Double Blinded, Placebo-Controlled Trial of Paliperidone Addition in SRI-Resistant Obsessive-Compulsive Disorder: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Double Blinded, Placebo-Controlled Trial of Paliperidone Addition in SRI-Resistant Obsessive-Compulsive Disorder (NCT00632229), a randomized phase 2 study. The primary outcome is Yale Brown Obsessive Compulsive Scale.

2. Clinical Question

The clinical question is about adding one medication to existing treatment, not about paliperidone used alone or compared with every other possible treatment. The trial record identifies the population as having SRI-resistant obsessive-compulsive disorder, but does not report the specific definition of resistance or the details of prior treatment. The results therefore address the recorded trial comparison and outcome, not all people with obsessive-compulsive disorder or every treatment setting. The registry record also includes a secondary symptom-severity measure, Clinical Global Impressions - Severity of Obsessive-Compulsive Symptoms. The interpretation of either measure depends on its numerical estimates, uncertainty, and the analysis method used.

3. Trial Design

The record describes a completed phase 2, randomized, quadruple-masked, parallel-group trial sponsored by the University of South Florida. The trial began in 2007-10 and had primary completion in 2013-09. Registry enrollment was 34. The posted outcome summaries list 17 participants in the paliperidone group and 17 in the placebo group for the primary measure. These are the reported group counts; the registry information does not explain how missing outcome observations, if any, were handled.

The parallel design means the record compares groups assigned to different study regimens rather than describing a sequence in which each participant received both regimens. Randomization is reported, but details of the randomization procedure, allocation concealment, and any stratification are not reported in the registry record. Quadruple masking is the registry’s stated masking category. The record does not specify which roles were masked or how masking was maintained.

The intervention was paliperidone and the comparator was pill placebo. The study question concerned adding the assigned study treatment to an existing medication regimen. The registry summary does not report the specific background medications, dosing schedule, adherence procedures, or treatment duration details beyond identifying the primary endpoint timeframe as the end of study (8 weeks).

The primary measure was the Yale Brown Obsessive Compulsive Scale. The posted analysis lists an ANCOVA and a p-value, but does not give the model’s adjusted effect estimate, confidence interval, covariates, or analysis population. An unadjusted recalculation can be made from the group means and standard deviations, but it is not the same analysis as the registry’s ANCOVA. The original design assumptions, sample-size justification, interim analyses, and full statistical analysis plan are not reported in the registry record.

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:

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 Yale Brown Obsessive Compulsive Scale, measured over End of study (8 weeks).

The primary endpoint is the Yale Brown Obsessive Compulsive Scale score at the end of study (8 weeks). The registry describes it as an interview-based measure covering 10 items. The item scores are summed to form a total score on a scale from 0 to 40, where higher scores correspond to more severe obsessive-compulsive symptoms.

A continuous total score retains information about differences across the scale rather than reducing each participant’s result to a binary category. Comparing group means can therefore describe the average score difference between the randomized groups. The standard deviation reported alongside each mean describes how spread out the observed scores were within that group; it does not describe uncertainty in the mean difference by itself.

In general, a symptom-severity scale is useful for quantifying the degree of symptoms at a specified assessment time. Interpretation depends on the scale’s direction, the comparison between groups, and the uncertainty around that comparison. In this trial, lower scores indicate less severe symptoms, but a numerical difference alone does not establish that the difference is reliable or clinically important. The registry record does not provide a threshold for a clinically meaningful difference or a change-from-baseline result. It also does not report the adjusted ANCOVA estimate or its confidence interval, so the posted unadjusted summary cannot answer every question about the planned or sponsor analysis.

7. Results Posted in the Registry

• Paliperidone: mean 19.14 versus 21.24 on control; difference -2.10 (95% CI -8.66 to 4.46), standardized effect d = -0.22; z-test p = 0.530.

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.

Clinical Global Impressions - Severity of Obsessive-Compulsive Symptoms

• 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:
  • Paliperidone: mean 4.09 versus 4.21 on control; difference -0.12 (95% CI -1.12 to 0.88), standardized effect d = -0.08; z-test p = 0.814.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Paliperidone and the control. The interval gives the range of effects that remain compatible with the data.

