This page provides an independent statistical analysis and educational interpretation of publicly reported results. ClinicalTrials.gov provides the official trial registry record. Numerical trial results on this page are restricted to the results posted in the ClinicalTrials.gov record; calculations added by Clinical Biostats are labelled as such.
1. Trial at a Glance
This page covers the registry results for Studying the Impact of Product Packaging in a Virtual Store Environment (NCT04381481), a randomized na study. The primary outcome is Percent of Participants Who Selected the Grape-Flavored Fruit Drink (Fruit Drink Experimental Task 1).
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT04381481 |
| Phase | NA |
| Condition | Obesity, Childhood |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Single |
| Enrollment | 2374 |
| Arms in the primary outcome | 4 |
| Lead sponsor | University of North Carolina, Chapel Hill |
| Results posted | Yes |
2. Clinical Question
Population
Adults in the United States who had at least one child aged 1-5 were eligible for recruitment if the youngest child meeting the birthday criterion had consumed at least one fruit drink in the previous week. The planned participant description also specified identification as non-Hispanic Black, non-Hispanic White, or Hispanic. The registry record describes recruitment through a panel research company. The completed study enrolled 2374 participants.
Intervention
Participants saw fruit drinks carrying one of three nutrition claims: “No Artificial Sweeteners,” “100% Vitamin C daily value,” or “100% All Natural.” They also encountered one of three snack-label conditions during the second shopping task: a text warning, a graphic warning with text, or a barcode control label.
Comparator
For the primary beverage outcome, the comparison group saw fruit drinks with no nutrition claim. The snack-label condition varied separately across the virtual-store versions, creating combinations of beverage and snack conditions.
Primary question
During the virtual shopping task, did the percentage of participants selecting the grape-flavored fruit drink rather than 100% grape juice differ across the beverage-claim groups and the no-claim control group? The registry identifies selection as an objectively measured behavior in the online task, rather than a stated intention.
3. Trial Design
The registry describes a completed randomized, single-masked, parallel-design behavioral trial conducted in an online virtual convenience store. Participants were assigned to one of 12 versions of the store. Each version combined one of four beverage conditions—no nutrition claim or one of three claims—with one of three snack-label conditions. Participants completed two shopping tasks: selecting beverages for a child aged 1-5 and selecting a snack for that same child. A survey followed the shopping tasks.
The study enrolled 2374 participants. The primary beverage comparison reports group sizes of 565 for the no-claim control, 554 for the “No Artificial Sweeteners” claim, 556 for the “100% Vitamin C daily value” claim, and 544 for the “100% All Natural” claim. The registry’s participant description refers to approximately 2,500 individuals as the recruitment target; it does not explain how that target was determined.
The study began on 2020-05-14, reached primary completion on 2020-07-24, and is listed as completed. The registry classifies the phase as NA. It identifies the University of North Carolina, Chapel Hill as sponsor. The meaning of single masking—specifically, which people involved in the study were masked—is not reported in the registry record. Details about sequence generation, allocation concealment, protocol deviations, or the original statistical analysis plan are also not reported in the registry record.
The virtual-store setting allows observation of a choice made within a controlled shopping task, but it is not the same as observing purchases in a physical store or later consumption. The findings therefore describe choices and survey responses in the study setting.
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.
Only the first 6 of 12 groups are shown.
Overall Study
| Stage | Control Beverage, Text Snack | Control Beverage, Control Snack | Control Beverage, Graphic Snack | Claim 1 Beverage, Text Snack | Claim 1 Beverage, Control Snack | Claim 1 Beverage, Graphic Snack |
|---|---|---|---|---|---|---|
| STARTED | 200 | 205 | 199 | 197 | 199 | 195 |
| COMPLETED | 185 | 190 | 190 | 183 | 191 | 180 |
| NOT COMPLETED | 15 | 15 | 9 | 14 | 8 | 15 |
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.
Population: Data reported for those participants who completed the entire trial.
