Feasibility and Acceptability of a Beverage Intervention for Hispanic Adults: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Feasibility and Acceptability of a Beverage Intervention for Hispanic Adults (NCT02911753), a randomized na study. The primary outcome is Treatment Satisfaction.

2. Clinical Question

3. Trial Design

The registry describes a randomized, single-masked, parallel-group study. Participants were assigned to Mediterranean Lemonade, Green Tea, or Flavored Water. In a parallel design, each participant is assigned to a group and outcomes are assessed within that assignment; the record does not describe a crossover between beverages. The registry identifies the study as completed and records enrollment of 50. The study start is listed as 2016-06, with primary completion in 2017-08.

The three group descriptions specify daily consumption of 32 ounces of the assigned beverage over six weeks. Beverages were to be prepared and packaged by study personnel, with weekly supplies. The record does not report adherence summaries, the method used to randomize participants, or which people were masked. “Single” is the recorded masking designation; the identity of the masked party is not reported in the registry record.

The study aim included assessing feasibility and acceptability and examining preliminary effects on cholesterol, triglycerides, blood pressure, glucose, and inflammation markers. The posted primary outcome is treatment satisfaction at week 6, reported as a mean and standard deviation. Four secondary outcomes are listed: changes in total cholesterol, fasting glucose, hemoglobin A1C, and body weight between baseline and week 6. Numerical results for those secondary outcomes are not reported in the registry record.

The registry does not report the original statistical analysis plan, the method used to determine the enrollment target, or the intended handling of missing measurements. The trial’s own design assumptions, including any planned power calculation, are not reported in the registry record. Accordingly, the design can be described from its recorded allocation, masking, groups, and outcome definitions, but not reconstructed beyond those details.

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 Treatment Satisfaction, measured over Week 6.

The primary endpoint is treatment satisfaction at week 6. Participants were asked to rate overall satisfaction with the intervention for changing dietary patterns on a scale from 1, meaning low, to 4, meaning high. The posted group summaries report the mean rating and its standard deviation for each beverage group. The registry description also mentions whether participants would recommend the program to others, but does not report a result for that question.

Satisfaction is relevant to a feasibility and acceptability study because it captures participants’ reported response to the intervention, rather than a biological marker. Such ratings can help describe whether an assigned approach was viewed favorably by participants. As a general statistical point, a mean summarizes the average response, while a standard deviation describes how much individual ratings vary around that average. Neither statistic alone shows how many participants would recommend the program, how consistently the regimen was followed, or whether a change in a health measure occurred.

The endpoint should be read within its stated scale and time point. These results concern ratings at week 6, not satisfaction over a longer period. The registry record does not report a prespecified threshold for a meaningful satisfaction score, a separate analysis of the recommendation question, or a numerical acceptability criterion. The reported means therefore describe the observed ratings; they do not by themselves establish whether the intervention met a formal feasibility target.

7. Results Posted in the Registry

• Treatment Satisfaction Mediterranean Lemonade: mean 3.40 versus 3.30 on control; difference 0.10 (95% CI -0.68 to 0.88), standardized effect d = 0.10; z-test p = 0.802.
• Treatment Satisfaction Green Tea: mean 3.30 versus 3.30 on control; difference 0.00 (95% CI -0.82 to 0.82), standardized effect d = 0.00; z-test p = 1.000.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary endpoint is a continuous rating summarized by a mean and standard deviation. The rating scale runs from 1 (low) to 4 (high), and the recorded assessment time is week 6. A mean gives a compact description of the average rating in a group. The standard deviation describes the spread of individual ratings around that group mean. General statistical guidance: a mean is useful for summarizing a group, but it does not show the full distribution or reveal whether ratings cluster at particular scale values. The registry record does not report the distribution of individual responses.

The posted comparisons use Flavored Water as the reference group and report mean differences for Mediterranean Lemonade and Green Tea. A mean difference expresses the contrast between two group averages, with the sign indicating which group’s average is higher under the reported comparison. The posted difference is 0.1 for Mediterranean Lemonade versus Flavored Water and 0.0 for Green Tea versus Flavored Water. These are unadjusted contrasts. The record does not report a model that adjusts for baseline characteristics or other covariates, nor does it specify the exact test or estimation procedure used for the posted p-values and confidence intervals.

A confidence interval describes a range of values compatible with the data under the statistical method used. In general, a wider interval means less precision, while a narrower interval means greater precision for the estimate. For both satisfaction contrasts, the posted intervals cross zero. That means the interval includes no mean difference as well as values in either direction. It does not prove that the true difference is zero. The registry record does not report a prespecified margin for deciding whether a difference would be too small to matter, so the intervals cannot be used as a formal equivalence assessment.