The registry posts one secondary outcome: Clinical Global Impressions - Severity of Obsessive-Compulsive Symptoms. Its unadjusted group summaries do not show a clear separation, and the recalculated interval includes zero. The registry nevertheless lists an ANCOVA p-value below 0.05 for this outcome, without an adjusted estimate or confidence interval. As with the primary measure, the registry’s own analysis takes precedence over the unadjusted recalculation, while the missing effect and interval details limit assessment of magnitude and precision.

The overall pattern therefore includes disagreement between the unadjusted recalculations and the reported ANCOVA results for the posted outcomes. That makes it important not to interpret a secondary p-value in isolation. A secondary measure may provide additional context about the outcome pattern, but it does not independently resolve the discrepancy in the primary analysis or establish how large an effect is.

In general, testing multiple outcomes increases the chance that at least one result may cross a significance threshold even when there is no corresponding underlying effect. Statistical methods can control or account for that multiplicity, but the registry record does not report whether an adjustment was planned or used. The secondary finding should therefore carry less weight than a clear, fully reported primary analysis. The record does not provide enough information to assess a hierarchy of tests, pre-specification of the secondary outcome, or the multiplicity strategy. These omissions do not negate the posted result, but they limit how confidently it can be interpreted alongside the primary result.

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

• Clinical Global Impressions - Severity of Obsessive-Compulsive Symptoms

9. Statistical Interpretation

10. Statistical Methods Explained

There are two different kinds of results to distinguish: the analysis reported by the registry and a simple unadjusted calculation based on the posted group summaries. Both can be informative, but they answer the comparison using different methods. The registry lists ANCOVA for the outcome analyses. The recalculated mean difference uses the reported group means and standard deviations without adjustment. Since the registry flags a discrepancy, the sponsor’s own analysis takes precedence as the trial’s reported analysis.

What does the unadjusted mean difference describe?

For a continuous outcome, the unadjusted mean difference is the mean in one group minus the mean in the other. Here it is expressed as paliperidone minus placebo. A negative estimate means the observed average score was lower in the paliperidone group. For the primary scale, lower scores correspond to less severe obsessive-compulsive symptoms. This sign describes the direction of the observed difference; it does not, on its own, establish that the difference is reliable, clinically important, or caused by the intervention.

The group means are summaries of the observed scores. The standard deviations describe variability among scores within each group. They are not confidence intervals for the group means, and they should not be read as the range containing most or all participants. The standard error of an estimate concerns the precision of an estimated quantity, while a standard deviation concerns spread in the observations. In general, a mean difference is more uncertain when the outcome is variable and the amount of information is limited.

What does a confidence interval add?

In general, a confidence interval gives a range of values compatible with the observed data under the assumptions of the analysis. It communicates both the direction and the precision of an estimate. An interval that includes zero does not show a clear difference at the corresponding conventional two-sided significance level. It does not prove that the groups are identical, nor does it rule out effects in either direction. The primary unadjusted interval extends from -8.66 to 4.46, so it includes zero and also spans values on both sides of zero. The registry does not report a confidence interval for its ANCOVA estimate, which prevents the same assessment of the sponsor analysis’s precision.

What is ANCOVA?

In general, analysis of covariance estimates a group difference while accounting for one or more covariates included in the model. Depending on the covariates and model specification, an adjusted estimate can differ from a raw comparison of group means. The registry identifies ANCOVA, but the covariates, adjustment details, model assumptions, missing-data approach, and analysis population are not reported in the registry record. It is therefore not possible to determine from the record why the ANCOVA p-value differs from the unadjusted recalculation. The posted result gives p < 0.05, but the effect estimate and confidence interval are absent.

How should the p-values be read?

In general, a p-value describes how unusual data at least as incompatible with a specified null model would be, if the null model and the analysis assumptions were correct. It is not the probability that the null hypothesis is true, and it does not measure the probability that the result occurred by chance in a simple everyday sense. Nor does a p-value report the size or clinical importance of an effect. The unadjusted primary p-value is 0.53; the registry’s ANCOVA result is reported as p < 0.05. These values come from different analyses and should remain clearly attributed to their respective methods.

For the secondary outcome, the same distinction applies. A simple unadjusted calculation from group summaries is not equivalent to the listed ANCOVA. The registry reports p < 0.05 for that ANCOVA but does not give its adjusted effect estimate or confidence interval. Because there is no reported adjustment for testing multiple outcomes, the p-values should not be treated as if each were the only analysis conducted.