Only the first 6 of 13 groups are shown.
| Characteristic | Unit | Control Beverage, Text Snack | Control Beverage, Control Snack | Control Beverage, Graphic Snack | Claim 1 Beverage, Text Snack | Claim 1 Beverage, Control Snack | Claim 1 Beverage, Graphic Snack |
|---|---|---|---|---|---|---|---|
| Participants analysed | 185 | 190 | 190 | 183 | 191 | 180 | |
| Age, Categorical: Age – <=18 years | Participants | 1 | 0 | 0 | 0 | 0 | 0 |
| Age, Categorical: Age – Between 18 and 65 years | Participants | 184 | 190 | 190 | 183 | 190 | 180 |
| Age, Categorical: Age – >=65 years | Participants | 0 | 0 | 0 | 0 | 1 | 0 |
| Sex/Gender, Customized: Gender – Man | Participants | 56 | 61 | 67 | 63 | 70 | 69 |
| Sex/Gender, Customized: Gender – Woman | Participants | 126 | 129 | 121 | 113 | 115 | 108 |
| Sex/Gender, Customized: Gender – Transgender or other gender identity | Participants | 0 | 0 | 0 | 0 | 0 | 0 |
| Ethnicity (NIH/OMB): Hispanic or Latino | Participants | 60 | 63 | 64 | 62 | 56 | 53 |
| Ethnicity (NIH/OMB): Not Hispanic or Latino | Participants | 125 | 127 | 126 | 121 | 135 | 127 |
| Ethnicity (NIH/OMB): Unknown or Not Reported | Participants | 0 | 0 | 0 | 0 | 0 | 0 |
| Race (NIH/OMB): American Indian or Alaska Native | Participants | 0 | 1 | 2 | 1 | 1 | 2 |
| Race (NIH/OMB): Asian | Participants | 0 | 2 | 1 | 1 | 0 | 1 |
| Race (NIH/OMB): Native Hawaiian or Other Pacific Islander | Participants | 0 | 0 | 0 | 0 | 1 | 0 |
| Race (NIH/OMB): Black or African American | Participants | 42 | 49 | 41 | 39 | 32 | 39 |
| Race (NIH/OMB): White | Participants | 129 | 124 | 137 | 131 | 149 | 128 |
| Race (NIH/OMB): More than one race | Participants | 5 | 5 | 5 | 4 | 2 | 5 |
| Race (NIH/OMB): Unknown or Not Reported | Participants | 9 | 9 | 4 | 7 | 6 | 5 |
6. Primary Endpoint
The registry lists the primary outcome as Percent of Participants Who Selected the Grape-Flavored Fruit Drink (Fruit Drink Experimental Task 1), measured over During virtual shopping task which will last ~5 minutes.
| Element | Registry entry |
|---|---|
| Result type | Number |
| Measure of spread | not applicable |
| Unit | percentage of participants |
| Endpoint classification | Binary Endpoint |
The primary endpoint is the percentage of participants who selected the grape-flavored fruit drink rather than 100% grape juice during the first virtual shopping task. The registry describes this as an objectively measured choice. Its stated timeframe is the shopping task, which was expected to last about 5 minutes.
This endpoint captures a behavioral selection within the experimental store, rather than a participant’s opinion about the drink or stated intention to buy it. That distinction is useful because a choice in a task is closer to a purchasing decision than a rating or intention, while still remaining a simulated choice rather than a real-world transaction. The endpoint also gives a direct way to compare the no-claim beverage group with the three groups that saw a nutrition claim.
The measure is a percentage, so the reported group results describe the share of participants making the specified selection. It does not measure how much of the drink was purchased or consumed, whether a child later drank it, or the healthfulness of the overall shopping basket. Those outcomes are not reported as the primary endpoint in the registry record.
7. Results Posted in the Registry
- Claim 1 Beverage: 44.9% (249/554) versus 32.0% (181/565) on control; risk difference 12.9 percentage points (95% CI 7.3 to 18.6), risk ratio 1.40 (1.21–1.63); unadjusted two-proportion z-test p = <0.001.
- Claim 2 Beverage: 51.1% (284/556) versus 32.0% (181/565) on control; risk difference 19.0 percentage points (95% CI 13.4 to 24.7), risk ratio 1.59 (1.38–1.84); unadjusted two-proportion z-test p = <0.001.
- Claim 3 Beverage: 54.0% (294/544) versus 32.0% (181/565) on control; risk difference 22.0 percentage points (95% CI 16.3 to 27.7), risk ratio 1.69 (1.46–1.95); unadjusted two-proportion z-test p = <0.001.
