A Walking Intervention Through Text Messaging: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for A Walking Intervention Through Text Messaging (NCT02053259), a randomized na study. The primary outcome is Change in Fitbit-measured Steps/Day and Moderate-to-vigorous Physical Activity Between Study Arms..

2. Clinical Question

3. Trial Design

This was a randomized, single-masked, 2×2 factorial trial sponsored by Arizona State University. The registry lists an enrollment of 96 and a completed status. The study started in 2014-02, with primary completion in 2014-12. The phase is listed as NA. The four groups combined two goal-setting approaches—adaptive or static—with two reinforcement approaches—immediate or delayed financial reinforcement.

In a factorial design, participants are assigned combinations of interventions, allowing investigators to assess the separate, or main, effects of each factor. The registry says the goal-setting comparison pools participants across reinforcement conditions, while the reinforcement comparison pools participants across goal-setting conditions. The primary description says the main-effect sample size was 96 for each comparison, with 49 participants in the adaptive-goal group and 47 in the static-goal group, and 49 in the immediate-reinforcement group and 47 in the delayed, non-contingent reinforcement group.

All four groups received the intervention through a semi-automated text message system developed by the study team. The stated primary measurement period was daily for 4 months. The registry also lists outcomes related to fitness, body composition, cardiovascular risk and inflammatory markers, and self-reported physical activity. The record does not report detailed eligibility criteria, the masking role, the allocation procedure beyond randomized assignment, or the original sample-size justification.

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

Analysis population for the primary outcome, as defined in the registry: 2x2 factorial design main effects reported. Main effects for goal setting (n=49 for adaptive vs. n=47 for static) and reinforcement conditions (n=49 for immediate reinforcement vs. n=47 for delayed, non-contingent reinforcement).

5. Baseline Characteristics

The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.

6. Primary Endpoint

The registry lists the primary outcome as Change in Fitbit-measured Steps/Day and Moderate-to-vigorous Physical Activity Between Study Arms., measured over Daily for 4 months.

The primary endpoint is described as change in Fitbit-measured steps per day and moderate-to-vigorous physical activity between study arms, measured daily for 4 months. Steps per day provide a continuous measure of activity volume: each participant’s activity is represented by a numerical count rather than a category such as active or inactive. Continuous outcomes can be summarized with a mean and a measure of spread, which helps describe both the group’s typical recorded activity and variation among participants.

The registry’s stated primary aim focuses on change in physical activity, specifically pedometer-measured steps per day in its brief summary, and the primary outcome title names Fitbit measurement. The posted group results give means and standard deviations for steps per day. They do not separately report a numerical estimate for moderate-to-vigorous physical activity or a clearly identified change-from-baseline estimate. Consequently, the numerical interpretation is limited to the posted steps-per-day results and their listed comparisons; the exact construction of a change score is not reported in the registry record.

Step counts are useful for an intervention focused on walking because they quantify movement over time in a way that can be compared across groups. In general, a mean difference describes the estimated separation between group averages, while the standard deviation describes how dispersed individual measurements are within a group. Neither measure alone describes every participant’s experience.

7. Results Posted in the Registry

• Static Goals: mean 9,836 versus 9,695 on control; difference 141.00 (95% CI -1,435 to 1,717), standardized effect d = 0.04; z-test p = 0.861.
• Immediate Reinforcement: mean 10,562 versus 9,695 on control; difference 867.00 (95% CI -713.02 to 2,447), standardized effect d = 0.22; z-test p = 0.282.
• Delayed Non-contingent Reinforcement: mean 8,969 versus 9,695 on control; difference -726.00 (95% CI -2,276 to 824.30), standardized effect d = -0.19; z-test p = 0.359.

8. Statistical Interpretation

9. Statistical Methods Explained

The numerical results concern a continuous outcome summarized by means and standard deviations. The comparisons are expressed as mean differences, with confidence intervals and unadjusted p-values. The registry describes the design as a 2×2 factorial trial and states that main effects pool participants across the other factor. That pooling is central to the intended interpretation: the goal-setting effect compares adaptive with static goals across reinforcement assignments, while the reinforcement effect compares timing groups across goal-setting assignments.

What does a factorial main effect represent?