Why can over-dispersion matter?

In general, over-dispersion refers to observed variability that is greater than a model assumes. When a model understates variability, standard errors can be too small and inferential results can appear more precise than warranted. The posted outcomes are continuous measures summarized by means and standard deviations; the registry does not report an over-dispersion assessment or a model diagnostic finding. This general issue should not be taken as evidence that over-dispersion occurred in this trial.

All recalculated comparisons are unadjusted and based on summary statistics rather than individual participant data. They cannot reproduce a covariate-adjusted analysis or assess assumptions that require participant-level information. The record does not report an analysis plan detailed enough to resolve the difference between the recalculation and the sponsor’s ANCOVA.

11. Confidence Intervals and Precision

The primary unadjusted mean difference is -2.1, with a 95% confidence interval from -8.66 to 4.46. The point estimate is on the lower-score side for paliperidone minus placebo, but the interval includes zero and extends to values in the opposite direction. This means the posted unadjusted result is not precise enough to establish the direction of the underlying difference. The range also permits differences of varying magnitude, so the estimate should not be described as a precise measure of benefit or lack of benefit.

In general, a confidence interval is more informative than a point estimate alone because it displays uncertainty around the estimated contrast. It is not a guarantee that the true effect lies in the interval, and its interpretation depends on the analysis assumptions. Here the interval is for an unadjusted calculation based on group summaries. The registry does not report the confidence interval for the ANCOVA result, even though it reports an ANCOVA p-value. Therefore the precision of the sponsor’s adjusted estimate cannot be evaluated from the registry entry.

The secondary outcome also has an unadjusted interval that includes zero. The registry does not report an adjusted interval for its ANCOVA result. The absence of those adjusted estimates and intervals is especially important because the unadjusted and registry-reported p-values differ. A p-value alone cannot show whether the adjusted effect is large or small, or how wide its uncertainty is. The record also provides no threshold for a clinically meaningful score difference, so statistical precision cannot be translated into a judgment about clinical importance.

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 participants or total events. They are illustrations based on the observed effect, not the original trial’s sample-size plan. The stated assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, a normal approximation, and an effect to detect set to the stated fraction of the observed effect. The trial’s original design assumptions and sample-size justification are not reported in the registry record.

The 80% power column describes the number of participants per arm in a hypothetical study that would have an 80% chance of detecting the chosen effect under the stated assumptions, if that effect and the assumptions were correct. The 90% power column gives the corresponding planning target for a higher chance of detection. These are design targets for a future study, not estimates of what happened in this trial. This is not observed power.

For the primary measure, planning for 100% of the observed effect gives 339 participants per arm for 80% power and 454 participants per arm for 90% power. Planning for 75% of the observed effect gives 603 participants per arm for 80% power and 807 participants per arm for 90% power. Planning for 50% of the observed effect gives 1,356 participants per arm for 80% power and 1,816 participants per arm for 90% power.

The pattern reflects a general planning principle: smaller effects are harder to distinguish from random variation and therefore require more participants to detect at the same power target. Because these illustrations use an observed effect from a small trial and the registry’s ANCOVA result differs from the unadjusted calculation, they should not be mistaken for a definitive sample-size recommendation.

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 = -2.100; pooled standard deviation σ = 9.759.
2. n = 2 × (1.96 + 0.842)² × 9.759² / -2.100² = 339.0, rounded up to 339 participants per arm for 80% power.

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

R code

alpha <- 0.05
z_a   <- qnorm(1 - alpha / 2)          # two-sided
delta <- -2.1                      # observed difference in means
sigma <- 9.7586500090945                     # 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(632229)
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 = 339 (80% power), 454 (90% power)
 75% of observed effect: n per arm = 603 (80% power), 807 (90% power)
 50% of observed effect: n per arm = 1,356 (80% power), 1,816 (90% power)
power.t.test: 339.9 
Simulated power at n = 339 per arm: 0.799 (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 registry lists ANCOVA as the sponsor-reported method for the primary outcome and gives p < 0.05. It does not give the adjusted mean difference, confidence interval, covariates, or other model details. The recalculated unadjusted mean difference is -2.1, with a 95% confidence interval from -8.66 to 4.46 and p = 0.53. The registry flags a discrepancy between the recalculation and the reported analysis.