The p-values are listed as unadjusted. In general, a p-value measures how unusual data at least as inconsistent with a specified null model would be if that model and the test assumptions held. It does not measure effect size, importance, or the chance that a treatment hypothesis is true. The unadjusted value for the Mediterranean Lemonade contrast is 0.802, and the value for Green Tea is 1.0. The registry record does not provide enough detail to identify all test assumptions or to determine whether the calculations account for the rating scale’s bounded, discrete nature.

The trial is recorded as randomized, single-masked, and parallel-group. Randomization is generally intended to reduce systematic differences between assigned groups, while masking can reduce some forms of knowledge-related influence on measurement or behavior. Those general aims do not establish that allocation was concealed or identify who was masked in this study. The record does not report the randomization procedure, concealment method, or masked party. The parallel structure means the posted groups represent different assignments rather than repeated beverage periods for the same participants, as far as the registry description indicates.

The primary endpoint is reported at one follow-up point, week 6. The registry lists four secondary measures as changes from baseline to week 6: total cholesterol, fasting glucose, hemoglobin A1C, and body weight. It also describes broader aims involving triglycerides, blood pressure, and markers of inflammation. Numerical results for these measures are not reported in the registry record. The presence of an outcome in a study description does not mean a result for it is available in the posted record.

Multiplicity is relevant when several outcomes or group comparisons are examined. In general, making multiple inferences can increase the chance of at least one apparently notable result if each is considered separately. Whether and how to control that issue depends on the prespecified analysis plan and the intended claims. The registry record does not report a multiplicity strategy. The satisfaction comparisons should therefore be read as the reported unadjusted contrasts, not as results known to have been adjusted for all outcomes or comparisons.

Missing-data methods and analysis populations also affect interpretation. For example, an analysis may include all randomized participants, only those with an observed endpoint, or a defined subset; these choices can lead to different interpretations. The registry record does not report the analysis population, the amount or pattern of missing satisfaction data, imputation methods, or sensitivity analyses. Group counts accompanying the satisfaction summaries do not establish how missing observations were handled.

The sample-size illustrations use the observed Mediterranean Lemonade versus Flavored Water effect as a planning input. Their stated assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation; the effect to detect is a stated fraction of the observed effect. In general, over-dispersion means observed variability is greater than a model assumes; when present, it can make simple model-based uncertainty too optimistic. The registry does not report whether over-dispersion was assessed or relevant to these continuous ratings. These planning calculations are separate from the trial’s own design, whose original assumptions are not reported in the registry record.

10. Confidence Intervals and Precision

The estimated mean difference is 0.1 for Mediterranean Lemonade compared with Flavored Water and 0.0 for Green Tea compared with Flavored Water. Each comparison has a confidence interval that crosses zero and extends to values on both sides of it. The interval for each contrast therefore reflects uncertainty about both the direction and the magnitude of any group difference. The posted intervals are wide relative to the small estimated contrasts, so the summaries do not pinpoint a precise difference.

In general, a confidence interval is not a guarantee that the true value lies inside its particular endpoints. It is an uncertainty summary produced by a statistical procedure, interpreted under that procedure’s assumptions. Here, the small group counts reported with the ratings are relevant to precision: fewer observations generally provide less information about a group mean, all else being equal. The actual precision also depends on variability, reflected in the group standard deviations, and on the method used to construct the interval.

The p-values of 0.802 and 1.0 do not replace the intervals. A p-value alone does not say which range of differences remains compatible with the data or how large a difference might still be plausible. Because the intervals include zero, the results do not establish a difference in either direction. Because no equivalence margin is reported, they also do not establish that the beverages produce equivalent satisfaction ratings.

The registry record does not report a clinically or practically meaningful difference threshold for this scale, and it does not describe a prespecified precision target. As a result, the intervals can be interpreted as uncertainty around the posted mean contrasts, but not as a pass-or-fail assessment against an acceptability boundary. The rating scale is bounded from 1 to 4, and the record does not provide individual-level data or distributional details that would support a fuller assessment of how the scale’s shape affects precision.

11. Planning a Similar Trial: Sample Size

This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.

The sample-size figures are planning illustrations for the Mediterranean Lemonade versus Flavored Water satisfaction contrast. They are expressed as participants per arm, not as a combined total. The displayed planning rows consider 100%, 75%, and 50% of the observed effect. For 100% of the observed effect, the illustration gives 1,467 participants per arm for 80% power and 1,964 participants per arm for 90% power. For 75% of the observed effect, it gives 2,607 participants per arm for 80% power and 3,490 participants per arm for 90% power. For 50% of the observed effect, it gives 5,866 participants per arm for 80% power and 7,853 participants per arm for 90% power.

