For most, Overall Mood is generally highest after an average of 11 hours of Sleep Start Time over the previous 8 days.

### Trait Correlation Between Sleep Start Time and Overall Mood

### Sleep Start Time Distribution

### Average Sleep Start Time by Day of Week

### Average Sleep Start Time by Month

### Overall Mood Distribution

### Average Overall Mood by Day of Week

### Average Overall Mood by Month

## Abstract

Aggregated data from 23 study participants suggests with a medium degree of confidence (p=0.21698961901618, 95% CI -0.488 to 0.391) that Sleep Start Time has a very weakly negative predictive relationship (R=-0.0486) with Overall Mood. The highest quartile of Overall Mood measurements were observed following an average 11 hours Sleep Start Time. The lowest quartile of Overall Mood measurements were observed following an average 11.700896733211 h Sleep Start Time.

## Objective

The objective of this study is to determine the nature of the relationship (if any) between Sleep Start Time and Overall Mood. Additionally, we attempt to determine the Sleep Start Time values most likely to produce optimal Overall Mood values.

## Participant Instructions

Get Fitbit here and use it to record your Sleep Start Time. Once you have a Fitbit account, you can import your data from the Import Data page. Your data will automatically be imported and analyzed.

Record your Overall Mood daily in the reminder inbox or using the interactive web or mobile notifications.

## Design

This study is based on data donated by 23 participants. Thus, the study design is equivalent to the aggregation of 23 separate n=1 observational natural experiments.

## Data Analysis

It was assumed that 0 hours would pass before a change in Sleep Start Time would produce an observable change in Overall Mood. It was assumed that Sleep Start Time could produce an observable change in Overall Mood for as much as 8 days after the stimulus event.

## Data Sources

The QuantiModo platform was used to aggregate data from these data sources.

## Limitations

As with any human experiment, it was impossible to control for all potentially confounding variables. Correlation does not necessarily imply correlation. We can never know for sure if one factor is definitely the cause of an outcome. However, lack of correlation definitely implies the lack of a causal relationship. Hence, we can with great confidence rule out non-existent relationships. For instance, if we discover no relationship between mood and an antidepressant this information is just as or even more valuable than the discovery that there is a relationship.

We can also take advantage of several characteristics of time series data from many subjects to infer the likelihood of a causal relationship if we do find a correlational relationship. The criteria for causation are a group of minimal conditions necessary to provide adequate evidence of a causal relationship between an incidence and a possible consequence. The list of the criteria is as follows:

1. Strength (effect size): A small association does not mean that there is not a causal effect, though the larger the association, the more likely that it is causal.

2. Consistency (reproducibility): Consistent findings observed by different persons in different places with different samples strengthens the likelihood of an effect.

3. Specificity: Causation is likely if a very specific population at a specific site and disease with no other likely explanation. The more specific an association between a factor and an effect is, the bigger the probability of a causal relationship.

4. Temporality: The effect has to occur after the cause (and if there is an expected delay between the cause and expected effect, then the effect must occur after that delay).

5. Biological gradient: Greater exposure should generally lead to greater incidence of the effect. However, in some cases, the mere presence of the factor can trigger the effect. In other cases, an inverse proportion is observed: greater exposure leads to lower incidence.

6. Plausibility: A plausible mechanism between cause and effect is helpful.

7. Coherence: Coherence between epidemiological and laboratory findings increases the likelihood of an effect.

8. Experiment: Occasionally it is possible to appeal to experimental evidence.

9. Analogy: The effect of similar factors may be considered.

The confidence in a causal relationship is bolstered by the fact that time-precedence was taken into account in all calculations. Furthermore, in accordance with the law of large numbers (LLN), the predictive power and accuracy of these results will continually grow over time. 127 paired data points were used in this analysis. Assuming that the relationship is merely coincidental, as the participant independently modifies their Sleep Start Time values, the observed strength of the relationship will decline until it is below the threshold of significance. To it another way, in the case that we do find a spurious correlation, suggesting that banana intake improves mood for instance, one will likely increase their banana intake. Due to the fact that this correlation is spurious, it is unlikely that you will see a continued and persistent corresponding increase in mood. So over time, the spurious correlation will naturally dissipate. Furthermore, it will be very enlightening to aggregate this data with the data from other participants with similar genetic, diseasomic, environmentomic, and demographic profiles.

## Relationship Statistics

Property | Value |
---|---|

Cause Variable Name | Sleep Start Time |

Effect Variable Name | Overall Mood |

Sinn Predictive Coefficient | 0.031447377475967 |

Confidence Level | medium |

Confidence Interval | 0.43969942146969 |

Forward Pearson Correlation Coefficient | -0.0486 |

Critical T Value | 1.697202935331 |

Average Sleep Start Time Over Previous 8 days Before ABOVE Average Overall Mood | 11 hours |

Average Sleep Start Time Over Previous 8 days Before BELOW Average Overall Mood | 12 hours |

Duration of Action | 8 days |

Effect Size | very weakly negative |

Number of Paired Measurements | 127 |

Optimal Pearson Product | 0.097371075511997 |

P Value | 0.21698961901618 |

Statistical Significance | 0.4822 |

Strength of Relationship | 0.43969942146969 |

Study Type | population |

Analysis Performed At | 2017-12-12 |

Number of Participants | 23 |

## Sleep Start Time Statistics

Property | Value |
---|---|

Variable Name | Sleep Start Time |

Aggregation Method | MEAN |

Analysis Performed At | 2018-11-20 |

Duration of Action | 24 hours |

Kurtosis | 68.400490488415 |

Maximum Allowed Value | 7 days |

Mean | 10 hours |

Median | 10 hours |

Minimum Allowed Value | 0 seconds |

Number of Correlations | 648 |

Number of Measurements | 95941 |

Onset Delay | 0 seconds |

Standard Deviation | 1.8514009058263 |

Unit | Hours |

Variable ID | 5211821 |

Variance | 6.2550638829994 |

## Overall Mood Statistics

Property | Value |
---|---|

Variable Name | Overall Mood |

Aggregation Method | MEAN |

Analysis Performed At | 2018-11-19 |

Duration of Action | 24 hours |

Kurtosis | 3.7416256154524 |

Maximum Allowed Value | 5 out of 5 |

Mean | 3.1155337108594 out of 5 |

Median | 3.1365425423606 out of 5 |

Minimum Allowed Value | 1 out of 5 |

Number of Correlations | 1151 |

Number of Measurements | 606419 |

Onset Delay | 0 seconds |

Standard Deviation | 0.57006455569065 |

Unit | 1 to 5 Rating |

UPC | 767674073845 |

Variable ID | 1398 |

Variance | 0.4399449452354 |