These results should not be combined or treated as if they were estimates from the same model. ANCOVA can adjust for covariates, whereas the recalculation uses only the posted arm means and standard deviations. In general, adjustment can change an estimate and its uncertainty, but the registry does not provide enough detail to establish which features explain the difference in this trial.

The sponsor’s own analysis takes precedence as the trial’s reported inferential result. That precedence does not remove the need for transparency: without its adjusted estimate and interval, readers cannot assess the magnitude or precision of the sponsor’s finding. The unadjusted calculation remains a descriptive check on the posted summaries, not a replacement for the reported ANCOVA or an explanation of why the results differ.

15. Multiplicity, Missing Data and Analysis Populations

The registry identifies the Yale Brown Obsessive Compulsive Scale as the primary outcome and Clinical Global Impressions - Severity of Obsessive-Compulsive Symptoms as a secondary outcome. It reports two outcome measures and two analyses. Both analysis listings identify ANCOVA, and each gives a p-value below 0.05 without an adjusted effect estimate or confidence interval. The record does not report whether the analyses were prespecified in a detailed statistical analysis plan or whether any multiplicity correction was applied.

In general, multiplicity arises when several hypotheses are tested. If each test is interpreted at the same threshold without adjustment, the chance of at least one false-positive finding can increase. Adjustment methods or a prespecified testing hierarchy can address this issue, but no such approach is described in the registry record. This matters particularly when considering a secondary outcome: its p-value should not be interpreted as though it were the sole planned test.

Important analysis-population details are also not reported in the registry record. The posted summaries list 17 participants per group for the outcomes, but the record does not say whether these are all randomized participants, participants with observed endpoint data, or another analysis population. It does not report how missing values were handled, whether participants were analyzed according to randomized assignment, or whether sensitivity analyses were performed. No inference about attrition or missingness can be made from the information recorded.

The registry also does not provide the ANCOVA covariates, model specification, baseline adjustment details, or analysis assumptions. Without these items, readers cannot reproduce the sponsor analysis or judge whether its assumptions were met. The discrepancy between the ANCOVA p-values and the unadjusted recalculations reinforces the importance of reporting estimates, intervals, and analysis details—not only thresholded p-values.

16. 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 5% reporting threshold.

Most frequent non-serious adverse event terms

The serious adverse event summaries report 17 participants at risk in each group and zero participants affected by serious adverse events in both the paliperidone and placebo groups. No serious adverse event terms are listed. The registry’s death values are not populated, so death counts are not reported in the registry record; a blank value should not be interpreted as a reported count of zero.

The record also reports other adverse events affecting 15 participants in the paliperidone group and 12 in the placebo group, with 17 at risk in each group. These figures are distinct from the serious adverse event counts. The registry does not list the individual other adverse event terms or provide further detail about severity, duration, relatedness, or event-level counts.

These are descriptive safety entries for the recorded trial period. They do not establish that the groups had equivalent safety profiles, and the absence of reported serious events does not rule out uncommon or longer-term events. The registry information does not provide enough detail for broader safety conclusions.

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

The posted primary group means are lower in the paliperidone arm than in the placebo arm on a scale where higher scores indicate more severe obsessive-compulsive symptoms. The unadjusted estimate is uncertain: its confidence interval includes zero and extends in both directions. The registry’s ANCOVA result is reported as p < 0.05, but the record does not provide its adjusted effect estimate or confidence interval. Because the registry flags a discrepancy, the reported sponsor analysis takes precedence, while the missing details limit interpretation of its size and precision.

Statistical significance is not the same as clinical importance. The registry does not report a threshold for a clinically meaningful difference, nor does it provide an adjusted estimate that could be compared with such a threshold. The p-value alone cannot tell whether an effect is large enough to matter to patients, nor can the unadjusted estimate answer that question with certainty.

The results concern the recorded comparison of paliperidone added to existing medication versus placebo added to existing medication in people described as having SRI-resistant obsessive-compulsive disorder. They do not answer whether paliperidone is effective as a standalone treatment, how it compares with other approaches, or whether a result would apply to people outside the trial population. The primary endpoint is at 8 weeks, so these results do not establish longer-term effects.

