Higher Calcium Intake Predicts Slightly Lower Attentiveness for Population

Higher Calcium Intake Predicts Slightly Lower Attentiveness for Population

Contents

Variables

A
Calcium 47
A
Attentiveness 1093

Categories

A
Nutrients 313
A
Emotions 2028

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Low Confidence
Weak Effect Size
Negative Relationship
Population Study
cause image gauge image effect image
Participants reported a 0.3% average decrease in Attentiveness following above average Calcium Intake.

Abstract

Attentiveness was generally 0% higher than average after a total of 0.283 grams of Calcium over the previous 7 days.

Aggregated data from 2 study participants suggests with a LOW degree of confidence (p=0.399, 95% CI -1.121 to 0.675) that Calcium has a weakly negative predictive relationship (R=-0.223) with Attentiveness.

The highest quartile of Attentiveness measurements were observed following an average 0.37 grams Calcium per day.

The lowest quartile of Attentiveness measurements were observed following an average 0.391 grams of Calcium per day.

After an onset delay of 0 seconds, Attentiveness is typically 0% lower than average over the 7 days following around 0.391 grams of Calcium Calcium.

Keywords: Calcium, Attentiveness, N-of-1 trials, real-world evidence, causal inference, observational study

Preliminary: Based on 2 participants. Results may change as more data is collected.

Results

Primary Findings

Analysis of 13 paired observations from 2 participants revealed a minimal reduction in Attentiveness following above-average Calcium exposure.

-0.3%
Change from Baseline
Minimal effect on Attentiveness
0.04
Predictor Impact Score
Insufficient evidence for causal relationship

Supporting Statistics

Medium
Confidence
-0.223
Correlation (r)
p = 0.044
Significance
z = 0.02
Effect Magnitude
φ = 0.99
Temporality

What This Means

When participants had above-average Calcium:

  • Attentiveness decreased by 0.3% on average
  • Temporal analysis supports Calcium as the predictor (not the outcome)
  • This relationship is statistically significant (p = 0.044)

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 2 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 Calcium values associated with high and low Attentiveness 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

Calcium Distribution

Attentiveness Distribution

Relationship Analysis

Statistical Summary

Relationship Statistics

Property Value
Cause Variable Name Calcium Intake
Effect Variable Name Attentiveness
Sinn Predictive Coefficient 0.040495549174615
Confidence Level LOW
Confidence Interval 0.89805
Forward Pearson Predictive Coefficient -0.2234
Critical T Value 1.771
Total Calcium Intake Over Previous 7 days Before ABOVE Average Attentiveness 0.37 grams
Total Calcium Intake Over Previous 7 days Before BELOW Average Attentiveness 0.391 grams
Duration of Action 7 days
Effect Size weakly negative
Number of Paired Measurements 13
Optimal Pearson Product 0.00014676635509559
P Value 0.39879
Statistical Significance 0.0436
Strength of Relationship 0.89805
Study Type population
Analysis Performed At 2026-01-04
Number of Participants 2

Calcium Info

Property Value
Variable Name Calcium
Aggregation Method SUM
Analysis Performed At 2021-01-25
Duration of Action 7 days
Filling Value 0
Kurtosis 23.624773998753
Mean 0.0183603425 grams
Median 0.0037005 grams
Minimum Allowed Value 0 grams
Number of Aggregate Predictors 0
Number of Aggregate Outcomes 47
Number of Measurements 258
Number of Measurements (including those generated by tagged, joined, or child variables) 258
Public true
Onset Delay 0 seconds
Standard Deviation 0.02826254965045
Unit Grams
User Variables 4
UPC 074312134395
Variable Category Nutrients
Variable ID 1279
Variance 0.0014548860293919

Attentiveness Info

Property Value
Variable Name Attentiveness
Aggregation Method MEAN
Analysis Performed At 2020-09-17
Duration of Action 24 hours
Kurtosis 2.8989604447383
Maximum Allowed Value 5 out of 5
Mean 2.6104259171135 out of 5
Median 2.603650254387 out of 5
Minimum Allowed Value 1 out of 5
Number of Aggregate Predictors 979
Number of Aggregate Outcomes 114
Number of Measurements 20541
Number of Measurements (including those generated by tagged, joined, or child variables) 20486
Public true
Onset Delay 0 seconds
Standard Deviation 0.46181906465469
Unit 1 to 5 Rating
User Variables 1464
UPC 0
Variable Category Emotions
Variable ID 1267
Variance 0.46818963151551

Introduction

Background

Calcium (Nutrients) and Attentiveness (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 Calcium affect Attentiveness?

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 Calcium for maximizing Attentiveness?

Study Objective

The objective of this study is to determine the nature of the relationship (if any) between Calcium and Attentiveness. Additionally, we attempt to determine the Calcium values most likely to produce optimal Attentiveness 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 0.3% reduction in Attentiveness following above-average Calcium exposure. The Predictor Impact Score (PIS) of 0.04 indicates insufficient evidence for a causal relationship. This finding is statistically significant (p = 0.044).

Statistical Significance

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

After treatment, a 0.3% decrease (-0.0139 out of 5) from the mean baseline 4.13 out of 5 was observed. The relative standard deviation at baseline was 20.7%. The observed change was 0.016265 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: 0.027
Critical t-value: 1.771

Since t = 0.03 < 1.77, 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 Calcium might influence Attentiveness.

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

Conclusion

📊 Preliminary Findings: With 2 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 Calcium was associated with a 0.3% reduction in Attentiveness—a minimal effect. The Predictor Impact Score of 0.04 indicates this relationship is requiring additional data before conclusions.

Bottom Line: Based on a PIS of 0.04 and a 0.3% 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 Calcium may influence Attentiveness 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 2 participants. Thus, the study design is equivalent to the aggregation of 2 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 Calcium would produce an observable change in Attentiveness.
  • Duration of Action: It was assumed that Calcium could produce an observable change in Attentiveness for as much as 7 days after the stimulus event.

Statistical Methods

For each participant, we calculated the Pearson correlation coefficient between Calcium values and subsequent Attentiveness 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

Calcium data was primarily collected using General Spreadsheet. Import from a spreadsheet containing a Variable Name, Value, Measurement Event Time, and Abbreviated Unit Name field. Here is an <a href="http://bit.ly/2jz7CNl" target="_blank">example spreadsheet</a> with allowed column names, units and time format.

Attentiveness 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 Calcium Affect Attentiveness?. The Journal of Citizen Science. https://studies.crowdsourcingcures.org/study/cause-1279-effect-1267-population-study
BibTeX 
@misc{sinn_cause_1279_effect_1267_population_study_2026,
  author = {Sinn, Mike P.},
  title = {Causal Analysis: Does Calcium Affect Attentiveness?},
  year = {2026},
  publisher = {The Journal of Citizen Science},
  url = {https://studies.crowdsourcingcures.org/study/cause-1279-effect-1267-population-study},
  note = {Accessed: January 9, 2026}
}
Chicago/Turabian
Sinn, Mike P. "Causal Analysis: Does Calcium Affect Attentiveness?." The Journal of Citizen Science. Accessed January 9, 2026. https://studies.crowdsourcingcures.org/study/cause-1279-effect-1267-population-study.
Harvard
Sinn, M.P., 2026. Causal Analysis: Does Calcium Affect Attentiveness?. [Aggregated N-of-1 Study] The Journal of Citizen Science. Available at: https://studies.crowdsourcingcures.org/study/cause-1279-effect-1267-population-study [Accessed January 9, 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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