Risk difference: Claim 1 Beverage
95% CI: 7.3 to 18.6 percentage points
Recalculated from the posted summary statistics
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.
| Secondary outcome | Type | Effect measure | Estimate (95% CI) | Planning size, 80% power |
|---|---|---|---|---|
| Percent of Participants Who Misperceive That the Fruit Drink Does Not Have Added Sugar (Fruit Drink Experimental Task 1) | Binary Endpoint | Risk difference | +30.1 pts (25.1 to 35.0) | 33 per arm |
| Percent of Participants Who Misperceive That the Fruit Drink is 100% Fruit Juice (Fruit Drink Experimental Task 1) | Binary Endpoint | Risk difference | +14.1 pts (8.8 to 19.4) | 161 per arm |
| Number of Teaspoons of Added Sugar Participants Think the Fruit Drink Contains (Fruit Drink Experimental Task 1) | Continuous Endpoint | Mean difference | -0.60 (-1.10 to -0.10) | 582 per arm |
Percent of Participants Who Misperceive That the Fruit Drink Does Not Have Added Sugar (Fruit Drink Experimental Task 1)
- Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Claim 1 Beverage: 42.0% (227/540) versus 11.9% (67/561) on control; risk difference 30.1 percentage points (95% CI 25.1 to 35.0), risk ratio 3.52 (2.75–4.50); unadjusted two-proportion z-test p = <0.001.
- Claim 2 Beverage: 22.1% (120/544) versus 11.9% (67/561) on control; risk difference 10.1 percentage points (95% CI 5.7 to 14.5), risk ratio 1.85 (1.40–2.43); unadjusted two-proportion z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the proportion with the event is statistically higher for Claim 1 Beverage than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
- The 95% confidence interval excludes no difference, so the proportion with the event is statistically higher for Claim 2 Beverage than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Percent of Participants Who Misperceive That the Fruit Drink is 100% Fruit Juice (Fruit Drink Experimental Task 1)
- Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Claim 1 Beverage: 36.0% (195/541) versus 21.9% (123/561) on control; risk difference 14.1 percentage points (95% CI 8.8 to 19.4), risk ratio 1.64 (1.36–1.99); unadjusted two-proportion z-test p = <0.001.
- Claim 2 Beverage: 34.9% (190/544) versus 21.9% (123/561) on control; risk difference 13.0 percentage points (95% CI 7.7 to 18.3), risk ratio 1.59 (1.31–1.93); unadjusted two-proportion z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the proportion with the event is statistically higher for Claim 1 Beverage than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
- The 95% confidence interval excludes no difference, so the proportion with the event is statistically higher for Claim 2 Beverage than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Number of Teaspoons of Added Sugar Participants Think the Fruit Drink Contains (Fruit Drink Experimental Task 1)
- 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:
- Claim 1 Beverage: mean 5.80 versus 6.40 on control; difference -0.60 (95% CI -1.10 to -0.10), standardized effect d = -0.16; z-test p = 0.020.
- Claim 2 Beverage: mean 5.70 versus 6.40 on control; difference -0.70 (95% CI -1.19 to -0.21), standardized effect d = -0.18; z-test p = 0.005.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically lower for Claim 1 Beverage than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
- The 95% confidence interval excludes no difference, so the mean is statistically lower for Claim 2 Beverage than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
The posted secondary results relate to participants’ understanding and perceptions of the drinks after the shopping task. Across the available binary perception outcomes, the claim groups generally have more reported misperception than the no-claim group for the measures concerning added sugar and whether the drink is 100% fruit juice. For the continuous estimate of perceived teaspoons of added sugar, the posted claim-group means are lower than the control mean for the comparisons with results available. The direction of these outcomes is therefore not uniform across measures.
This pattern provides context for the primary result that selection of the grape-flavored drink was more common in each claim group. It does not establish that a specific perception mediated or caused the selection. The outcomes are measured at different levels: one records a choice in the virtual store, while others record survey responses about beliefs and perceptions. No causal mediation analysis is reported in the registry record.
The registry states that there are 28 outcome measures and 28 analyses, while only 26 secondary outcomes are posted. Results for secondary outcomes not described in the posted record are not reported in the registry record. The registry reports regression-based tests for the secondary outcomes with results available, but it does not report a multiplicity plan or adjustment.
