Higher Single-Serve Capsules & Pods Consumption Predicts Very Slightly Higher Deep Sleep for Population

Higher Single-Serve Capsules & Pods Consumption Predicts Very Slightly Higher Deep Sleep for Population

Contents

Variables

A
Single-Serve Capsules & Pods 300
A
Deep Sleep 1384

Categories

A
Foods 13415
A
Sleep 111

Tags

Medium Confidence
Very Weak Effect Size
Positive Relationship
Population Study
cause image gauge image effect image
Participants reported a 2.4% average increase in Deep Sleep following above average Single-Serve Capsules & Pods Consumption.

Abstract

Deep Sleep was generally 4% higher than average after a total of 21.3 serving of Single-Serve Capsules & Pods over the previous 14 days.

Aggregated data from 4 study participants suggests with a MEDIUM degree of confidence (p=0.165, 95% CI -0.069 to 0.109) that Single-Serve Capsules & Pods has a very weakly positive predictive relationship (R=0.0203) with Deep Sleep.

The highest quartile of Deep Sleep measurements were observed following an average 8.22 serving Single-Serve Capsules & Pods per day.

The lowest quartile of Deep Sleep measurements were observed following an average 7.33 serving of Single-Serve Capsules & Pods per day.

After an onset delay of 30 minutes, Deep Sleep is typically 6% lower than average over the 14 days following around 7.33 serving of Single-Serve Capsules & Pods Single-Serve Capsules & Pods.

Keywords: Single-Serve Capsules & Pods, Deep Sleep, N-of-1 trials, real-world evidence, causal inference, observational study

Preliminary: Based on 4 participants. Results may change as more data is collected.

Results

Primary Findings

Analysis of 211 paired observations from 4 participants revealed a minimal improvement in Deep Sleep following above-average Single-Serve Capsules & Pods exposure.

+3.0%
Change from Baseline
Minimal effect on Deep Sleep
0.00
Predictor Impact Score
Insufficient evidence for causal relationship

Supporting Statistics

Medium
Confidence
0.020
Correlation (r)
p = 0.305
Significance
z = 0.40
Effect Magnitude
φ = 1.00
Temporality

What This Means

When participants had above-average Single-Serve Capsules & Pods:

  • Deep Sleep increased by 3.0% on average
  • Temporal analysis supports Single-Serve Capsules & Pods 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 4 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 4 participants and 211 observations, these optimal values are preliminary estimates. As more data is collected, precision will improve significantly.

21.3 serving
Value Predicting Higher Deep Sleep
Average Single-Serve Capsules & Pods when Deep Sleep exceeded its mean
3.3 serving
Value Predicting Lower Deep Sleep
Average Single-Serve Capsules & Pods when Deep Sleep was below its mean

What This Suggests

Deep Sleep tended to be highest when Single-Serve Capsules & Pods was around 21.3 serving.

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

Single-Serve Capsules & Pods Distribution

Deep Sleep Distribution

Relationship Analysis

Statistical Summary

Relationship Statistics

Property Value
Cause Variable Name Single-Serve Capsules & Pods Consumption
Effect Variable Name Deep Sleep
Sinn Predictive Coefficient 0.0033462516820817
Confidence Level MEDIUM
Confidence Interval 0.088837098034463
Forward Pearson Predictive Coefficient 0.0203
Critical T Value 1.684
Total Single- Serve Capsules & Pods Consumption Over Previous 14 days Before ABOVE Average Deep Sleep 8.22 serving
Total Single- Serve Capsules & Pods Consumption Over Previous 14 days Before BELOW Average Deep Sleep 7.33 serving
Duration of Action 14 days
Effect Size very weakly positive
Number of Paired Measurements 211
Optimal Pearson Product 0.064861318738475
P Value 0.16483037911755
Statistical Significance 0.3045
Strength of Relationship 0.088837098034463
Study Type population
Analysis Performed At 2026-01-04
Number of Participants 4

