Higher Water Intake Predicts Very Slightly Higher Walk Or Run Distance for Population

Higher Water Intake Predicts Very Slightly Higher Walk Or Run Distance for Population

Contents

Variables

A
Water 228
A
Walk or Run Distance 891

Categories

A
Foods 13415
A
Physical Activity 1719

Actions

A
Join Study
A
Your Data

Tags

Medium Confidence
Very Weak Effect Size
Positive Relationship
Population Study
cause image gauge image effect image
Participants reported a 13.7% average increase in Walk Or Run Distance following above average Water Intake.

Abstract

Walk Or Run Distance was generally 14% higher than average after a total of 1690 milliliters of Water over the previous 6 days.

Aggregated data from 86 study participants suggests with a MEDIUM degree of confidence (p=0.143, 95% CI -845.52 to 845.691) that Water has a very weakly positive predictive relationship (R=0.0853) with Walk Or Run Distance.

The highest quartile of Walk Or Run Distance measurements were observed following an average 2030 milliliters Water per day.

The lowest quartile of Walk Or Run Distance measurements were observed following an average 1600 milliliters of Water per day.

After an onset delay of 30 minutes, Walk Or Run Distance is typically 5% lower than average over the 6 days following around 1600 milliliters of Water Water.

Keywords: Water, Walk Or Run Distance, N-of-1 trials, real-world evidence, causal inference, observational study

High Confidence: With 86 participants, these findings have strong statistical power.

Results

Primary Findings

Analysis of 362 paired observations from 86 participants revealed a minimal reduction in Walk Or Run Distance following above-average Water exposure.

0.0%
Change from Baseline
Minimal effect on Walk Or Run Distance
0.04
Predictor Impact Score
Insufficient evidence for causal relationship

Supporting Statistics

Medium
Confidence
0.085
Correlation (r)
p = 0.522
Significance
z = 0.00
Effect Magnitude
φ = 0.95
Temporality

What This Means

When participants had above-average Water:

  • Walk Or Run Distance decreased by 0.0% on average
  • Temporal analysis supports Water as the predictor (not the outcome)

Interpreting the Predictor Impact Score

The Predictor Impact Score (PIS) integrates multiple Bradford Hill causal criteria into a single metric. Use this guide to interpret the score:

PIS Range Interpretation Recommended Action
≥ 0.5 Strong evidence High priority for RCT validation
0.3 - 0.5 Moderate evidence Consider for experimental investigation
0.1 - 0.3 Weak evidence Monitor for additional data
< 0.1 Insufficient evidence Low priority; may be noise

Note: PIS is a prioritization heuristic, not proof of causation. High scores indicate relationships worth investigating, not confirmed causal effects.

Optimal Daily Values (Precision Dosing)

Based on the observed relationship, we can estimate the predictor values associated with the best and worst outcomes. These values enable personalized dosing recommendations.

ℹ️ Moderate Confidence: Based on 86 participants. Values are reasonably reliable but may refine with additional data.

1,693.2 mL
Value Predicting Higher Walk Or Run Distance
Average Water when Walk Or Run Distance exceeded its mean
374.3 mL
Value Predicting Lower Walk Or Run Distance
Average Water when Walk Or Run Distance was below its mean

What This Suggests

Walk Or Run Distance tended to be highest when Water was around 1,693.2 mL.

Important: These values reflect correlations, not guaranteed causal effects. Individual responses may vary. Use as a starting point for personal experimentation, not as a definitive prescription. Consult healthcare providers before making treatment decisions.

Population Correlation

Water Distribution

Walk Or Run Distance Distribution

Relationship Analysis

Statistical Summary

Relationship Statistics

Property Value
Cause Variable Name Water Intake
Effect Variable Name Walk Or Run Distance
Sinn Predictive Coefficient 0.042642147148939
Confidence Level MEDIUM
Confidence Interval 845.60569261281
Forward Pearson Predictive Coefficient 0.0853
Critical T Value 1.6511744186047
Total Water Intake Over Previous 6 days Before ABOVE Average Walk Or Run Distance 2030 milliliters
Total Water Intake Over Previous 6 days Before BELOW Average Walk Or Run Distance 1600 milliliters
Duration of Action 6 days
Effect Size very weakly positive
Number of Paired Measurements 362
Optimal Pearson Product 0.046893261371305
P Value 0.14319007552721
Statistical Significance 0.5221
Strength of Relationship 845.60569261281
Study Type population
Analysis Performed At 2026-01-04
Number of Participants 86

