registry

• Low Intensity Exercise: mean 48.22 versus 19.11 on control; difference 29.11 (95% CI -58.02 to 116.24), standardized effect d = 0.21; z-test p = 0.513.
• Quiet Rest: mean -4.14 versus 19.11 on control; difference -23.25 (95% CI -74.88 to 28.38), standardized effect d = -0.28; z-test p = 0.377.

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.

Conditioned Pain Modulation

• 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:
  • Low Intensity Exercise: mean -21.41 versus -34.44 on control; difference 13.03 (95% CI -37.94 to 64.00), standardized effect d = 0.16; z-test p = 0.616.
  • Quiet Rest: mean -54.03 versus -34.44 on control; difference -19.59 (95% CI -75.06 to 35.88), standardized effect d = -0.22; z-test p = 0.489.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Low Intensity Exercise and the control. The interval gives the range of effects that remain compatible with the data.
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Quiet Rest and the control. The interval gives the range of effects that remain compatible with the data.

Conditioned pain modulation was the listed secondary outcome. The posted group means are negative in all three groups, with different group averages and substantial variation. The comparisons against high-intensity exercise point in different directions: the low-intensity comparison has a positive mean difference, while the quiet-rest comparison has a negative mean difference. Both intervals include zero, and both p values are unadjusted. Overall, these secondary data do not show a consistent separation of the comparison groups from high-intensity exercise.

The secondary outcome concerns a related aspect of pain measurement, but it is not interchangeable with the primary pressure pain threshold endpoint. The registry does not provide a detailed account of how conditioned pain modulation was measured or how it was analyzed. The secondary results therefore add context about the posted pain-related measures, but they do not resolve the uncertainty in the primary comparisons or the uncertainty about which body site is represented by the primary summaries.

Unadjusted secondary results carry less weight when several outcomes or comparisons may be examined. In general, making multiple statistical comparisons increases the chance that at least one appears unusual by chance, unless the analysis plan accounts for multiplicity. The registry lists one secondary outcome and no reported analyses, but does not report the full prespecified testing plan or any multiplicity adjustment. The secondary p values should be treated as exploratory evidence rather than as standalone confirmation.

The record does not report a hierarchy of endpoints, a confirmatory role for the secondary outcome, or a plan for interpreting a pattern across outcomes. Accordingly, the overall secondary pattern is best described as variable and uncertain. It does not provide a clear independent basis for a broader conclusion about exercise intensity, nor should it be used to overrule the imprecision of the primary comparisons.

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

• Conditioned Pain Modulation

9. Statistical Interpretation

10. Statistical Methods Explained

The registry identifies pressure pain threshold as a continuous outcome summarized by a mean and standard deviation. A mean is a group’s average measurement. A standard deviation describes how much individual measurements tend to vary around that average. In general, a larger standard deviation indicates greater spread among the measurements, not greater uncertainty about the mean by itself. Uncertainty in a group comparison also depends on the number of participants and the variability in both groups.

What does a mean difference describe?

A mean difference compares the average in one group with the average in another. The posted primary comparison uses high-intensity exercise as the reference and reports a mean difference for low-intensity exercise and for quiet rest. The sign indicates the direction of the reported contrast according to the registry’s ordering. The registry does not report a direct low-intensity exercise versus quiet-rest comparison, so that comparison cannot be inferred from the posted comparisons without doing a new calculation.

What does a confidence interval contribute?

A confidence interval gives a range of values that are compatible with the observed data under the statistical procedure used. As a general explanation, it conveys the precision of an estimate: a wider interval indicates less precision than a narrower interval. If an interval includes zero for a mean difference, the data do not rule out a zero difference under that procedure. An interval is not a guarantee that the true value lies within its endpoints, and it does not describe the range of individual participant outcomes.

How should a p value be read?