Single-Serve Capsules & Pods Info

Property Value
Variable Name Single-Serve Capsules & Pods
Aggregation Method SUM
Analysis Performed At 2021-08-29
Duration of Action 14 days
Filling Value 0
Kurtosis 10.826565440243
Maximum Allowed Value 40 serving
Mean 0.86276337293729 serving
Median 0.79620462046205 serving
Minimum Allowed Value 0 serving
Number of Aggregate Predictors 0
Number of Aggregate Outcomes 300
Number of Measurements 10
Number of Measurements (including those generated by tagged, joined, or child variables) 4184
Public true
Onset Delay 30 minutes
Standard Deviation 0.27091033365696
Unit Serving
User Variables 596
UPC 0
Variable Category Foods
Variable ID 5978734
Variance 0.28020609619797

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

Introduction

Background

Single-Serve Capsules & Pods (Foods) and Deep Sleep (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

Do Single-Serve Capsules & Pods affect Deep Sleep?

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 Single-Serve Capsules & Pods for maximizing Deep Sleep?

Study Objective

The objective of this study is to determine the nature of the relationship (if any) between Single-Serve Capsules & Pods and Deep Sleep. Additionally, we attempt to determine the Single-Serve Capsules & Pods values most likely to produce optimal Deep Sleep 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 3.0% improvement in Deep Sleep following above-average Single-Serve Capsules & Pods 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 Deep Sleep is not statistically significant at a 95% confidence interval. This suggests that the Single-Serve Capsules & Pods value may not have a significant influence on the Deep Sleep value, or that more data is needed to detect an effect.

After treatment, a 2.4% increase (0.0325 out of 1) from the mean baseline 0.568 out of 1 was observed. The relative standard deviation at baseline was 31.25%. The observed change was 0.397373 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: 1.443
Critical t-value: 1.684

Since t = 1.44 < 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 Single-Serve Capsules & Pods might influence Deep Sleep.

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 Single-Serve Capsules & Pods 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 Single-Serve Capsules & Pods
  • Confirmation through prospective or randomized designs
  • Biological mechanisms underlying the observed effects

Conclusion

📊 Preliminary Findings: With 4 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 Single-Serve Capsules & Pods was associated with a 3.0% improvement in Deep Sleep—a minimal 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 3.0% 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 Single-Serve Capsules & Pods may influence Deep Sleep 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 4 participants. Thus, the study design is equivalent to the aggregation of 4 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 Single-Serve Capsules & Pods would produce an observable change in Deep Sleep.
  • Duration of Action: It was assumed that Single-Serve Capsules & Pods could produce an observable change in Deep Sleep for as much as 14 days after the stimulus event.

Statistical Methods

For each participant, we calculated the Pearson correlation coefficient between Single-Serve Capsules & Pods values and subsequent Deep Sleep 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

Single-Serve Capsules & Pods 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.

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.

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 Single-Serve Capsules & Pods Affect Deep Sleep?. The Journal of Citizen Science. https://studies.crowdsourcingcures.org/study/cause-5978734-effect-53709-population-study
BibTeX 
@misc{sinn_cause_5978734_effect_53709_population_study_2026,
  author = {Sinn, Mike P.},
  title = {Causal Analysis: Does Single-Serve Capsules & Pods Affect Deep Sleep?},
  year = {2026},
  publisher = {The Journal of Citizen Science},
  url = {https://studies.crowdsourcingcures.org/study/cause-5978734-effect-53709-population-study},
  note = {Accessed: January 10, 2026}
}
Chicago/Turabian
Sinn, Mike P. "Causal Analysis: Does Single-Serve Capsules & Pods Affect Deep Sleep?." The Journal of Citizen Science. Accessed January 10, 2026. https://studies.crowdsourcingcures.org/study/cause-5978734-effect-53709-population-study.
Harvard
Sinn, M.P., 2026. Causal Analysis: Does Single-Serve Capsules & Pods Affect Deep Sleep?. [Aggregated N-of-1 Study] The Journal of Citizen Science. Available at: https://studies.crowdsourcingcures.org/study/cause-5978734-effect-53709-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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