Water Info

Property Value
Variable Name Water (mL)
Aggregation Method SUM
Analysis Performed At 2020-10-11
Duration of Action 14 days
Filling Value 0
Kurtosis 168.9035754896
Maximum Allowed Value 5000 milliliters
Mean 291.96324979639 milliliters
Median 234.04866468843 milliliters
Minimum Allowed Value 0 milliliters
Number of Aggregate Predictors 0
Number of Aggregate Outcomes 228
Number of Measurements 58290
Number of Measurements (including those generated by tagged, joined, or child variables) 5630
Public true
Onset Delay 30 minutes
Standard Deviation 222.15818986681
Unit Milliliters
User Variables 656
UPC 075720004096
Variable Category Foods
Variable ID 109592
Variance 256166.90856561

Walk or Run Distance Info

Property Value
Variable Name Walk Or Run Distance
Aggregation Method SUM
Analysis Performed At 2020-09-11
Duration of Action 7 days
Kurtosis 18.843598392696
Maximum Allowed Value 175000 meters
Mean 3558.0042632859 meters
Median 3158.90008036 meters
Minimum Allowed Value 1 meters
Number of Aggregate Predictors 642
Number of Aggregate Outcomes 249
Number of Measurements 123085
Number of Measurements (including those generated by tagged, joined, or child variables) 87104
Public true
Onset Delay 0 seconds
Standard Deviation 2361.166855319
Unit Meters
User Variables 378
UPC 744960759935
Variable Category Physical Activity
Variable ID 1304
Variance 9674812.3231088

Introduction

Background

Water (Foods) and Walk Or Run Distance (Physical Activity) are both important factors in understanding human health and well-being. This study investigates the relationship between these two variables using real-world observational data.

Traditional randomized controlled trials (RCTs), while the gold standard for causal inference, are often impractical, expensive, or unethical for studying many health relationships. Aggregated N-of-1 observational studies offer a complementary approach that leverages within-subject comparisons across large populations to identify meaningful patterns.

Research Question

Does Water affect Walk Or Run Distance?

Additionally, we seek to determine:

  1. What is the direction and magnitude of any effect?
  2. How confident can we be in this relationship based on the available data?
  3. What are the optimal levels of Water for maximizing Walk Or Run Distance?

Study Objective

The objective of this study is to determine the nature of the relationship (if any) between Water and Walk Or Run Distance. Additionally, we attempt to determine the Water (mL) values most likely to produce optimal Walk Or Run Distance values.

Study Overview

This is a population-level observational study using aggregated N-of-1 methodology. By aggregating individual N-of-1 experiments, we can identify population-level patterns while accounting for the substantial individual variation that exists in most health relationships. Effect sizes are reported as percent change from baseline, enabling intuitive interpretation and comparison across different measures.

Full Methodology: Framework for Real-World Evidence-Based Pharmacovigilance: Aggregated N-of-1 Trials for Quantifying Treatment Effects

Discussion

Interpretation of Findings

Participants experienced a 0.0% reduction in Walk Or Run Distance following above-average Water exposure. The Predictor Impact Score (PIS) of 0.04 indicates insufficient evidence for a causal relationship.

Statistical Significance

Using a two-tailed t-test with alpha = 0.05, it was determined that the change in Walk Or Run Distance is statistically significant at a 95% confidence interval. The p-value of 0.5221 indicates there is less than a 52.21% probability that this result occurred by chance.

T-Test Details
Observed t-value: 2.489
Critical t-value: 1.651

Since t = 2.49 > 1.65, we reject the null hypothesis.

Biological Plausibility

A plausible bio-chemical mechanism between predictor and outcome is critical for interpreting observational findings. This is where human judgment excels beyond statistical analysis.

Community feedback on the biological plausibility of this relationship is still being collected. Consider the known mechanisms by which Water might influence Walk Or Run Distance.

Bradford Hill Criteria Assessment

The Bradford Hill criteria provide a framework for assessing causality in observational studies. Our methodology operationalizes six of the nine criteria through the Predictor Impact Score (PIS):

Criterion How Addressed Metric
Strength Effect size magnitude Percent change from baseline (Δ%), z-score
Consistency Cross-participant replication Number of users (N), number of pairs (n)
Temporality Predictor precedes outcome Temporality factor (φ), onset delay (δ > 0)
Biological Gradient Dose-response relationship Gradient coefficient (φgradient)
Plausibility Biological mechanism assessment Community votes on mechanism plausibility
Specificity Category appropriateness Interest factor (finterest)

Predictor Impact Score (PIS)

The PIS integrates multiple Bradford Hill criteria into a composite metric quantifying how reliably a predictor affects an outcome. Higher scores indicate stronger evidence:

Population-Level PIS:

$$\text{PIS}_{\text{agg}} = |r_{\text{forward}}| \cdot w \cdot \phi_{\text{users}} \cdot \phi_{\text{pairs}} \cdot \phi_{\text{change}} \cdot \phi_{\text{gradient}}$$

Where φ-factors are saturation functions approaching 1 as evidence accumulates:

  • φusers = 1 - e-N/10 (user saturation)
  • φpairs = 1 - e-n/nsig (pair saturation)
  • φchange = 1 - e-Δspread/Δsig (effect spread saturation)
  • w = weighted average of plausibility votes

Temporality Assessment

We assess evidence for correct causal direction using the temporality factor:

$$\phi_{\text{temporal}} = \frac{|r_{\text{forward}}|}{|r_{\text{forward}}| + |r_{\text{reverse}}|}$$

Values approaching 1 indicate the predictor precedes the outcome (supporting causation); values near 0.5 suggest ambiguous directionality; values near 0 suggest reverse causation or confounding by indication.

Limitations

As with any observational study, correlation does not prove causation. Key limitations include:

  • Unmeasured confounders: Variables not tracked may influence results
  • Self-selection bias: Health trackers may differ from the general population
  • Measurement error: Self-reported data may contain recall bias
  • Confounding by indication: Sicker individuals may use more treatments

However, within-subject comparison and temporal precedence analysis partially mitigate these limitations. If the relationship is merely coincidental, as participants independently modify their Water values, the observed strength will decline over time. Spurious correlations naturally dissipate as more data is collected.

Future Directions

Future research should examine:

  • Subgroup analyses to identify individual differences in response
  • Potential confounders and mediators of the observed relationship
  • Optimal dosing and timing for Water
  • Confirmation through prospective or randomized designs
  • Biological mechanisms underlying the observed effects

Conclusion

Above-average Water was associated with a 0.0% reduction in Walk Or Run Distance—a minimal effect. The Predictor Impact Score of 0.04 indicates this relationship is requiring additional data before conclusions.

Bottom Line: Based on a PIS of 0.04 and a 0.0% effect size, this relationship currently lacks sufficient evidence. Continue monitoring as more data becomes available.

These findings contribute to our understanding of how Water may influence Walk Or Run Distance in real-world conditions. While preliminary, these results may inform future research directions.

Help End Unnecessary Suffering

Current clinical trials are 82x more expensive than necessary and take 17 years to bring treatments to market. Pragmatic trials integrated into standard healthcare could reduce costs from $41,000 to $500 per participant and compress timelines to just 2 years. Learn how redirecting just 1% of global military spending could accelerate cures for the 2 billion people suffering from treatable diseases.

Make Suffering Optional

Methods

Study Design

This study is based on data donated by 86 participants. Thus, the study design is equivalent to the aggregation of 86 separate n=1 observational natural experiments.

This within-subject design is powerful because it controls for all stable individual characteristics (genetics, baseline health status, socioeconomic factors) that might otherwise confound the relationship between variables.

Data Analysis

Temporal Assumptions

The analysis incorporates temporal assumptions about the relationship between variables:

  • Onset Delay: It was assumed that 30 minutes would pass before a change in Water would produce an observable change in Walk Or Run Distance.
  • Duration of Action: It was assumed that Water could produce an observable change in Walk Or Run Distance for as much as 6 days after the stimulus event.

Statistical Methods

For each participant, we calculated the Pearson correlation coefficient between Water values and subsequent Walk Or Run Distance values. Individual correlations were then aggregated using Fisher's z-transformation to produce a population-level estimate:

Individual Correlation:

$$r_i = \frac{\sum(x_{ij} - \bar{x}_i)(y_{ij} - \bar{y}_i)}{\sqrt{\sum(x_{ij} - \bar{x}_i)^2 \sum(y_{ij} - \bar{y}_i)^2}}$$

Fisher's Z-Transformation:

$$z_i = \frac{1}{2} \ln\left(\frac{1 + r_i}{1 - r_i}\right)$$

Aggregated Correlation:

$$\bar{r} = \tanh(\bar{z}) \quad \text{where} \quad \bar{z} = \frac{1}{N}\sum_{i=1}^{N} z_i$$

Effect Size Calculation

Effect sizes are reported as percent change from baseline. For each participant, we compare the outcome following above-average predictor values to the overall baseline outcome:

$$\Delta\%_{\text{baseline}} = \frac{\bar{O}_{\text{follow-up}} - \bar{O}_{\text{baseline}}}{\bar{O}_{\text{baseline}}} \times 100$$

Effect Magnitude (Z-Score)

To assess effect magnitude relative to natural variability, we calculate the z-score:

$$z = \frac{|\Delta\%_{\text{baseline}}|}{\text{RSD}_{\text{baseline}}}$$

where RSDbaseline is the relative standard deviation of outcome during baseline period

A z-score > 2 indicates statistical significance (p < 0.05), meaning the observed change exceeds typical baseline fluctuation and is unlikely due to random variation.

