Higher Deep Sleep Predicts Very Slightly Higher Calories Burned for Population

Higher Deep Sleep Predicts Very Slightly Higher Calories Burned for Population

Contents

Variables

A
Deep Sleep 1384
A
Calories Burned 878

Categories

A
Sleep 111
A
Physical Activity 1719

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Your Data

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Medium Confidence
Very Weak Effect Size
Positive Relationship
Population Study
cause image gauge image effect image
Participants reported a 4.6% average increase in Calories Burned following above average Deep Sleep.

Abstract

Calories Burned was generally 2% higher than average after an average of 0.436 out of 1 of Deep Sleep over the previous 7 days.

Aggregated data from 3 study participants suggests with a MEDIUM degree of confidence (p=0.24, 95% CI -77.531 to 77.669) that Deep Sleep has a very weakly positive predictive relationship (R=0.0691) with Calories Burned.

The highest quartile of Calories Burned measurements were observed following an average 0.46 out of 1 Deep Sleep.

The lowest quartile of Calories Burned measurements were observed following an average 0.429 out of 1 of Deep Sleep.

After an onset delay of 0 seconds, Calories Burned is typically 1% lower than average over the 7 days following around 0.429 out of 1 of Deep Sleep Deep Sleep.

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

Preliminary: Based on 3 participants. Results may change as more data is collected.

Results

Primary Findings

Analysis of 142 paired observations from 3 participants revealed a minimal improvement in Calories Burned following above-average Deep Sleep exposure.

+0.7%
Change from Baseline
Minimal effect on Calories Burned
0.01
Predictor Impact Score
Insufficient evidence for causal relationship

Supporting Statistics

Medium
Confidence
0.069
Correlation (r)
p = 0.435
Significance
z = 0.26
Effect Magnitude
φ = 1.00
Temporality

What This Means

When participants had above-average Deep Sleep:

  • Calories Burned increased by 0.7% on average
  • Temporal analysis supports Deep Sleep 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. With only 3 participants, these scores are preliminary and will become more reliable as additional data is collected.

Optimal Daily Values

No clear dose-response relationship detected. The Deep Sleep values associated with high and low Calories Burned are too similar to provide meaningful dosing guidance. This may indicate a threshold effect (any amount works equally well), no effect, or insufficient data variance. With more participants, a clearer pattern may emerge.

Population Correlation

Deep Sleep Distribution

Calories Burned Distribution

Statistical Summary

Relationship Statistics

Property Value
Cause Variable Name Deep Sleep
Effect Variable Name Calories Burned
Sinn Predictive Coefficient 0.0089547304708121
Confidence Level MEDIUM
Confidence Interval 77.600341158012
Forward Pearson Predictive Coefficient 0.0691
Critical T Value 1.6773333333333
Average Deep Sleep Over Previous 7 days Before ABOVE Average Calories Burned 0.46 out of 1
Average Deep Sleep Over Previous 7 days Before BELOW Average Calories Burned 0.429 out of 1
Duration of Action 7 days
Effect Size very weakly positive
Number of Paired Measurements 142
Optimal Pearson Product 0.054415117049936
P Value 0.23965763814964
Statistical Significance 0.4348
Strength of Relationship 77.600341158012
Study Type population
Analysis Performed At 2026-01-04
Number of Participants 3

Deep Sleep Info

Property Value
Variable Name Deep Sleep
Aggregation Method MEAN
Analysis Performed At 2020-10-11
Duration of Action 7 days
Kurtosis 3.8099479591447
Maximum Allowed Value 1 out of 1
Mean 0.57104939589141 out of 1
Median 0.58178050572753 out of 1
Minimum Allowed Value 0 out of 1
Number of Aggregate Predictors 1265
Number of Aggregate Outcomes 119
Number of Measurements 10312
Number of Measurements (including those generated by tagged, joined, or child variables) 9055
Public true
Onset Delay 0 seconds
Standard Deviation 0.14112482692665
Unit 0 to 1 Rating
User Variables 65
UPC 884904543333
Variable Category Sleep
Variable ID 53709
Variance 0.023357512360836

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

Deep Sleep (Sleep) 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 Deep Sleep 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 Deep Sleep for maximizing Calories Burned?