In general, a factorial design studies more than one intervention factor within the same trial. A main effect estimates the average contrast for one factor while combining the levels of another factor. This can use information from all relevant combinations rather than treating each combination as an isolated comparison. The interpretation depends on the analysis actually used and on whether effects of one factor vary across levels of the other. The registry states the intended pooling but does not report an interaction estimate or a detailed model specification.

The four assigned groups were adaptive goals with immediate reinforcement, adaptive goals with delayed reinforcement, static goals with immediate reinforcement, and static goals with delayed reinforcement. The primary description reports the pooled group sizes for the two main effects. The group means and comparison summaries are posted separately. Their precise statistical relationship and any adjustment for repeated daily measurements are not detailed in the registry record, so no particular longitudinal model should be assumed.

How should a mean difference be read?

In general, a mean difference expresses how far apart two group averages are, in the outcome’s units. A positive or negative sign depends on the ordering of the groups in the contrast. The registry provides a named comparison and an estimate for each result. The estimate is not an individual-level change and does not indicate that every participant changed by that amount. Because the endpoint title refers to change but the posted values do not clearly identify a baseline-adjusted or change-score calculation, the exact estimand is not reported in the registry record.

The standard deviation describes the spread of measurements among participants in a group. It is different from the standard error, which describes uncertainty in an estimated mean. The registry includes standard deviations for the arm summaries and pooled standard deviations for the contrasts. In general, larger variability can reduce precision when group sizes are otherwise similar. The reported standard deviations indicate substantial variation in steps across participants.

What do confidence intervals and p-values add?

In general, a confidence interval gives a range of values compatible with the data under the method used to construct it. Its width conveys precision: a wider interval leaves more uncertainty about the size and direction of the underlying difference. An interval crossing zero means the results are compatible with no average difference, but also with differences on either side of zero. A p-value measures how unusual the data would be under a specified null hypothesis and statistical model. It is not the probability that the null hypothesis is true, nor a measure of clinical importance.

The listed p-values are labelled unadjusted. The registry does not report whether they come from a repeated-measures model, an adjusted analysis, or another specific inferential method. It also does not report the analysis population, handling of missing daily measurements, covariate adjustments, or an analysis plan. The p-values should therefore be interpreted as the posted, unadjusted results, not as a fully documented account of the trial’s inferential procedure.

Why can over-dispersion matter?

In general, over-dispersion means that variability in the observed data is greater than a statistical model expects. When a model underestimates variability, standard errors may be too small and confidence intervals too narrow. Step counts are continuous measurements, and the record reports standard deviations, but it does not report an over-dispersion assessment or a model that requires such an adjustment. Over-dispersion should not be presumed to have occurred in this trial; it is a general consideration when a statistical model’s assumptions are evaluated.

The registry lists an analysis count of 0 while also displaying primary comparison estimates and p-values. That combination leaves the analysis documentation incomplete. Detailed model assumptions, multiplicity handling, interim analyses, missing-data methods, and the original statistical analysis plan are not reported in the registry record. The results can be described as posted, but the precise analytic pathway cannot be reconstructed from the record.

10. Confidence Intervals and Precision

Precision is best assessed through the confidence intervals, not by looking at the point estimates alone. The adaptive-versus-static-goal estimate is 141.0 steps, with a 95% confidence interval from -1435.0 to 1717.0. The interval crosses zero and spans values in both directions. It therefore leaves considerable uncertainty about whether the average contrast favors adaptive goals, static goals, or neither.

The Immediate Reinforcement estimate is 867.0 steps, with a 95% confidence interval from -713.0 to 2447.0. The Delayed Non-contingent Reinforcement estimate is -726.0 steps, with a 95% confidence interval from -2276.0 to 824.3. Each interval includes zero and extends to differences on either side. The estimates are thus not precise enough to isolate a single direction or a narrow magnitude of difference.

In general, a 95% confidence interval describes the uncertainty around an estimate under the analysis assumptions; it does not mean that 95% of participants’ values fall inside the interval. Nor does the interval describe the range of individual step counts. The group standard deviations, which range from 3802.0 to 4032.0 steps, describe participant-level spread, whereas the intervals describe uncertainty in group contrasts.

The registry does not report confidence intervals for the secondary outcomes, and no numerical result for those outcomes is posted. Precision therefore cannot be assessed for them from the registry record. The record also does not provide enough analysis detail to evaluate the interval-construction method or any adjustments for the repeated daily measurements.

