Higher Deep Sleep Predicts Moderately Lower Inspiration for Population

Higher Deep Sleep Predicts Moderately Lower Inspiration for Population

Contents

Variables

A
Deep Sleep 177
A
Inspiration 1050

Categories

A
Sleep 111
A
Emotions 2028

Tags

Low Confidence
Weak Effect Size
Negative Relationship
Population Study
cause image gauge image effect image
Participants reported a 4.2% average decrease in Inspiration following above average Deep Sleep.

Abstract

Inspiration was generally 2% higher than average after an average of 0.427 out of 1 of Deep Sleep over the previous 7 days.

Aggregated data from 1 study participants suggests with a LOW degree of confidence (p=0.173, 95% CI -0.436 to -0.168) that Deep Sleep has a moderately negative predictive relationship (R=-0.302) with Inspiration.

The highest quartile of Inspiration measurements were observed following an average 0.39 out of 1 Deep Sleep.

The lowest quartile of Inspiration measurements were observed following an average 0.468 out of 1 of Deep Sleep.

After an onset delay of 0 seconds, Inspiration is typically 2% lower than average over the 7 days following around 0.468 out of 1 of Deep Sleep Deep Sleep.

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

Preliminary: Based on 1 participants. Results may change as more data is collected.

Results

Primary Findings

Analysis of 9 paired observations from 1 participants revealed a minimal reduction in Inspiration following above-average Deep Sleep exposure.

-4.1%
Change from Baseline
Minimal effect on Inspiration
0.03
Predictor Impact Score
Insufficient evidence for causal relationship

Supporting Statistics

High
Confidence
-0.302
Correlation (r)
p = 0.006
Significance
z = 0.67
Effect Magnitude
φ = 1.00
Temporality

What This Means

When participants had above-average Deep Sleep:

  • Inspiration decreased by 4.1% on average
  • Temporal analysis supports Deep Sleep as the predictor (not the outcome)
  • This relationship is statistically significant (p = 0.006)

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 1 participants, these scores are preliminary and will become more reliable as additional data is collected.

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.

⚠️ Preliminary Data: With 1 participants and 9 observations, these optimal values are preliminary estimates. As more data is collected, precision will improve significantly.

0.4 /1
Value Predicting Higher Inspiration
Average Deep Sleep when Inspiration exceeded its mean
0.5 /1
Value Predicting Lower Inspiration
Average Deep Sleep when Inspiration was below its mean

What This Suggests

Inspiration tended to be lowest (best) when Deep Sleep was around 0.5 /1.

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

Deep Sleep Distribution

Inspiration Distribution

Statistical Summary

Relationship Statistics

Property Value
Cause Variable Name Deep Sleep
Effect Variable Name Inspiration
Sinn Predictive Coefficient 0.028739098437206
Confidence Level LOW
Confidence Interval 0.13380552219922
Forward Pearson Predictive Coefficient -0.302
Critical T Value 1.833
Average Deep Sleep Over Previous 7 days Before ABOVE Average Inspiration 0.39 out of 1
Average Deep Sleep Over Previous 7 days Before BELOW Average Inspiration 0.468 out of 1
Duration of Action 7 days
Effect Size moderately negative
Number of Paired Measurements 9
Optimal Pearson Product 0.29005791290106
P Value 0.1731790811647
Statistical Significance 0.0063
Strength of Relationship 0.13380552219922
Study Type population
Analysis Performed At 2026-01-04
Number of Participants 1

Deep Sleep Info

Property Value
Variable Name Deep Sleep (/1)
Aggregation Method MEAN
Analysis Performed At 2020-10-09
Duration of Action 7 days
Kurtosis 4.480920546951
Maximum Allowed Value 1 out of 1
Mean 0.495378 out of 1
Median 0.48399 out of 1
Minimum Allowed Value 0 out of 1
Number of Aggregate Predictors 154
Number of Aggregate Outcomes 23
Number of Measurements 569
Number of Measurements (including those generated by tagged, joined, or child variables) 569
Public true
Onset Delay 0 seconds
Standard Deviation 0.1258535268134
Unit 0 to 1 Rating
User Variables 5
UPC 884904543333
Variable Category Sleep
Variable ID 5930076
Variance 0.016153310191236