The stated calculation assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The target effect is the stated fraction of the observed effect. In plain language, 80% power means that, under the calculation’s assumptions and if the target effect were real, the design would have an 80% chance of detecting it using the specified significance criterion. The 90% column describes the corresponding chance at the higher power target. These are planning probabilities, not probabilities that the result is true.

Smaller effects require more participants to detect under the same general assumptions, which is why the illustrated requirements increase as the target effect fraction decreases. These estimates are based on the observed effect and are not the original trial’s sample-size justification; the trial’s own design assumptions are not reported in the registry record. This is not observed power.

12. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z_1−α/2 = 1.960) and the desired power (z_1−β = 0.842 for 80% and 1.282 for 90%).

Formula

n is the number of participants in each arm, Δ is the difference in means to detect and σ is the common standard deviation.

Worked calculation for this trial

1. Observed difference Δ = 0.100; pooled standard deviation σ = 0.967.
2. n = 2 × (1.96 + 0.842)² × 0.967² / 0.100² = 1,466.4, rounded up to 1,467 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 <- 0.1                      # observed difference in means
sigma <- 0.966508112244529                     # 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(2911753)
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 = 1,467 (80% power), 1,964 (90% power)
 75% of observed effect: n per arm = 2,607 (80% power), 3,490 (90% power)
 50% of observed effect: n per arm = 5,866 (80% power), 7,853 (90% power)
power.t.test: 1467.3 
Simulated power at n = 1,467 per arm: 0.804 (20000 replicates)

The simulation draws many sets of group means and variances at the planned sample size and counts how often the two-sample t-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.

13. Multiplicity, Missing Data and Analysis Populations

The registry lists one primary endpoint, treatment satisfaction at week 6, and four secondary outcomes measured as changes from baseline to week 6. The broader study description also refers to cholesterol and triglyceride levels, blood pressure, glucose, and inflammation markers. The registry record does not report an analysis plan specifying how these outcomes were prioritized beyond naming the primary and secondary outcomes, or how multiple comparisons were handled.

Multiplicity matters when several outcomes or contrasts are examined. In general, each additional statistical test creates another opportunity for a result to appear unusual by chance under its null model. Methods such as adjusting significance thresholds or defining a hierarchy of outcomes can address this issue, but the appropriate approach depends on the intended claims and prespecified plan. No multiplicity adjustment is reported for the satisfaction comparisons. Their p-values are explicitly unadjusted and should be read as such, rather than as evidence that all possible comparisons and outcomes were considered together.

The registry record lists no analysis entries. It does provide satisfaction summaries and pairwise comparison statistics, but does not report whether these came from a prespecified analysis, how the analysis population was defined, or how departures from the intended intervention were treated. The record does not report the number or pattern of missing primary endpoint observations, a missing-data method, or sensitivity analyses addressing missingness. It also does not state whether analyses followed an intention-to-treat, per-protocol, or other population definition.

These omissions do not change the reported means, but they limit assessment of how robustly the summaries represent all randomized participants and how the comparisons were selected. The group counts attached to the satisfaction summaries should not be taken as a complete account of missingness or adherence. Results for the listed secondary outcomes are not reported in the registry record, so their statistical significance, precision, and relationship to the primary endpoint cannot be assessed from the posted results.

14. 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.

Most frequent non-serious adverse event terms

The registry records serious adverse events in the three beverage groups: 0 in Mediterranean Lemonade, 0 in Green Tea, and 0 in Flavored Water. The numbers listed as at risk for serious adverse events are 21, 19, and 10, respectively. These are the registry’s posted serious-event figures for the groups during the recorded study period.

A zero count means that no serious adverse events are recorded in these results; it does not establish that the risk is zero or rule out uncommon events. The amount of information about safety is limited by the number of participants observed and by the study’s duration. The registry record does not report further detail about the method of event collection, event definitions beyond the serious-event category, or follow-up after the six-week intervention.

The record lists 2 other adverse events in the Mediterranean Lemonade group and 0 in each of the other groups. These non-serious figures are distinct from the serious-event counts. The serious-event summary should be interpreted as a descriptive safety record, not as a definitive comparison of risk between beverages. No treatment recommendation follows from these figures.

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

The posted primary results answer a narrow question: what were the average week-6 satisfaction ratings in the three beverage groups, and how did the two named beverage groups compare with Flavored Water? The averages were 3.3 for Flavored Water, 3.4 for Mediterranean Lemonade, and 3.3 for Green Tea on a scale from 1 to 4. The reported mean differences were 0.1 and 0.0, with confidence intervals crossing zero. These figures describe satisfaction ratings among the participants represented in the summaries.