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, not observed trial results. They give participants per arm for 80% power and participants per arm for 90% power. In plain terms, the 80% column describes the planned group size associated with an 80% chance of detecting the specified effect if that effect and the stated assumptions were correct; the 90% column uses a higher target chance of detection. Neither column is a count of participants enrolled in this trial.

The illustration uses a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. It sets the effect to detect at the stated fraction of the observed effect. The rows therefore explore planning for 100%, 75%, and 50% of the observed effect. Smaller effects need more participants to detect under the same planning assumptions. For a continuous outcome, the entries are participants per arm, not a total across both arms and not total events.

These calculations are based on the observed effect rather than the trial’s original design assumptions. They are not observed power. The trial’s own sample-size justification and original planning assumptions are not reported in the registry record. The curve should be read as a visual representation of the same planning relationship, not as additional evidence about the trial’s achieved result.

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 = 141.000; pooled standard deviation σ = 3939.202.
2. n = 2 × (1.96 + 0.842)² × 3939.202² / 141.000² = 12,252.3, rounded up to 12,253 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 <- 141                      # observed difference in means
sigma <- 3939.20176599162                     # 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(2053259)
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 = 12,253 (80% power), 16,403 (90% power)
 75% of observed effect: n per arm = 21,782 (80% power), 29,160 (90% power)
 50% of observed effect: n per arm = 49,010 (80% power), 65,610 (90% power)
power.t.test: 12253.2 
Simulated power at n = 12,253 per arm: 0.795 (20000 replicates)

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

13. Multiplicity, Missing Data and Analysis Populations

The trial includes more than one outcome and more than one factorial comparison. The registry identifies a primary endpoint and lists secondary outcome areas, while the primary description specifies main effects for goal setting and reinforcement. Looking at multiple outcomes or contrasts can increase the chance of finding an apparently unusual result by chance. In general, multiplicity procedures account for this issue by controlling or describing the overall error rate across a family of tests.

The posted p-values are explicitly unadjusted. The registry does not report a multiplicity adjustment, a hierarchy for testing outcomes, or which comparisons formed a prespecified testing family. It also does not report whether the interaction between goal setting and reinforcement was tested. Consequently, the displayed p-values should not be treated as multiplicity-adjusted evidence, and the relationship between the stated hypotheses and all analyses cannot be fully assessed.

The record names five secondary outcome areas, but numerical results for those outcomes are not reported in the registry record. The registry’s analysis count is 0 even though it also displays primary comparison estimates and p-values. This makes the analysis documentation incomplete rather than evidence that no analysis occurred.

Missing-data methods and analysis populations are not reported in the registry record. In particular, the record does not explain whether all randomized participants were included, how incomplete daily step measurements were handled, or whether participants with missing outcome data were excluded or otherwise accounted for. It also does not report interim analyses, the full statistical analysis plan, or whether any analyses were adjusted for baseline characteristics. These omissions limit assessment of potential bias and of how closely the posted comparisons follow the planned analysis.

14. 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 0% reporting threshold.

The adverse-event record reports zero serious adverse events and zero other adverse events in each of the four groups. The numbers at risk were 25 in Arm 1, 24 in Arm 2, 24 in Arm 3, and 23 in Arm 4 for both the serious and other adverse-event summaries. No serious-event terms are listed. Death counts are not reported in the registry record.

These figures describe what is recorded for the listed groups; they do not establish that no unrecorded events occurred. The safety groups are labelled Arm 1 through Arm 4 in the adverse-event record, and their mapping to the named intervention combinations is not reported there. The record also does not describe event-collection procedures, duration of safety follow-up, or whether adverse events were assessed for relatedness to the intervention. Accordingly, the counts should be read as the registry’s posted safety summary, not as a complete account of all possible harms.

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

The posted primary results estimate average differences in steps per day for goal-setting and reinforcement comparisons. Each reported confidence interval includes zero, and each unadjusted p-value is listed alongside its estimate. The results therefore do not provide a precise separation between the compared groups. They leave uncertainty about both the direction and size of any average difference.

This does not show that the interventions are equivalent, nor does it prove that there is no difference. Establishing equivalence or ruling out differences of a meaningful size requires a defined margin and an analysis designed for that question; such a margin is not reported in the registry record. Likewise, the estimates should not be presented as proof that one approach is superior. The registry’s hypotheses are stated, but the posted estimates do not resolve them with precision.