A p value describes how unusual data at least as incompatible with a specified null hypothesis would be if that hypothesis and the analysis assumptions were true. It is not the probability that the null hypothesis is true, nor does it measure the size or clinical importance of a difference. The primary comparison p values are explicitly unadjusted. The registry does not report which test or model generated them, so no more specific account of their calculation is available.

Why can variation matter?

In general, high variability can make a group mean difference difficult to estimate precisely, particularly when the groups are not large. The posted outcome standard deviations and comparison intervals indicate that the estimates are uncertain. This does not mean the measurements are invalid; it means the group averages should not be read as precise predictions for individual participants. A parallel-group design compares separate assigned groups rather than repeated measurements from the same participants across interventions.

What is not specified about the analysis?

The registry record lists zero reported analyses. It does not identify a statistical model, covariate adjustment, handling of repeated measurements, or a testing strategy across outcome locations. The measurement description names both the quadriceps and upper trapezius, but the posted primary summary does not state whether results are separate by location or aggregated. Those details are important for determining exactly what estimand the reported mean differences address. It would be inappropriate to infer an analysis method from the summary statistics alone.

Random assignment is a design feature, not a statistical result. In general, randomization aims to make groups comparable in expectation, while the achieved balance in any particular trial can still vary. The registry does not report baseline characteristics or details of the randomization procedure. It also does not describe missing-data handling or define the population included in the analyses. These omissions prevent a full appraisal of the analysis population and the assumptions underlying the posted estimates.

Finally, the planning illustrations are based on the observed effects and specified assumptions, not the original trial’s design justification. The trial’s own design assumptions are not reported in the registry record. General power calculations concern the chance of detecting a specified effect under assumptions; they do not change the uncertainty in the observed comparisons and cannot be treated as evidence that the trial did or did not have adequate power.

11. Confidence Intervals and Precision

The primary comparison intervals are broad. For low-intensity exercise relative to high-intensity exercise, the interval ranges from -58.02 to 116.2 kilopascals. For quiet rest relative to high-intensity exercise, it ranges from -74.88 to 28.38 kilopascals. Both intervals include zero, so neither excludes a no-difference value under the interval procedure. Their endpoints also allow effects in both directions. The estimates therefore do not pinpoint the magnitude or direction of a difference with much precision.

Confidence intervals should be interpreted as uncertainty about a group-level contrast, not as a range expected to contain most participant measurements. The standard deviations describe the observed spread of measurements within the groups, while the intervals describe uncertainty in the estimated comparisons. These answer different questions. The registry does not provide confidence limits for the individual arm means.

Precision is also constrained by what the record leaves unclear. The primary outcome description includes testing at two body sites, but the posted primary arm summaries do not identify the site or explain whether the results combine measurements. A statistically precise estimate would still need a clear definition of the outcome to be interpreted properly. In this case, the available intervals and the outcome-location ambiguity both matter.

The intervals are consistent with uncertainty, not proof that the groups are equivalent. Establishing equivalence would require a prespecified margin and an analysis designed for that purpose; neither is reported in the registry record. Nor does an interval alone determine whether a difference would matter clinically. The registry does not report a threshold for clinical importance. The posted estimates should therefore be read as uncertain comparisons rather than definitive evidence of sameness or separation.

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 estimates are participants per arm, not total event counts. They apply to continuous outcomes and use a normal approximation. The stated assumptions are a two-sided significance level of 0.05 and equal allocation between the two arms being compared. The effect used for planning is a stated fraction of the observed effect. The registry’s original design assumptions and sample-size justification are not reported in the registry record.

The 80% power column gives the estimated number of participants per arm under which the planning procedure would have an 80% chance of detecting the effect specified for that row, assuming the calculation’s conditions hold. The 90% power column gives the corresponding estimate for a 90% chance. These are planning probabilities for a hypothetical study under stated assumptions, not probabilities that the observed result is correct.