They do not establish that the groups are equivalent. A failure to identify a clear difference is not the same as showing that any difference must be small enough to be unimportant. That stronger conclusion would require a prespecified equivalence or non-inferiority margin and an analysis designed around it; neither is reported in the registry record. The posted intervals also leave uncertainty about the size and direction of the contrasts.

The ratings do not establish whether participants adhered to the assigned beverage regimen or whether the approach was feasible under everyday conditions. The registry describes weekly beverage supplies and daily consumption instructions, but adherence, completion, and recommendation results are not reported. Likewise, the primary endpoint does not answer whether the listed health markers changed. Although the record names secondary outcomes, their numerical results are not reported in the registry record.

The study is described as evaluating preliminary effects, not as providing a definitive assessment of health outcomes. Its satisfaction summaries should therefore be kept separate from any claim about cholesterol, glucose, hemoglobin A1C, weight, or other health markers. The results also do not show that one beverage is preferable or that any beverage changes health. They characterize the posted satisfaction data and their uncertainty, within the scope of the recorded endpoint and follow-up.

16. Why This Trial Matters Statistically

This study illustrates a statistical distinction between acceptability and clinical or biological outcomes. Satisfaction is a participant-reported endpoint, while the study description also names laboratory and body-weight measures. The posted numerical results address satisfaction ratings only. Keeping these endpoints separate prevents an interpretation of an acceptability summary from being mistaken for a health-effect result.

The group averages are close at the displayed precision, but the confidence intervals cross zero and the comparisons are unadjusted. This combination highlights why an estimate, its uncertainty, and the analysis context all matter. A small point estimate alone does not prove that meaningful differences are absent; an interval that includes zero does not establish equivalence. Without a prespecified margin, the statistical question of equivalence remains unanswered.

The record also demonstrates the importance of reporting analysis details. It identifies randomization, masking, outcome timing, and group summaries, but does not report the randomization procedure, masked party, missing-data handling, analysis population, multiplicity approach, or original sample-size justification. Those details help readers judge the reliability and scope of an inference, particularly when a study examines several outcomes.

Finally, the planning illustrations show how the observed contrast can be used as a hypothetical input for future planning, while making clear that the original design assumptions are not recorded. This is distinct from calculating the probability that the present trial detected an effect. The statistical value of the results is therefore descriptive and exploratory: they provide information about observed satisfaction and its uncertainty, while leaving broader feasibility and health questions unresolved in the registry record.

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 main limitation for interpreting the primary outcome is that the registry reports group means and standard deviations, but not the distribution of individual satisfaction ratings. The scale is bounded from 1 to 4, and the record does not report how responses were distributed across those values. It also does not report a threshold defining satisfactory acceptability or a meaningful difference on the scale. The group averages therefore cannot be classified against a formal criterion using the recorded information.

The registry describes the study as randomized and single-masked but does not identify the masked party, the randomization method, or allocation concealment. It does not report adherence to the daily beverage instructions, reasons for discontinuation, or completion information. These omissions limit assessment of implementation and of whether the assigned regimen was followed as intended.

The primary endpoint is recorded at week 6, with no longer-term satisfaction results reported. The registry does not report whether all assigned participants contributed to the posted summaries, the amount of missing endpoint data, or how missing observations were handled. It also does not report a detailed statistical analysis plan, multiplicity handling, or the original sample-size rationale. The posted pairwise comparisons are unadjusted.

Although four secondary outcomes are listed, numerical results for them are not reported in the registry record. The study description names additional health measures, but the posted satisfaction results cannot be used to infer changes in those measures. The listed adverse-event figures are also limited summaries; further event-collection details and longer-term safety information are not reported. These limitations are specific to what the registry records and should not be replaced by assumptions about the study procedures.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Feasibility and Acceptability of a Beverage Intervention for Hispanic Adults — NCT02911753.
• Registry record last updated 2019-10-25; status last verified 2017-10.
• Results first posted 2019-10-25.
• 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, single-masked, parallel-group beverage study with enrollment of 50. The population is described as obese Hispanic adults ages 18-64 years. The three groups were assigned Mediterranean Lemonade, Green Tea, or Flavored Water, with instructions to consume 32 ounces daily for six weeks.

The primary endpoint was treatment satisfaction at week 6, rated from 1 (low) to 4 (high). Mean ratings were 3.4 for Mediterranean Lemonade, 3.3 for Green Tea, and 3.3 for Flavored Water. The posted unadjusted comparisons against Flavored Water had mean differences of 0.1 and 0.0, and both confidence intervals crossed zero. The registry lists four secondary outcomes but does not report their numerical results.

The registry records 0 serious adverse events in each group. It does not report the original sample-size rationale, detailed analysis plan, missing-data methods, or analysis population. The posted results support a description of satisfaction ratings and their uncertainty, not conclusions about unreported health outcomes or formal equivalence between beverages.