Higher Baby Carrots Consumption Predicts Moderately Lower Scaredness for Population

Higher Baby Carrots Consumption Predicts Moderately Lower Scaredness for Population

Contents

Variables

A
Baby Carrots 47
A
Scaredness 1066

Categories

A
Foods 13415
A
Emotions 2028

Tags

High Confidence
Weak Effect Size
Negative Relationship
Population Study
cause image gauge image effect image
Participants reported a 32.1% average decrease in Scaredness following above average Baby Carrots Consumption.

Abstract

Scaredness was generally 33.3% lower than average after 2 serving of Baby Carrots per 14 days.

Aggregated data from 1 study participants suggests with a HIGH degree of confidence (p=0.00443, 95% CI -0.648 to -0.054) that Baby Carrots has a moderately negative predictive relationship (R=-0.351) with Scaredness.

The highest quartile of Scaredness measurements were observed following an average 0 serving Baby Carrots per day.

The lowest quartile of Scaredness measurements were observed following an average 0.786 serving of Baby Carrots per day.

After an onset delay of 30 minutes, Scaredness is typically 29% lower than average over the 14 days following around 0.786 serving of Baby Carrots Baby Carrots.

Keywords: Baby Carrots, Scaredness, 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 12 paired observations from 1 participants revealed a substantial reduction in Scaredness following above-average Baby Carrots exposure.

-33.3%
Change from Baseline
Substantial effect on Scaredness
0.03
Predictor Impact Score
Insufficient evidence for causal relationship

Supporting Statistics

High
Confidence
-0.351
Correlation (r)
p = 0.010
Significance
z = 0.95
Effect Magnitude
φ = 1.00
Temporality

What This Means

When participants had above-average Baby Carrots:

  • Scaredness decreased by 33.3% on average
  • Temporal analysis supports Baby Carrots as the predictor (not the outcome)
  • This relationship is statistically significant (p = 0.010)

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 12 observations, these optimal values are preliminary estimates. As more data is collected, precision will improve significantly.

0.0 serving
Value Predicting Higher Scaredness
Average Baby Carrots when Scaredness exceeded its mean
2.0 serving
Value Predicting Lower Scaredness
Average Baby Carrots when Scaredness was below its mean

What This Suggests

Scaredness tended to be lowest (best) when Baby Carrots was around 2.0 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

Baby Carrots Distribution

Scaredness Distribution

Relationship Analysis

Statistical Summary

Relationship Statistics

Property Value
Cause Variable Name Baby Carrots Consumption
Effect Variable Name Scaredness
Sinn Predictive Coefficient 0.03340206731305
Confidence Level HIGH
Confidence Interval 0.297
Forward Pearson Predictive Coefficient -0.351
Critical T Value 1.782
Total Baby Carrots Consumption Over Previous 14 days Before ABOVE Average Scaredness 0 serving
Total Baby Carrots Consumption Over Previous 14 days Before BELOW Average Scaredness 0.786 serving
Duration of Action 14 days
Effect Size moderately negative
Number of Paired Measurements 12
Optimal Pearson Product 0.23934795336192
P Value 0.004431848411938
Statistical Significance 0.0097
Strength of Relationship 0.297
Study Type population
Analysis Performed At 2026-01-04
Number of Participants 1

Baby Carrots Info

Property Value
Variable Name Baby Carrots
Aggregation Method SUM
Analysis Performed At 2020-09-22
Duration of Action 14 days
Filling Value 0
Kurtosis 18.944750327955
Maximum Allowed Value 40 serving
Mean 0.38102923809524 serving
Median 0 serving
Minimum Allowed Value 0 serving
Number of Aggregate Predictors 0
Number of Aggregate Outcomes 47
Number of Measurements 29
Number of Measurements (including those generated by tagged, joined, or child variables) 15
Public true
Onset Delay 30 minutes
Standard Deviation 0.34537238761188
Unit Serving
User Variables 3
UPC 0
Variable Category Foods
Variable ID 1765
Variance 0.11950110905902