Statistical Significance

Correlation significance is assessed using a two-tailed t-test:

$$t = \frac{r\sqrt{n-2}}{\sqrt{1-r^2}}$$

We reject the null hypothesis (ρ = 0) at α = 0.05 when |t| exceeds the critical value, providing statistical evidence that the observed relationship is not due to chance.

Data Sources

Water data was primarily collected using Fitbit. Fitbit makes activity tracking easy and automatic.

Walk Or Run Distance data was primarily collected using Fitbit. Fitbit makes activity tracking easy and automatic.

Data Quality

Data quality measures were applied to ensure reliable results:

  • Minimum Data Requirement: Only participants with sufficient paired observations were included in the analysis.
  • Outlier Handling: Extreme values were winsorized to reduce the influence of measurement errors.
  • Missing Data: Days with missing values were handled using appropriate filling strategies based on the variable type.
  • Test User Exclusion: Test accounts and invalid users were excluded from all analyses.

Principal Investigator

Program & Methods

Mike P. Sinn
Sinn, M. P.

Designed and implemented data collection, aggregation, causal inference pipeline, and automated study generation framework. Developed the Predictor Impact Score methodology operationalizing Bradford Hill criteria for ranking causal relationships in observational data. When he tells people this at parties, they usually say they have to go check on their car.

Individual study outputs are automated, reproducible, and open to external audit. (Which I would seriously recommend.)

Contact

Cite This Study

APA Format
Sinn, M. P. (2026). Causal Analysis: Does Water (mL) Affect Walk Or Run Distance?. The Journal of Citizen Science. https://studies.crowdsourcingcures.org/study/cause-109592-effect-1304-population-study
BibTeX 
@misc{sinn_cause_109592_effect_1304_population_study_2026,
  author = {Sinn, Mike P.},
  title = {Causal Analysis: Does Water (mL) Affect Walk Or Run Distance?},
  year = {2026},
  publisher = {The Journal of Citizen Science},
  url = {https://studies.crowdsourcingcures.org/study/cause-109592-effect-1304-population-study},
  note = {Accessed: January 6, 2026}
}
Chicago/Turabian
Sinn, Mike P. "Causal Analysis: Does Water (mL) Affect Walk Or Run Distance?." The Journal of Citizen Science. Accessed January 6, 2026. https://studies.crowdsourcingcures.org/study/cause-109592-effect-1304-population-study.
Harvard
Sinn, M.P., 2026. Causal Analysis: Does Water (mL) Affect Walk Or Run Distance?. [Aggregated N-of-1 Study] The Journal of Citizen Science. Available at: https://studies.crowdsourcingcures.org/study/cause-109592-effect-1304-population-study [Accessed January 6, 2026].

Study Type: Aggregated N-of-1 Observational Mega-Study
Evidence Level: Level II (Real-World Evidence)
Methodology: Bradford Hill Criteria with Predictor Impact Score (PIS)

References

This framework was originally developed in 2013 based on the Bradford Hill criteria. Subsequent literature has independently validated similar approaches to causal inference from observational data:

  1. Hill, A.B. (1965). The environment and disease: association or causation? Proceedings of the Royal Society of Medicine, 58(5), 295-300. [Bradford Hill criteria]
  2. Lillie, E.O., et al. (2011). The n-of-1 clinical trial: the ultimate strategy for individualizing medicine? Personalized Medicine, 8(2), 161-173. [N-of-1 methodology]
  3. Pearl, J. (2009). Causality: Models, Reasoning, and Inference . Cambridge University Press. [Causal inference]
  4. Hernán, M.A., & Robins, J.M. (2020). Causal Inference: What If . Chapman & Hall/CRC. [Free textbook]
  5. FDA (2018). Framework for FDA's Real-World Evidence Program . U.S. Food and Drug Administration. [Regulatory context]
  6. Duan, N., et al. (2013). Single-patient (n-of-1) trials: a pragmatic clinical decision methodology . Journal of Clinical Epidemiology, 66(8), S21-S28.
  7. Platt, R., et al. (2018). The FDA Sentinel Initiative—an evolving national resource . New England Journal of Medicine, 379(22), 2091-2093.

This information is for research and educational purposes only, not medical advice. Consult a healthcare provider before making health decisions. Terms of Service

LinkedIn Reddit