Each comparison has its own set of estimates because the observed effects and variability differ. Rows planning for 75% or 50% of the observed effect ask what enrollment might be needed to detect a smaller effect. Smaller effects are harder to distinguish from random variation, so they require more participants under the same assumptions. The figures are illustrations based on observed effects, not the trial’s own original enrollment target or justification. They are not observed power.

A sample-size curve, when read alongside these estimates, is a way to visualize how the estimated enrollment changes as the effect to be detected changes. It should be interpreted as a planning aid rather than a description of the study’s observed evidence. The actual trial enrolled 20 participants in each group; the planning illustrations do not alter that fact or strengthen the precision of the posted comparisons.

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 = 29.110; pooled standard deviation σ = 140.582.
2. n = 2 × (1.96 + 0.842)² × 140.582² / 29.110² = 366.1, rounded up to 367 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 <- 29.11                      # observed difference in means
sigma <- 140.58185729318                     # 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(5561582)
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 = 367 (80% power), 491 (90% power)
 75% of observed effect: n per arm = 651 (80% power), 872 (90% power)
 50% of observed effect: n per arm = 1,465 (80% power), 1,961 (90% power)
power.t.test: 367.1 
Simulated power at n = 367 per arm: 0.795 (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 record does not report the sponsor’s statistical analysis plan, a hierarchy among outcomes, or a multiplicity procedure. The primary outcome description covers pressure pain threshold at the quadriceps and upper trapezius, while the record also lists conditioned pain modulation as a secondary outcome. Multiple sites, outcomes, or group comparisons can create multiple opportunities to observe an apparently notable result. As a general statistical issue, prespecifying which comparisons are confirmatory and how multiplicity will be handled helps distinguish primary evidence from exploratory findings.

The posted primary and secondary p values are unadjusted. No adjustment should be assumed, and the record does not establish whether additional analyses were conducted outside the posted results. The registry lists no reported analyses. It is therefore not possible to determine which statistical tests were planned, whether the reported comparisons were prespecified, or whether other comparisons were made.

Missing-data procedures are not reported in the registry record. The record does not state whether any outcome values were missing, how missing observations were handled, or whether the posted group summaries include all randomized participants. Although the enrollment and arm summaries list 20 participants per group, that does not by itself establish the analysis population or the completeness of every measurement.

The registry also does not define an intention-to-treat or per-protocol population, describe exclusions after randomization, or report sensitivity analyses. These are relevant because analysis populations and missing-data assumptions can affect how a randomized comparison is interpreted. No specific concern about missingness or exclusions can be inferred from their absence in the record; the appropriate conclusion is that the details are not reported in the registry record.

Finally, the primary outcome summaries do not clarify how measurements from the quadriceps and upper trapezius were represented. This is an outcome-definition issue as well as an analysis-reporting limitation: separate site-specific comparisons and a combined summary would answer different questions. The record does not explain which approach generated the posted primary results.

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

The posted results describe group averages and unadjusted comparisons for pressure pain threshold and conditioned pain modulation after a single session. They show that the group means were not identical, but the primary comparison intervals include zero and cover values in both directions. The estimates are therefore too uncertain to establish a clear difference between high-intensity exercise and either low-intensity exercise or quiet rest.

That interpretation is not the same as concluding that the groups are equivalent. A failure to establish a difference does not demonstrate that any possible difference is negligible. The registry does not report an equivalence margin or a noninferiority framework. It also does not provide a threshold for deciding whether a particular measurement difference would be clinically important.

The results do not establish that exercise changes pain sensitivity, that one intensity is preferable, or that any effect persists beyond the study session. Such claims would go beyond the posted outcomes and time frame. The study was designed to compare immediate measurements, and the registry does not report later follow-up results. The data also should not be interpreted as advice about exercise or pain management.

Interpretation is further limited because the primary results do not identify whether they refer to quadriceps measurements, upper trapezius measurements, or a combined measure. The registry’s measurement description makes the two sites relevant to the intended question, but the posted summary does not make the site-specific meaning clear. This prevents a more detailed explanation of whether the reported contrast is local or measured away from the exercising muscle.

