Higher Water Intake Predicts Slightly Higher Calories Burned for Population

Higher Water Intake Predicts Slightly Higher Calories Burned for Population

Contents

Variables

A
Water 228
A
Calories Burned 878

Categories

A
Foods 13415
A
Physical Activity 1719

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High Confidence
Weak Effect Size
Positive Relationship
Population Study
cause image gauge image effect image
Participants reported a 11% average increase in Calories Burned following above average Water Intake.

Abstract

Calories Burned was generally 9% higher than average after a total of 2110 milliliters of Water over the previous 14 days.

Aggregated data from 41 study participants suggests with a HIGH degree of confidence (p=0.0757, 95% CI -102.426 to 102.902) that Water has a weakly positive predictive relationship (R=0.238) with Calories Burned.

The highest quartile of Calories Burned measurements were observed following an average 205 milliliters Water per day.

The lowest quartile of Calories Burned measurements were observed following an average 4010 milliliters of Water per day.

After an onset delay of 30 minutes, Calories Burned is typically 2% lower than average over the 14 days following around 4010 milliliters of Water Water.

Keywords: Water, Calories Burned, N-of-1 trials, real-world evidence, causal inference, observational study

High Confidence: With 41 participants, these findings have strong statistical power.

Results

Primary Findings

Analysis of 18,421 paired observations from 41 participants revealed a modest improvement in Calories Burned following above-average Water exposure.

+11.4%
Change from Baseline
Modest effect on Calories Burned
0.61
Predictor Impact Score
Strong evidence for causal relationship

Supporting Statistics

High
Confidence
0.238
Correlation (r)
p = 0.445
Significance
z = 0.64
Effect Magnitude
φ = 1.00
Temporality

What This Means

When participants had above-average Water:

  • Calories Burned increased by 11.4% on average
  • The Predictor Impact Score of 0.61 suggests this relationship warrants high priority for experimental validation
  • 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 41 participants. Values are reasonably reliable but may refine with additional data.

2,108.5 mL
Value Predicting Higher Calories Burned
Average Water when Calories Burned exceeded its mean
75.1 mL
Value Predicting Lower Calories Burned
Average Water when Calories Burned was below its mean

What This Suggests

Calories Burned tended to be highest when Water was around 2,108.5 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

Calories Burned Distribution

Relationship Analysis

Statistical Summary

Relationship Statistics

Property Value
Cause Variable Name Water Intake
Effect Variable Name Calories Burned
Sinn Predictive Coefficient 0.60874151662268
Confidence Level HIGH
Confidence Interval 102.66350873322
Forward Pearson Predictive Coefficient 0.238
Critical T Value 1.6518292682927
Total Water Intake Over Previous 14 days Before ABOVE Average Calories Burned 205 milliliters
Total Water Intake Over Previous 14 days Before BELOW Average Calories Burned 4010 milliliters
Duration of Action 14 days
Effect Size weakly positive
Number of Paired Measurements 18421
Optimal Pearson Product 0.14879982979357
P Value 0.075666393583241
Statistical Significance 0.4449
Strength of Relationship 102.66350873322
Study Type population
Analysis Performed At 2026-01-04
Number of Participants 41

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

Calories Burned Info

Property Value
Variable Name Calories Burned
Aggregation Method SUM
Analysis Performed At 2020-09-23
Duration of Action 7 days
Kurtosis 10.719482104079
Maximum Allowed Value 20000 kilocalories
Mean 1693.6119981094 kilocalories
Median 1643.7344918892 kilocalories
Minimum Allowed Value 100 kilocalories
Number of Aggregate Predictors 667
Number of Aggregate Outcomes 211
Number of Measurements 122895
Number of Measurements (including those generated by tagged, joined, or child variables) 21949
Public true
Onset Delay 0 seconds
Standard Deviation 420.78331639612
Unit Kilocalories
User Variables 393
UPC 0
Variable Category Physical Activity
Variable ID 1280
Variance 236738.41913029

Introduction

Background

Water (Foods) and Calories Burned (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 Calories Burned?

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 Calories Burned?

Study Objective

The objective of this study is to determine the nature of the relationship (if any) between Water and Calories Burned. Additionally, we attempt to determine the Water (mL) values most likely to produce optimal Calories Burned 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 11.4% improvement in Calories Burned following above-average Water exposure. The Predictor Impact Score (PIS) of 0.61 indicates strong evidence for a causal relationship.

Statistical Significance

Using a two-tailed t-test with alpha = 0.05, it was determined that the change in Calories Burned is statistically significant at a 95% confidence interval. The p-value of 0.4449 indicates there is less than a 44.49% probability that this result occurred by chance.

After treatment, a 11% increase (221 kilocalories) from the mean baseline 2040 kilocalories was observed. The relative standard deviation at baseline was 19.3317%. The observed change was 0.644034 times the standard deviation.

A common rule of thumb considers a change greater than twice the baseline standard deviation on two separate pre-post experiments may be considered significant. This occurrence would have only a 5% likelihood of resulting from random fluctuation (a p-value < 0.05).

T-Test Details
Observed t-value: 4.114
Critical t-value: 1.652

Since t = 4.11 > 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.

Based on community responses so far, 1 person feels that there is a plausible mechanism of action and 0 feel that any relationship observed between Water and Calories Burned is coincidental.

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 11.4% improvement in Calories Burned—a modest effect. The Predictor Impact Score of 0.61 indicates this relationship is high priority for experimental validation.

Bottom Line: Based on a PIS of 0.61 and a 11.4% effect size, this relationship shows strong evidence and should be prioritized for experimental validation through randomized controlled trials.

These findings contribute to our understanding of how Water may influence Calories Burned in real-world conditions. The combination of effect size, sample size, and temporal evidence supports this as a meaningful relationship worth investigating further.

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Methods

Study Design

This study is based on data donated by 41 participants. Thus, the study design is equivalent to the aggregation of 41 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 Calories Burned.
  • Duration of Action: It was assumed that Water could produce an observable change in Calories Burned for as much as 14 days after the stimulus event.

Statistical Methods

For each participant, we calculated the Pearson correlation coefficient between Water values and subsequent Calories Burned 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.

Calories Burned 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 Calories Burned?. The Journal of Citizen Science. https://studies.crowdsourcingcures.org/study/cause-109592-effect-1280-population-study
BibTeX 
@misc{sinn_cause_109592_effect_1280_population_study_2026,
  author = {Sinn, Mike P.},
  title = {Causal Analysis: Does Water (mL) Affect Calories Burned?},
  year = {2026},
  publisher = {The Journal of Citizen Science},
  url = {https://studies.crowdsourcingcures.org/study/cause-109592-effect-1280-population-study},
  note = {Accessed: January 6, 2026}
}
Chicago/Turabian
Sinn, Mike P. "Causal Analysis: Does Water (mL) Affect Calories Burned?." The Journal of Citizen Science. Accessed January 6, 2026. https://studies.crowdsourcingcures.org/study/cause-109592-effect-1280-population-study.
Harvard
Sinn, M.P., 2026. Causal Analysis: Does Water (mL) Affect Calories Burned?. [Aggregated N-of-1 Study] The Journal of Citizen Science. Available at: https://studies.crowdsourcingcures.org/study/cause-109592-effect-1280-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

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