Study Objective

The objective of this study is to determine the nature of the relationship (if any) between Deep Sleep and Calories Burned. Additionally, we attempt to determine the Deep Sleep 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 0.7% improvement in Calories Burned following above-average Deep Sleep exposure. The Predictor Impact Score (PIS) of 0.01 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 Calories Burned is not statistically significant at a 95% confidence interval. This suggests that the Deep Sleep value may not have a significant influence on the Calories Burned value, or that more data is needed to detect an effect.

After treatment, a 4.6% increase (-5.36 kilocalories) from the mean baseline 1360 kilocalories was observed. The relative standard deviation at baseline was 12.9%. The observed change was 0.264684 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: 1.009
Critical t-value: 1.677

Since t = 1.01 < 1.68, we cannot 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 Deep Sleep might influence Calories Burned.

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 Deep Sleep 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 Deep Sleep
  • Confirmation through prospective or randomized designs
  • Biological mechanisms underlying the observed effects

Conclusion

📊 Preliminary Findings: With 3 participants, these results are based on limited data. Effect sizes and confidence will improve as more participants contribute data. Consider these findings directional rather than definitive.

Above-average Deep Sleep was associated with a 0.7% improvement in Calories Burned—a minimal effect. The Predictor Impact Score of 0.01 indicates this relationship is requiring additional data before conclusions.

Bottom Line: Based on a PIS of 0.01 and a 0.7% effect size, this relationship currently lacks sufficient evidence. Continue monitoring as more data becomes available. Note: These conclusions may strengthen or change direction as more data is collected.

These findings contribute to our understanding of how Deep Sleep may influence Calories Burned in real-world conditions. While preliminary, these results may inform future research directions. As more participants contribute data, the reliability and precision of these findings will improve substantially.

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Methods

Study Design

This study is based on data donated by 3 participants. Thus, the study design is equivalent to the aggregation of 3 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 0 seconds would pass before a change in Deep Sleep would produce an observable change in Calories Burned.
  • Duration of Action: It was assumed that Deep Sleep could produce an observable change in Calories Burned for as much as 7 days after the stimulus event.

Statistical Methods

For each participant, we calculated the Pearson correlation coefficient between Deep Sleep 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

Deep Sleep data was primarily collected using QuantiModo. QuantiModo allows you to easily track mood, symptoms, or any outcome you want to optimize in a fraction of a second. You can also import your data from over 30 other apps and devices. QuantiModo then analyzes your data to identify which hidden factors are most likely to be influencing your mood or symptoms.

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 Deep Sleep Affect Calories Burned?. The Journal of Citizen Science. https://studies.crowdsourcingcures.org/study/cause-53709-effect-1280-population-study
BibTeX 
@misc{sinn_cause_53709_effect_1280_population_study_2026,
  author = {Sinn, Mike P.},
  title = {Causal Analysis: Does Deep Sleep Affect Calories Burned?},
  year = {2026},
  publisher = {The Journal of Citizen Science},
  url = {https://studies.crowdsourcingcures.org/study/cause-53709-effect-1280-population-study},
  note = {Accessed: January 6, 2026}
}
Chicago/Turabian
Sinn, Mike P. "Causal Analysis: Does Deep Sleep Affect Calories Burned?." The Journal of Citizen Science. Accessed January 6, 2026. https://studies.crowdsourcingcures.org/study/cause-53709-effect-1280-population-study.
Harvard
Sinn, M.P., 2026. Causal Analysis: Does Deep Sleep Affect Calories Burned?. [Aggregated N-of-1 Study] The Journal of Citizen Science. Available at: https://studies.crowdsourcingcures.org/study/cause-53709-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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