The primary outcome title includes Fitbit-measured steps per day and moderate-to-vigorous physical activity, while the posted numerical results are steps-per-day summaries. A distinct numerical result for moderate-to-vigorous physical activity is not reported in the registry record. The record lists secondary outcomes concerning fitness, body composition, cardiovascular measures, biomarkers, and self-reported activity, but their results are also not reported.

In general, statistical estimates describe group averages under the analysis used; they do not predict an individual participant’s response. The findings are specific to the enrolled study population, the text-message intervention and the reported measurement period. Because eligibility details, missing-data handling, and the full analysis methods are not reported, the record does not support a broader claim about other populations or settings. No clinical recommendation follows from these statistical summaries alone.

16. Why This Trial Matters Statistically

This trial is statistically interesting because it uses a factorial design to examine two intervention components together: goal-setting approach and reinforcement timing. Pooling across the other factor can provide main-effect comparisons that use participants from multiple assigned combinations. It also makes the estimand important: a main effect is an average contrast across the other factor’s levels, not necessarily the effect within every individual combination.

The record states that the adaptive-goal group is compared with the static-goal group and that immediate reinforcement is compared with delayed reinforcement. It also describes a hypothesis about the combined adaptive-goals-and-reinforcement group. Those are distinct questions: main effects address average factor contrasts, while a claim about a particular combination concerns the joint pattern of factors. An interaction estimate or detailed model is not reported, so the combined-group hypothesis cannot be assessed from the posted main-effect summaries alone.

The case also illustrates why effect estimates and precision matter alongside p-values. The estimates are accompanied by broad confidence intervals that include zero, while the standard deviations show appreciable spread in step counts. The sample-size illustrations make clear that planning requirements depend strongly on the effect chosen for detection. Because those illustrations use observed effects and are not the original design justification, they do not explain how the enrolled sample size was selected.

Finally, a registry entry can include a completed-trial status and numerical primary comparisons while leaving important analytical details and secondary results unreported. Readers can describe the posted estimates, but a full assessment of the prespecified analysis, missing data, multiplicity, and secondary endpoints requires information not reported 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 registry record leaves several trial-specific uncertainties. Although the primary endpoint is framed as change in steps per day and moderate-to-vigorous physical activity, the posted numerical results give means and standard deviations for steps per day without clearly identifying a change-from-baseline estimate. The endpoint title names Fitbit measurement, while the brief summary refers to pedometer-measured steps. The record does not explain the relationship between those descriptions or provide a separate numerical result for moderate-to-vigorous physical activity.

The factorial design description says that the main effects pool participants across the other factor, but the detailed statistical model, interaction analysis, and exact construction of the posted contrasts are not reported. The record lists an analysis count of 0 despite displaying estimates and p-values. It also does not report the analysis populations, missing daily-measurement methods, original sample-size justification, interim analyses, or a full analysis plan.

The study enrolled 96 participants, and the confidence intervals for the posted contrasts are broad. No results are reported for the five listed secondary outcome areas. The record also does not give detailed eligibility criteria, explain who was masked, or describe the method and duration of adverse-event collection. Although zero serious and other adverse events are recorded for each group, death counts are not reported, and the adverse-event arm labels are not linked to the intervention combinations in that summary.

These reporting gaps limit evaluation of precision, potential missing-data bias, multiplicity, and generalizability. They do not by themselves establish that the trial methods were inadequate; they indicate that the registry record does not contain enough detail to assess those aspects fully.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: A Walking Intervention Through Text Messaging — NCT02053259.
• Registry record last updated 2021-09-22; status last verified 2021-08.
• Results first posted 2020-07-29.
• 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

NCT02053259, titled “A Walking Intervention Through Text Messaging,” is a completed randomized, single-masked, 2×2 factorial trial sponsored by Arizona State University. The registry lists enrollment of 96 and a primary measurement period of daily for 4 months. The four intervention combinations varied adaptive versus static goals and immediate versus delayed financial reinforcement, delivered through a semi-automated text message system.

The primary outcome concerns Fitbit-measured steps per day and moderate-to-vigorous physical activity. Posted numerical comparisons for steps per day have confidence intervals that include zero and are broad. The registry lists secondary outcomes but does not report their numerical results. Details about the original sample-size justification, missing-data methods, multiplicity handling, analysis populations, and the full statistical analysis are not reported in the registry record.