Unadjusted secondary results carry less weight because evaluating many outcomes and comparisons increases the chance that some findings will appear noteworthy by chance. Without a reported multiplicity strategy, the secondary comparisons are best treated as exploratory context rather than as independent confirmation of the primary result. Their p-values do not account for the full set of outcomes and comparisons unless an adjustment was performed, and such an adjustment is not reported in the registry record.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Percent of Participants Who Misperceive That the Fruit Drink Does Not Have Added Sugar (Fruit Drink Experimental Task 1)
- Percent of Participants Who Misperceive That the Fruit Drink is 100% Fruit Juice (Fruit Drink Experimental Task 1)
- Number of Teaspoons of Added Sugar Participants Think the Fruit Drink Contains (Fruit Drink Experimental Task 1)
- Mean Percent of Fruit Juice That Participants Believe the Fruit Drink Contains (Fruit Drink Experimental Task 1)
- Perceived Misleadingness of Fruit Drink (Fruit Drink Experimental Task 1)
- Perceived Product Healthfulness of Fruit Drink for Child's Daily Consumption (Fruit Drink Experimental Task 1)
- Interest in Giving the Fruit Drink to One's Child (Fruit Drink Experimental Task 1)
- Percent of Participants Who Selected Apple-flavored Fruit Drink (Fruit Drink Experimental Task 1)
9. Statistical Interpretation
The posted primary outcome shows that selection of the grape-flavored fruit drink rather than 100% grape juice was more common in each nutrition-claim group than in the no-claim control group. The registry’s arm-level percentages are 32.0 for control, 45.0 for “No Artificial Sweeteners,” 51.0 for “100% Vitamin C daily value,” and 54.0 for “100% All Natural.” These are descriptive group results from the virtual shopping task.
Unadjusted recalculations comparing each claim group with control estimate risk differences of 0.129, 0.190, and 0.220, respectively. Their reported confidence intervals are 0.073 to 0.186, 0.134 to 0.247, and 0.163 to 0.277. The corresponding recalculated p-values are each <0.001. These estimates describe the absolute difference in the probability of the selection between each claim group and control, on the proportion scale. They do not establish why participants made their choices.
The registry also reports a logistic-regression analysis across the four beverage groups, with p <0.001 and a superiority designation. The posted entry does not give the regression coefficient, its confidence interval, or further details about model specification. This is a group-level reported analysis; it should not be mistaken for a separate set of adjusted pairwise estimates.
Several secondary outcomes concern participants’ perceptions of added sugar, fruit-juice content, and the amount of sugar they thought the drink contained. Their overall pattern is not a single uniform shift in perception: some responses indicate more misperception in claim groups, while the reported mean estimates of perceived teaspoons of added sugar are lower than control for the claim groups with posted results. Those measures help describe possible perceptions accompanying the shopping choices, but they do not show that a particular perception caused a selection.
The experiment concerns a simulated task among the recruited adult participants and a specific set of drink claims and labels. It does not directly establish how the claims would affect actual purchases, children’s consumption, or outcomes outside this study setting. No clinical benefit or harm should be inferred from the selection outcome alone.
10. Statistical Methods Explained
What does the reported primary analysis compare?
The primary outcome is binary at the participant level: a participant either selected the grape-flavored fruit drink rather than 100% grape juice or did not. The registry reports percentages by beverage group and identifies the sponsor’s method as logistic regression. Logistic regression is a general statistical method for relating a binary outcome to group membership and, when specified, other explanatory variables. The registry record does not report which covariates, if any, were included, or the exact model specification.
The sponsor’s reported analysis covers the four beverage groups and gives p <0.001 with a superiority designation. This is an overall reported test across groups, not a displayed estimate for every individual claim-versus-control contrast. The registry does not provide a coefficient or confidence interval for that overall regression analysis.
What is a risk difference?
The recalculated pairwise results use risk differences. A risk difference is the probability of the outcome in one group minus the probability in the comparison group. Here, it expresses the difference in the proportion selecting the specified drink between a nutrition-claim group and the no-claim group. Positive estimates indicate a higher observed selection proportion in the claim group. The recalculated estimates are unadjusted comparisons of the posted group summaries; they are not presented as the sponsor’s regression coefficients.