The registry record does not report full eligibility criteria, background medication details, missing-data handling, analysis populations, or the adjusted ANCOVA estimates. These gaps constrain assessment of generalizability and reproducibility. The posted data are best read as a record of observed scores and reported analyses, not as a definitive conclusion about treatment effectiveness.

18. Why This Trial Matters Statistically

This trial illustrates why a p-value should be interpreted alongside an effect estimate, its uncertainty, and the method used to obtain it. The registry lists an ANCOVA p-value below 0.05, while the unadjusted calculation from the posted primary group summaries gives a p-value of 0.53 and a confidence interval that includes zero. The discrepancy is not a minor wording issue: readers need to know which analysis generated each result and what the estimated difference was.

It also shows why reporting only a thresholded p-value is incomplete. Without the adjusted ANCOVA estimate and confidence interval, the magnitude and precision of the sponsor analysis cannot be evaluated. Without model details, an independent analyst cannot reproduce that result. The unadjusted recalculation provides a transparent comparison based on the arm summaries, but it cannot substitute for an adjusted analysis that is not fully reported.

The trial’s 17 participants per group in the posted primary summaries also make precision an important consideration. The unadjusted interval spans both directions, illustrating that a point estimate should not be read in isolation. Planning illustrations based on an observed effect can help show how assumptions about target effect size influence future sample-size needs, but those illustrations are not a substitute for the trial’s original design rationale, which is not reported.

Finally, the secondary outcome and safety summaries show why outcome context matters. Multiple outcomes raise questions about multiplicity, while sparse safety information and unreported analysis details limit interpretation. The statistical value of this record lies not in a simple yes-or-no verdict, but in separating the reported analysis from the recalculation and identifying what remains uncertain.

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 leaves substantial methodological detail unreported. It does not give the eligibility criteria beyond the broad description of SRI-resistant obsessive-compulsive disorder, the specific background medications, or the intervention dosing details. The masking category is recorded as quadruple, but the roles masked and procedures used to preserve masking are not described.

For the primary and secondary outcomes, the registry lists ANCOVA but does not report the covariates, model specification, adjusted effect estimates, confidence intervals, analysis populations, or missing-data methods. These omissions are material because the reported ANCOVA p-values differ from the unadjusted calculations based on group summaries. The registry record does not explain the discrepancy, and the recalculations cannot reproduce the sponsor’s adjusted model.

The primary endpoint is recorded at 8 weeks. The record does not provide longer-term outcome results or a threshold for a clinically meaningful score difference. It also does not report a detailed multiplicity strategy, a sample-size justification, interim analyses, or the original design assumptions. The planning illustrations are based on observed effects and should not be mistaken for the trial’s design plan.

The safety summaries provide counts of participants affected, but do not list serious adverse event terms and do not provide details about other adverse event types, severity, or relatedness. Death values are not reported in the registry record. These limitations restrict conclusions about both the outcomes and safety beyond the specific summaries recorded.

20. Related Tutorials

21. Related Statistical Calculators

22. Sources

• ClinicalTrials.gov: Double Blinded, Placebo-Controlled Trial of Paliperidone Addition in SRI-Resistant Obsessive-Compulsive Disorder — NCT00632229.
• Registry record last updated 2014-02-06; status last verified 2013-10.
• Results first posted 2014-02-06.
• 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

This completed, randomized, quadruple-masked, parallel-group phase 2 trial compared paliperidone added to existing medication with pill placebo for SRI-resistant obsessive-compulsive disorder. Registry enrollment was 34. The primary outcome was the Yale Brown Obsessive Compulsive Scale at the end of study (8 weeks), with higher scores indicating more severe symptoms.

The posted group summaries show mean scores of 19.14 for paliperidone and 21.24 for placebo. The unadjusted mean difference is -2.1, with a 95% confidence interval from -8.66 to 4.46 and p = 0.53. The registry reports an ANCOVA p-value of p < 0.05, but does not provide its adjusted estimate or interval. The discrepancy means these results should be kept distinct; the sponsor’s own analysis takes precedence as the trial’s reported inferential result.

The record also includes one secondary symptom-severity measure and brief adverse-event counts. Missing methodological details, including the ANCOVA specification, multiplicity approach, analysis population, and missing-data handling, constrain interpretation of the results.