Higher Energy Predicts Very Slightly Lower Sleep Duration for Population

Higher Energy Predicts Very Slightly Lower Sleep Duration for Population

Contents

Variables

A
Energy 2158
A
Sleep Duration 3379

Categories

A
Emotions 2028
A
Sleep 111

Tags

High Confidence
Very Weak Effect Size
Negative Relationship
Population Study
cause image gauge image effect image
Participants reported a 2.4% average decrease in Sleep Duration following above average Energy.

Abstract

Sleep Duration was generally 22% higher than average after an average of 2.89 out of 5 of Energy over the previous 24 hours.

Aggregated data from 12 study participants suggests with a HIGH degree of confidence (p=0.249, 95% CI -1.875 to 1.754) that Energy has a very weakly negative predictive relationship (R=-0.0606) with Sleep Duration.

The highest quartile of Sleep Duration measurements were observed following an average 3.01 out of 5 Energy.

The lowest quartile of Sleep Duration measurements were observed following an average 3.03 out of 5 of Energy.

After an onset delay of 0 seconds, Sleep Duration is typically 12% lower than average over the 24 hours following around 3.03 out of 5 of Energy Energy.

Keywords: Energy, Sleep Duration, N-of-1 trials, real-world evidence, causal inference, observational study

Moderate Confidence: Based on 12 participants. More data would increase certainty.

Results

Primary Findings

Analysis of 1,537 paired observations from 12 participants revealed a modest reduction in Sleep Duration following above-average Energy exposure.

-7.2%
Change from Baseline
Modest effect on Sleep Duration
0.00
Predictor Impact Score
Insufficient evidence for causal relationship

Supporting Statistics

High
Confidence
-0.061
Correlation (r)
p = 0.255
Significance
z = 0.42
Effect Magnitude
φ = 1.00
Temporality

What This Means

When participants had above-average Energy:

  • Sleep Duration decreased by 7.2% on average
  • Temporal analysis supports Energy 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 12 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 Energy values associated with high and low Sleep Duration 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

Energy Distribution

Sleep Duration Distribution

Relationship Analysis

Statistical Summary

Relationship Statistics

Property Value
Cause Variable Name Energy
Effect Variable Name Sleep Duration
Sinn Predictive Coefficient 0.0021173815855976
Confidence Level HIGH
Confidence Interval 1.8147648284808
Forward Pearson Predictive Coefficient -0.0606
Critical T Value 1.7765
Average Energy Over Previous 24 hours Before ABOVE Average Sleep Duration 3.01 out of 5
Average Energy Over Previous 24 hours Before BELOW Average Sleep Duration 3.03 out of 5
Duration of Action 24 hours
Effect Size very weakly negative
Number of Paired Measurements 1537
Optimal Pearson Product 0.015602306490541
P Value 0.2488026831843
Statistical Significance 0.2551
Strength of Relationship 1.8147648284808
Study Type population
Analysis Performed At 2026-01-04
Number of Participants 12

Energy Info

Property Value
Variable Name Energy
Aggregation Method MEAN
Analysis Performed At 2022-08-31
Duration of Action 24 hours
Kurtosis 1.7963079252106
Maximum Allowed Value 5 out of 5
Mean 2.8605791891892 out of 5
Median 2.8725064864865 out of 5
Minimum Allowed Value 1 out of 5
Number of Aggregate Predictors 1883
Number of Aggregate Outcomes 275
Number of Measurements 8144
Number of Measurements (including those generated by tagged, joined, or child variables) 8144
Public true
Onset Delay 0 seconds
Standard Deviation 0.36971120901836
Unit 1 to 5 Rating
User Variables 458
UPC 637769766115
Variable Category Emotions
Variable ID 1306
Variance 0.38180313102113

Sleep Duration Info

Property Value
Variable Name Sleep Duration
Aggregation Method MEAN
Analysis Performed At 2020-10-11
Duration of Action 7 days
Kurtosis 3.1431132810239
Maximum Allowed Value 16 hours
Mean 7 hours
Median 7 hours
Minimum Allowed Value 6 minutes
Number of Aggregate Predictors 3162
Number of Aggregate Outcomes 217
Number of Measurements 43055
Number of Measurements (including those generated by tagged, joined, or child variables) 16052
Public true
Onset Delay 0 seconds
Standard Deviation 1.2204190250991
Unit Hours
User Variables 404
UPC 067981966602
Variable Category Sleep
Variable ID 1867
Variance 2.1855287054824

Introduction

Background

Energy (Emotions) and Sleep Duration (Sleep) 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 Energy affect Sleep Duration?

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 Energy for maximizing Sleep Duration?

Study Objective

The objective of this study is to determine the nature of the relationship (if any) between Energy and Sleep Duration. Additionally, we attempt to determine the Energy values most likely to produce optimal Sleep Duration 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 7.2% reduction in Sleep Duration following above-average Energy exposure. The Predictor Impact Score (PIS) of 0.00 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 Sleep Duration is statistically significant at a 95% confidence interval. The p-value of 0.2551 indicates there is less than a 25.51% probability that this result occurred by chance.

After treatment, a 2.4% decrease (negative 8 minutes) from the mean baseline 6 hours was observed. The relative standard deviation at baseline was 56.0917%. The observed change was 0.420565 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: 1.885
Critical t-value: 1.777

Since t = 1.88 > 1.78, 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 Energy might influence Sleep Duration.

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

Conclusion

📊 Preliminary Findings: With 12 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 Energy was associated with a 7.2% reduction in Sleep Duration—a modest effect. The Predictor Impact Score of 0.00 indicates this relationship is requiring additional data before conclusions.

Bottom Line: Based on a PIS of 0.00 and a 7.2% 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 Energy may influence Sleep Duration 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 12 participants. Thus, the study design is equivalent to the aggregation of 12 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 Energy would produce an observable change in Sleep Duration.
  • Duration of Action: It was assumed that Energy could produce an observable change in Sleep Duration for as much as 24 hours after the stimulus event.

Statistical Methods

For each participant, we calculated the Pearson correlation coefficient between Energy values and subsequent Sleep Duration 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

Energy 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.

Sleep Duration 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 Energy Affect Sleep Duration?. The Journal of Citizen Science. https://studies.crowdsourcingcures.org/study/cause-1306-effect-1867-population-study
BibTeX 
@misc{sinn_cause_1306_effect_1867_population_study_2026,
  author = {Sinn, Mike P.},
  title = {Causal Analysis: Does Energy Affect Sleep Duration?},
  year = {2026},
  publisher = {The Journal of Citizen Science},
  url = {https://studies.crowdsourcingcures.org/study/cause-1306-effect-1867-population-study},
  note = {Accessed: January 10, 2026}
}
Chicago/Turabian
Sinn, Mike P. "Causal Analysis: Does Energy Affect Sleep Duration?." The Journal of Citizen Science. Accessed January 10, 2026. https://studies.crowdsourcingcures.org/study/cause-1306-effect-1867-population-study.
Harvard
Sinn, M.P., 2026. Causal Analysis: Does Energy Affect Sleep Duration?. [Aggregated N-of-1 Study] The Journal of Citizen Science. Available at: https://studies.crowdsourcingcures.org/study/cause-1306-effect-1867-population-study [Accessed January 10, 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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