Inspiration Info

Property Value
Variable Name Inspiration
Aggregation Method MEAN
Analysis Performed At 2020-10-11
Duration of Action 24 hours
Kurtosis 1.9445163556302
Maximum Allowed Value 5 out of 5
Mean 2.443560781967 out of 5
Median 2.4107853769992 out of 5
Minimum Allowed Value 1 out of 5
Number of Aggregate Predictors 934
Number of Aggregate Outcomes 116
Number of Measurements 21838
Number of Measurements (including those generated by tagged, joined, or child variables) 21668
Public true
Onset Delay 0 seconds
Standard Deviation 0.54709683163225
Unit 1 to 5 Rating
User Variables 1342
UPC 0
Variable Category Emotions
Variable ID 1355
Variance 0.6033744215066

Introduction

Background

Deep Sleep (Sleep) and Inspiration (Emotions) 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 Inspiration?

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 Inspiration?

Study Objective

The objective of this study is to determine the nature of the relationship (if any) between Deep Sleep and Inspiration. Additionally, we attempt to determine the Deep Sleep (/1) values most likely to produce optimal Inspiration 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 4.1% reduction in Inspiration following above-average Deep Sleep exposure. The Predictor Impact Score (PIS) of 0.03 indicates insufficient evidence for a causal relationship. This finding is statistically significant (p = 0.006).

Statistical Significance

Using a two-tailed t-test with alpha = 0.05, it was determined that the change in Inspiration is not statistically significant at a 95% confidence interval. This suggests that the Deep Sleep value may not have a significant influence on the Inspiration value, or that more data is needed to detect an effect.

After treatment, a 4.2% decrease (-0.0943 out of 5) from the mean baseline 2.3 out of 5 was observed. The relative standard deviation at baseline was 6.2%. The observed change was 0.665015 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: 1.292
Critical t-value: 1.833

Since t = 1.29 < 1.83, 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 Inspiration.

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 1 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 4.1% reduction in Inspiration—a minimal effect. The Predictor Impact Score of 0.03 indicates this relationship is requiring additional data before conclusions.

Bottom Line: Based on a PIS of 0.03 and a 4.1% 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 Inspiration in real-world conditions. The within-subject design and temporal analysis provide confidence in these relationships, though observational limitations remain.

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Methods

Study Design

This study is based on data donated by 1 participants. Thus, the study design is equivalent to the aggregation of 1 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 Inspiration.
  • Duration of Action: It was assumed that Deep Sleep could produce an observable change in Inspiration 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 Inspiration 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 Sleep as Android. Smart alarm clock with sleep cycle tracking. Wakes you gently in optimal moment for pleasant mornings.

Inspiration 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.

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 (/1) Affect Inspiration?. The Journal of Citizen Science. https://studies.crowdsourcingcures.org/study/cause-5930076-effect-1355-population-study
BibTeX 
@misc{sinn_cause_5930076_effect_1355_population_study_2026,
  author = {Sinn, Mike P.},
  title = {Causal Analysis: Does Deep Sleep (/1) Affect Inspiration?},
  year = {2026},
  publisher = {The Journal of Citizen Science},
  url = {https://studies.crowdsourcingcures.org/study/cause-5930076-effect-1355-population-study},
  note = {Accessed: January 10, 2026}
}
Chicago/Turabian
Sinn, Mike P. "Causal Analysis: Does Deep Sleep (/1) Affect Inspiration?." The Journal of Citizen Science. Accessed January 10, 2026. https://studies.crowdsourcingcures.org/study/cause-5930076-effect-1355-population-study.
Harvard
Sinn, M.P., 2026. Causal Analysis: Does Deep Sleep (/1) Affect Inspiration?. [Aggregated N-of-1 Study] The Journal of Citizen Science. Available at: https://studies.crowdsourcingcures.org/study/cause-5930076-effect-1355-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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