The page also reports relative risks and odds ratios for the recalculated comparisons. In general, a relative risk compares the outcome probabilities between groups, while an odds ratio compares the outcome odds. These are different scales for describing group contrasts and should not be read as absolute percentage-point differences. For a common outcome, an odds ratio can be farther from the null value than the corresponding relative risk. The registry’s sponsor analysis is logistic regression, but the registry does not state that the reported regression is the source of the displayed recalculated odds ratios.
What does a p-value tell the reader?
In general, a p-value measures how incompatible the observed data are with a specified null model, under the assumptions of the statistical test. It is not the probability that the null hypothesis is true, and it does not measure the size or practical importance of an effect. The sponsor’s overall p-value and the recalculated pairwise p-values address different reported comparisons. The recalculated pairwise p-values are unadjusted for the multiple comparisons and outcomes in this study.
How should a confidence interval be understood?
In general, a confidence interval describes sampling uncertainty around an estimate under the method used to calculate it. A narrower interval indicates greater precision on that scale; a wider interval leaves more uncertainty about the size of the contrast. The recalculated intervals are for unadjusted risk differences between the claim groups and control. They quantify uncertainty in those pairwise estimates, not uncertainty about every feature of the study design, measurement, or external applicability.
Why are some secondary outcomes analyzed differently?
The posted secondary summaries include binary outcomes, such as whether a participant misperceived a drink’s contents, and a continuous outcome, the number of teaspoons of added sugar participants thought it contained. The registry identifies logistic regression for the binary outcomes and linear regression for the continuous outcome. In general, logistic regression is suited to a binary response, while linear regression models a mean outcome on a continuous scale. The registry does not provide complete model details, such as covariate adjustment or diagnostic checks.
The recalculated mean differences for perceived teaspoons compare group averages. A negative mean difference indicates a lower reported average in the claim group than in control. The posted spread is a standard deviation, which describes variation among participant responses rather than the precision of the mean. The recalculated confidence intervals for these mean differences reflect sampling uncertainty under the calculation method; they do not indicate that individual participants’ responses were close to the group average.
What information is not available?
The registry record does not report the trial’s original statistical analysis plan, the prespecified model covariates, handling of missing outcome data, or details of any interim analyses. It also does not report whether any multiplicity adjustment was planned or applied. Accordingly, the recalculated pairwise statistics are best interpreted as transparent, unadjusted contrasts based on the posted summaries, while the sponsor’s reported regression result remains the registry’s own analysis. The registry’s stated results should not be expanded into claims about undocumented methods.
11. Confidence Intervals and Precision
The recalculated risk-difference confidence intervals are entirely above zero for each comparison with the no-claim control: 0.073 to 0.186 for “No Artificial Sweeteners,” 0.134 to 0.247 for “100% Vitamin C daily value,” and 0.163 to 0.277 for “100% All Natural.” In general, an interval gives a range of values reasonably compatible with the observed data under the calculation method. These intervals suggest that the positive differences are estimated with more precision than would be conveyed by a single point estimate alone, while still allowing uncertainty about the exact size of each difference.
The interval widths are similar across these three recalculated comparisons, but the point estimates differ. Confidence intervals are not guarantees that the true effect lies within the specific interval, nor do they account for potential limitations such as unreported missing-data handling or the simulated setting. They also do not by themselves address the consequences of making multiple comparisons.
For the reported secondary continuous outcome, the recalculated mean-difference intervals are -1.105 to -0.095 for “No Artificial Sweeteners” and -1.192 to -0.208 for “100% Vitamin C daily value.” These intervals are on the teaspoons scale and concern the difference in group means, not a percentage or selection probability. Across all intervals, precision is specific to the outcome and contrast being estimated; a confidence interval for one endpoint does not establish the precision of other outcomes.
The registry’s own overall logistic-regression result does not include a reported confidence interval or effect estimate. Its precision therefore cannot be assessed from the registry’s reported regression result alone. The recalculated intervals provide pairwise information on a different, unadjusted scale and should not be substituted for an unavailable interval from the sponsor’s model.