Scaredness Info

Property Value
Variable Name Scaredness
Aggregation Method MEAN
Analysis Performed At 2020-09-15
Duration of Action 24 hours
Kurtosis 3.0976747415301
Maximum Allowed Value 5 out of 5
Mean 2.1651484189506 out of 5
Median 2.1146016963526 out of 5
Minimum Allowed Value 1 out of 5
Number of Aggregate Predictors 964
Number of Aggregate Outcomes 102
Number of Measurements 19595
Number of Measurements (including those generated by tagged, joined, or child variables) 19551
Public true
Onset Delay 0 seconds
Standard Deviation 0.45133124256218
Unit 1 to 5 Rating
User Variables 1274
Variable Category Emotions
Variable ID 1441
Variance 0.50935659130322

Introduction

Background

Baby Carrots (Foods) and Scaredness (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

Do Baby Carrots affect Scaredness?

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 Baby Carrots for maximizing Scaredness?

Study Objective

The objective of this study is to determine the nature of the relationship (if any) between Baby Carrots and Scaredness. Additionally, we attempt to determine the Baby Carrots values most likely to produce optimal Scaredness 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 33.3% reduction in Scaredness following above-average Baby Carrots exposure. The Predictor Impact Score (PIS) of 0.03 indicates insufficient evidence for a causal relationship. This finding is statistically significant (p = 0.010).

Statistical Significance

Using a two-tailed t-test with alpha = 0.05, it was determined that the change in Scaredness is statistically significant at a 95% confidence interval. The p-value of 0.0097 indicates there is less than a 0.97% probability that this result occurred by chance.

After treatment, a 32.1% decrease (-0.5 out of 5) from the mean baseline 1.5 out of 5 was observed. The relative standard deviation at baseline was 35.1%. The observed change was 0.948683 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: 3.000
Critical t-value: 1.782

Since t = 3.00 > 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 Baby Carrots might influence Scaredness.

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 Baby Carrots 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 Baby Carrots
  • 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 Baby Carrots was associated with a 33.3% reduction in Scaredness—a substantial 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 33.3% 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 Baby Carrots may influence Scaredness 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 30 minutes would pass before a change in Baby Carrots would produce an observable change in Scaredness.
  • Duration of Action: It was assumed that Baby Carrots could produce an observable change in Scaredness for as much as 14 days after the stimulus event.

Statistical Methods

For each participant, we calculated the Pearson correlation coefficient between Baby Carrots values and subsequent Scaredness 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

Baby Carrots data was primarily collected using MyFitnessPal. Lose weight with MyFitnessPal, the fastest and easiest-to-use calorie counter for iPhone and iPad. With the largest food database of any iOS calorie counter (over 3,000,000 foods), and amazingly fast food and exercise entry.

Scaredness 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 Baby Carrots Affect Scaredness?. The Journal of Citizen Science. https://studies.crowdsourcingcures.org/study/cause-1765-effect-1441-population-study
BibTeX 
@misc{sinn_cause_1765_effect_1441_population_study_2026,
  author = {Sinn, Mike P.},
  title = {Causal Analysis: Does Baby Carrots Affect Scaredness?},
  year = {2026},
  publisher = {The Journal of Citizen Science},
  url = {https://studies.crowdsourcingcures.org/study/cause-1765-effect-1441-population-study},
  note = {Accessed: January 10, 2026}
}
Chicago/Turabian
Sinn, Mike P. "Causal Analysis: Does Baby Carrots Affect Scaredness?." The Journal of Citizen Science. Accessed January 10, 2026. https://studies.crowdsourcingcures.org/study/cause-1765-effect-1441-population-study.
Harvard
Sinn, M.P., 2026. Causal Analysis: Does Baby Carrots Affect Scaredness?. [Aggregated N-of-1 Study] The Journal of Citizen Science. Available at: https://studies.crowdsourcingcures.org/study/cause-1765-effect-1441-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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