The sample-size illustrations are planning calculations based on observed effects, not evidence about the probability that the trial’s findings are true. The adverse-event record lists zero participants at risk in the reported categories for each group. Because the record gives no participants at risk, those entries cannot establish that no adverse events occurred among enrolled participants. In sum, the registry supports a cautious description of uncertain, immediate group comparisons, not a broad conclusion about effectiveness, safety, or clinical benefit.

16. Why This Trial Matters Statistically

This trial raises a useful statistical distinction between a numerical difference and a precise estimate of a difference. Group means can differ while the uncertainty around their comparison remains broad. The posted primary intervals illustrate why reading only the point estimates would give an incomplete account: the intervals include zero and permit effects in either direction.

The study also makes outcome definition important. Pressure pain threshold was described at an exercising muscle and a non-exercising muscle, but the primary result summaries do not say which location they represent. A clearly defined estimand—what population, measurement, and comparison a result is intended to describe—is necessary for readers to connect a statistical estimate to the scientific question. Without that detail, even a correctly reported mean difference can be difficult to interpret.

A randomized parallel-group design provides a framework for comparing assigned interventions, but the strength of the inference also depends on implementation and reporting. Details about the randomization procedure, analysis population, missing data, and statistical plan are not reported in the registry record. Their absence does not prove a flaw in the study; it limits what can be assessed from the public record.

Finally, planning from an observed effect can help illustrate the enrollment that a future study might require under explicit assumptions. Such estimates are sensitive to the effect chosen and the variability in the data. They are planning tools, not retrospective evidence that a completed trial had adequate power. This distinction is important when interpreting small or uncertain studies and when deciding what additional evidence would be needed to answer a focused question.

17. 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 leaves several trial-specific limitations unresolved. It describes measurements at the quadriceps and upper trapezius, but the posted primary arm means do not identify the measurement site or explain whether the locations were combined. This limits the connection between the intended local and non-local questions and the reported comparisons.

The record describes one session and an immediate outcome timeframe, so the posted results address only that setting. It does not report longer-term outcomes. The participant population is labeled healthy, but additional eligibility details and participant characteristics are not reported in the registry record. Generalizability beyond the enrolled population therefore cannot be assessed from these details.

The registry does not report the original sample-size justification, analysis plan, randomization procedure, allocation concealment, assessor masking, missing-data approach, or analysis population. It lists no reported analyses. These omissions mean that the statistical methods and the handling of participants and measurements cannot be fully evaluated. No specific implementation problem can be inferred solely from the lack of reporting.

The comparison results are imprecise, and the p values are unadjusted. The record does not state whether additional comparisons were planned or whether multiplicity was addressed. It also does not give a clinically important threshold for the primary measure. These limitations restrict both inferential and clinical interpretation.

The adverse-event summaries list zero participants at risk in the reported categories for all groups. That information does not establish the number of enrolled participants assessed for adverse events or support a conclusion that no events occurred. The record’s reporting does not permit a complete assessment of safety outcomes.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: The Effects of Intensity on Exercise-Induced Hypoalgesia During a Knee Extension Exercise — NCT05561582.
• Registry record last updated 2024-12-09; status last verified 2024-10.
• Results first posted 2024-12-09.
• 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.

21. Record Summary

The registry record describes a completed randomized, unmasked, parallel-group study with 60 participants. Participants were assigned to high-intensity knee extension exercise, low-intensity knee extension exercise, or quiet rest, with 20 participants in each group in the posted primary results. The study focused on immediate pressure pain threshold measurements and listed conditioned pain modulation as a secondary outcome.

The primary comparisons against high-intensity exercise are imprecise: both confidence intervals include zero, and the p values are unadjusted. The record does not specify which testing location the primary summaries represent, and it does not report the original design assumptions or statistical analysis plan. The findings are best read as uncertain group-level results for the registered session, not as evidence of equivalence or a basis for broad clinical claims.