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.
| Effect to detect | Participants per arm, 80% power | Participants per arm, 90% power |
|---|---|---|
| 100% of the observed effect | 222 | 297 |
| 75% of the observed effect | 389 | 520 |
| 50% of the observed effect | 859 | 1,150 |
The planning figures are expressed as participants per arm for the binary and continuous outcomes in this trial; they are not total event counts. The planning calculation uses a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. For each comparison, the assumed effect is a stated fraction of the observed effect. The registry does not report the original design assumptions or the original sample-size justification.
The 80% power column gives the estimated number of participants per arm needed, under those planning assumptions, for an 80% chance of detecting the specified effect if that effect were the true one. The 90% power column gives the corresponding planning number for a 90% chance. Power is a property of a planned design under assumptions; it does not say what happened in a completed study.
Planning for 100% of the observed effect uses the full observed contrast as the assumed effect. Planning for 75% or 50% uses smaller assumed contrasts. Smaller effects are harder to distinguish from random variation and therefore require more participants per arm to reach the same target power, all else being equal. The estimates are illustrations based on observed results, not the trial’s documented original design rationale.
These calculations are planning illustrations, not observed power. They should not be used as evidence that the trial had adequate or inadequate power for its original objectives, because the registry record does not report the original assumptions or a prespecified target effect. The actual enrollment and group sizes are separate details from these hypothetical planning estimates.
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 z1−α/2 = 1.960) and the desired power (z1−β = 0.842 for 80% and 1.282 for 90%).
Formula
n is the number of participants in each arm, p0 and p1 are the control and treatment proportions, and p̄ is their average.
Worked calculation for this trial
- Control proportion p0 = 0.320; treatment proportion p1 = 0.449; average p̄ = 0.385.
- First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6881 = 1.3487.
- Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.6820 = 0.5740.
- n = (1.3487 + 0.5740)2 / (0.1291)2 = 221.8, rounded up to 222 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
p0 <- 0.320353982300885 # control proportion
p1 <- 0.449458483754513 # treatment proportion
n_per_arm <- function(power, frac = 1) {
q1 <- p0 + (p1 - p0) * frac # smaller effect = fraction of the observed difference
pbar <- (p0 + q1) / 2
z_b <- qnorm(power)
ceiling(round((z_a * sqrt(2 * pbar * (1 - pbar)) + z_b * sqrt(p0 * (1 - p0) + q1 * (1 - q1)))^2 / (q1 - p0)^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 (unrounded n per arm)
cat("power.prop.test:", round(power.prop.test(p1 = p0, p2 = p1, power = 0.80)$n, 1), "\n")
# Simulation: how often does the z-test reject at the 80%-power sample size?
set.seed(4381481)
n <- n_per_arm(0.80)
reps <- 20000
x0 <- rbinom(reps, n, p0); x1 <- rbinom(reps, n, p1)
ph <- (x0 + x1) / (2 * n)
z <- ((x1 - x0) / n) / sqrt(ph * (1 - ph) * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(z) > z_a, na.rm = TRUE), reps))
Output from running the code
100% of observed effect: n per arm = 222 (80% power), 297 (90% power)
75% of observed effect: n per arm = 389 (80% power), 520 (90% power)
50% of observed effect: n per arm = 859 (80% power), 1,150 (90% power)
power.prop.test: 221.8
Simulated power at n = 222 per arm: 0.795 (20000 replicates)
The simulation draws many pairs of event counts at the planned sample size and counts how often the two-proportion z-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
| Method | Estimate | 95% CI | P-value |
|---|---|---|---|
| Regression, Logistic | not reported | < 0.001 |
The registry reports that the sponsor analyzed the primary outcome using logistic regression across the four beverage groups and recorded p <0.001 for a superiority analysis. The registry does not give the regression estimate, its confidence interval, covariate specification, or pairwise regression contrasts.
The recalculated results instead compare each claim group with control using unadjusted differences in the posted selection proportions. These are simple pairwise summaries, with their own confidence intervals and p-values. They provide an interpretable absolute-scale description of the differences, but they are not a reproduction of the sponsor’s full regression model. The sponsor’s overall test and the recalculated pairwise contrasts therefore answer related but not identical statistical questions.
The registry discrepancy indicator is false. There is no flagged conflict between the posted summaries and the recalculated results. That does not establish that the methods are identical; the available registry record does not include enough model detail to make that claim. Where the sponsor reports an analysis and the recalculation gives a separate unadjusted comparison, they should be identified as distinct sources of statistical information rather than combined into one estimate.
15. Multiplicity, Missing Data and Analysis Populations
The registry lists 28 outcome measures and 28 analyses, and identifies multiple beverage groups and secondary outcomes. The primary reported test compares the four beverage groups, while the recalculated summaries include separate claim-versus-control comparisons. Considering multiple outcomes and contrasts raises a multiplicity issue: when many tests are conducted, the chance of at least one apparently strong result can increase even if no true differences exist.
The registry record does not report whether the sponsor prespecified a hierarchy of outcomes, used a multiplicity adjustment, or treated secondary analyses as exploratory. It also does not report the original statistical analysis plan. The recalculated pairwise p-values are unadjusted, so they should not be interpreted as if they account for every outcome and comparison in the study. The sponsor’s overall test is a distinct analysis, but the available record does not explain its relationship to any planned family of tests.
Missing-data handling is not reported in the registry record. The number of participants differs across posted outcome summaries, but the record does not explain the reasons for the differing analysis counts, whether data were missing, or how missing observations were handled. The reported group sizes should therefore be understood as the counts attached to the specific outcomes, not as proof that all randomized participants contributed to every analysis.
The record also does not report details about analysis populations, such as whether analyses followed an intention-to-treat principle, whether participants were excluded after randomization, or how protocol deviations were treated. These omissions limit assessment of possible bias from missing outcomes or analysis exclusions. They do not negate the posted results, but they mean that the statistical record is incomplete for evaluating those aspects of the analysis.
16. Safety Results
The registry reports serious adverse events as affected participants divided by participants at risk.
| Arm | Participants with serious adverse events | Participants at risk | Percentage |
|---|---|---|---|
| Control Beverage, Text Snack | 0 | 200 | 0.0% |
| Control Beverage, Control Snack | 0 | 205 | 0.0% |
| Control Beverage, Graphic Snack | 0 | 199 | 0.0% |
| Claim 1 Beverage, Text Snack | 0 | 197 | 0.0% |
| Claim 1 Beverage, Control Snack | 0 | 199 | 0.0% |
| Claim 1 Beverage, Graphic Snack | 0 | 195 | 0.0% |
| Claim 2 Beverage, Text Snack | 0 | 194 | 0.0% |
| Claim 2 Beverage, Control Snack | 0 | 193 | 0.0% |
| Claim 2 Beverage, Graphic Snack | 0 | 214 | 0.0% |
| Claim 3 Beverage, Text Snack | 0 | 198 | 0.0% |
| Claim 3 Beverage, Control Snack | 0 | 192 | 0.0% |
| Claim 3 Beverage, Graphic Snack | 0 | 188 | 0.0% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Control Beverage, Text Snack | 0 of 200 |
| Control Beverage, Control Snack | 0 of 205 |
| Control Beverage, Graphic Snack | 0 of 199 |
| Claim 1 Beverage, Text Snack | 0 of 197 |
| Claim 1 Beverage, Control Snack | 0 of 199 |
| Claim 1 Beverage, Graphic Snack | 0 of 195 |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 0% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| Control Beverage, Text Snack | 0 of 200 |
| Control Beverage, Control Snack | 0 of 205 |
| Control Beverage, Graphic Snack | 0 of 199 |
| Claim 1 Beverage, Text Snack | 0 of 197 |
| Claim 1 Beverage, Control Snack | 0 of 199 |
| Claim 1 Beverage, Graphic Snack | 0 of 195 |
The registry lists serious adverse events, other adverse events, and deaths for the 12 combined beverage-and-snack groups. Each group has zero serious adverse events, zero other adverse events, and zero deaths recorded in the posted figures. The numbers at risk differ among groups, ranging from 188 to 214 in the listed safety groups.
These entries describe what was recorded in the registry for this behavioral virtual-store study. They do not establish that no adverse experiences occurred outside the recorded categories or observation process. The registry does not report additional details about adverse-event definitions, collection procedures, or the duration of safety follow-up. The absence of recorded events should therefore be read as a reporting result, not as proof of zero risk in all settings.
17. What the Result Does, and Does Not, Mean
The primary result describes choices made by adults in a controlled online shopping task. In that setting, participants assigned to each nutrition-claim condition selected the grape-flavored fruit drink rather than 100% grape juice more often than participants in the no-claim control group. The recalculated risk differences and their confidence intervals quantify the observed pairwise contrasts and their sampling uncertainty.
The result does not show that participants bought the drink in a real store, that a child consumed it, or that the claims changed dietary intake or health. It also does not identify the psychological process behind the choices. The secondary survey outcomes may help characterize perceptions, but they do not establish that those perceptions caused the primary outcome.
The study tested particular claims in a virtual convenience-store environment and recruited a defined group of adults with young children. The registry record does not report whether the findings generalize to other populations, store settings, products, or claim wording. Generalization beyond the recruited participants and experimental setting requires evidence beyond these posted results.
The primary endpoint is a selection measure, not a clinical endpoint. The trial record therefore supports interpretation about a measured choice within the experiment, not conclusions about obesity, children’s health, or the health effects of fruit drinks. No treatment recommendation follows from these data. The statistical findings should be read alongside the incomplete reporting about the original analysis plan, missing data, and multiplicity.
18. Why This Trial Matters Statistically
This trial offers a clear example of how a randomized experiment can isolate the effect of product information on a choice made in a controlled environment. The randomized assignment creates a structured comparison between claim and no-claim beverage conditions, while the observed selection is a behavioral outcome rather than only an attitude or intention. That makes the endpoint statistically direct, even though it remains a simulated choice.
The record also illustrates why multiple scales of effect matter. A group percentage describes the observed outcome level; a risk difference describes an absolute contrast; and relative risks or odds ratios describe the contrast on relative scales. These measures answer related questions but are not interchangeable. Confidence intervals add information about the precision of the estimated contrast, while p-values address compatibility with a null model rather than practical importance.
Finally, the study demonstrates the value of separating a sponsor’s model-based analysis from unadjusted recalculations of posted summary data. Both can contribute to interpretation, but they are not necessarily the same analysis. Missing details about multiplicity, missing outcomes, and the original analysis plan matter when assessing how much weight to give the reported results. Transparent distinction between the observed outcome, the statistical estimate, and its limits is central to sound interpretation.
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.
- Participant counts were reconstructed from posted percentages and arm sizes, so small rounding differences are possible.
The primary outcome comes from an online virtual-store task, not a record of real purchases or consumption. Choices in a simulated environment may not represent decisions in ordinary shopping settings. The registry record does not report whether participants’ behavior in the task was validated against real-world purchasing behavior.
The participant description is specific to adults with young children and includes stated eligibility criteria related to the child’s recent fruit-drink consumption and the adult’s identity. The record does not give detailed demographic characteristics of the enrolled sample or explain how closely the completed sample matched the intended recruitment population. Generalizability beyond the enrolled participants is therefore uncertain.
The trial combined beverage claims with snack-label conditions across 12 store versions. The record does not describe whether or how snack condition was handled in the sponsor’s primary model, or whether interactions between beverage and snack conditions were assessed. It also does not explain which party was masked under the single-masked designation.
For the posted outcomes, the registry does not report the original analysis plan, covariate adjustments, missing-data procedures, analysis populations, or multiplicity strategy. Those omissions limit assessment of robustness and of how the reported analyses relate to prespecified hypotheses. The reported safety entries have no recorded events, but collection and follow-up details are not reported in the registry record.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: Studying the Impact of Product Packaging in a Virtual Store Environment — NCT04381481.
- Registry record last updated 2021-06-18; status last verified 2021-05.
- Results first posted 2021-06-18.
- 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.
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23. Record Summary
NCT04381481 is a completed randomized, single-masked, parallel behavioral study of nutrition claims in an online virtual convenience store. It enrolled 2374 participants and compared three fruit-drink claim conditions with a no-claim control, alongside different snack-label conditions. The primary outcome was selection of a grape-flavored fruit drink rather than 100% grape juice during the shopping task.
The posted arm percentages were higher in each claim group than in control, and the registry reports an overall logistic-regression result of p <0.001. Recalculated unadjusted risk differences are positive for all three claim-versus-control comparisons. These findings concern a simulated choice and should not be extended to real-world purchases, consumption, or health outcomes. Details about multiplicity, missing-data handling, and the original analysis plan are not reported in the registry record.