This individual's Deep Sleep Duration is generally highest after an average of 1500 kilocalories of Calories Burned over the previous 7 days.
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Blue represents the mean of Calories Burned over the previous 7 days
An increase in 7 days cumulative Calories Burned is usually followed by an increase in Deep Sleep Duration. (R = 0.226)
Typical values for Deep Sleep Duration following a given amount of Calories Burned over the previous 7 days.
Typical Calories Burned seen over the previous 7 days preceding the given Deep Sleep Duration value.
Correlation between outcome and aggregated predictor measurements over given number of days
Peak correlation suggests the delay between predictor and observable outcome
This chart shows how Calories Burned changes over time.
Each column represents the number of days this value occurred.
This chart shows the typical value recorded for Calories Burned on each day of the week.
This chart shows the typical value recorded for Calories Burned for each month of the year.
This chart shows how Deep Sleep Duration changes over time.
Each column represents the number of days this value occurred.
This chart shows the typical value recorded for Deep Sleep Duration on each day of the week.
This chart shows the typical value recorded for Deep Sleep Duration for each month of the year.

Abstract

This individual's Deep Sleep Duration is generally 6% higher than normal after an average of 1475 kilocalories Calories Burned over the previous 7 days. This individual's data suggests with a high degree of confidence (p=8.0745886207114E-5, 95% CI -27.439 to 27.891) that Calories Burned has a weakly positive predictive relationship (R=0.23) with Deep Sleep Duration. The highest quartile of Deep Sleep Duration measurements were observed following an average 2 kilocalories Calories Burned. The lowest quartile of Deep Sleep Duration measurements were observed following an average 1977.1130963881 kcal Calories Burned.Deep Sleep Duration is generally 8% lower than normal after an average of 1977.1130963881 kilocalories of Calories Burned over the previous 7 days. Deep Sleep Duration is generally 6% higher after an average of 2 kilocalories of Calories Burned over the previous 7 days.

Objective

The objective of this study is to determine the nature of the relationship (if any) between Calories Burned and Deep Sleep Duration. Additionally, we attempt to determine the Calories Burned values most likely to produce optimal Deep Sleep Duration values.

Participant Instructions

Get Fitbit here and use it to record your Calories Burned. Once you have a Fitbit account, you can import your data from the Import Data page. This individual's data will automatically be imported and analyzed.
Get Fitbit here and use it to record your Deep Sleep Duration. Once you have a Fitbit account, you can import your data from the Import Data page. This individual's data will automatically be imported and analyzed.

Design

This study is based on data donated by one participant. Thus, the study design is consistent with an n=1 observational natural experiment.

Data Analysis

Calories Burned Pre-Processing
No minimum allowed measurement value was defined for Calories Burned. No maximum allowed measurement value was defined for Calories Burned. No missing data filling value was defined for Calories Burned so any gaps in data were just not analyzed instead of assuming zero values for those times.
Calories Burned Analysis Settings

Deep Sleep Duration Pre-Processing
Deep Sleep Duration measurement values below 60 seconds were assumed erroneous and removed. Deep Sleep Duration measurement values above 7 days were assumed erroneous and removed. No missing data filling value was defined for Deep Sleep Duration so any gaps in data were just not analyzed instead of assuming zero values for those times.
Deep Sleep Duration Analysis Settings

Predictive Analytics
It was assumed that 0 hours would pass before a change in Calories Burned would produce an observable change in Deep Sleep Duration. It was assumed that Calories Burned could produce an observable change in Deep Sleep Duration for as much as 7 days after the stimulus event.
Predictive Analysis Settings

Data Quantity
180 raw Calories Burned measurements with 149 changes spanning 185 days from 2018-10-26 to 2019-04-28 were used in this analysis. 323 raw Deep Sleep Duration measurements with 307 changes spanning 344 days from 2018-05-06 to 2019-04-15 were used in this analysis.

Data Sources

Calories Burned data was primarily collected using Fitbit. Fitbit makes activity tracking easy and automatic.

Deep Sleep Duration data was primarily collected using Fitbit. Fitbit makes activity tracking easy and automatic.

Limitations

As with any human experiment, it was impossible to control for all potentially confounding variables. Correlation does not necessarily imply causation. 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:
Strength (A.K.A. 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. There is a weakly positive relationship between Calories Burned and Deep Sleep Duration

Consistency (A.K.A. Reproducibility)
Consistent findings observed by different persons in different places with different samples strengthens the likelihood of an effect. Furthermore, in accordance with the law of large numbers (LLN), the predictive power and accuracy of these results will continually grow over time. 141 paired data points were used in this analysis. Assuming that the relationship is merely coincidental, as the participant independently modifies their Calories Burned 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.

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.

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). The confidence in a causal relationship is bolstered by the fact that time-precedence was taken into account in all calculations.

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.

Plausibility
A plausible bio-chemical mechanism between cause and effect is critical. This is where human brains excel. Based on our responses so far, 1 humans feel that there is a plausible mechanism of action and 0 feel that any relationship observed between Calories Burned and Deep Sleep Duration is coincidental.

Coherence
Coherence between epidemiological and laboratory findings increases the likelihood of an effect. It will be very enlightening to aggregate this data with the data from other participants with similar genetic, diseasomic, environmentomic, and demographic profiles.

Experiment
All of human life can be considered a natural experiment. Occasionally, it is possible to appeal to experimental evidence.

Analogy
The effect of similar factors may be considered.

Relationship Statistics

Property Value
Cause Variable Name Calories Burned
Effect Variable Name Deep Sleep Duration
Sinn Predictive Coefficient 0.2204
Confidence Level high
Confidence Interval 27.665056392641
Forward Pearson Correlation Coefficient 0.226
Critical T Value 1.646
Average Calories Burned Over Previous 7 days Before ABOVE Average Deep Sleep Duration 2 kilocalories
Average Calories Burned Over Previous 7 days Before BELOW Average Deep Sleep Duration 1 kilocalories
Duration of Action 7 days
Effect Size weakly positive
Number of Paired Measurements 141
Optimal Pearson Product 0.09402792815485
P Value 8.0745886207114E-5
Statistical Significance 0.9754
Strength of Relationship 27.665056392641
Study Type individual
Analysis Performed At 2019-07-01

Calories Burned Statistics

Property Value
Variable Name Calories Burned
Aggregation Method MEAN
Analysis Performed At 2019-06-30
Duration of Action 7 days
Kurtosis 3.798746620135
Mean 2088.2 kilocalories
Median 2110 kilocalories
Number of Changes 149
Number of Correlations 3278
Number of Measurements 180
Onset Delay 0 seconds
Standard Deviation 486.76377696545
Unit Kilocalories
Variable ID 1280
Variance 236938.97456567

Deep Sleep Duration Statistics

Property Value
Variable Name Deep Sleep Duration
Aggregation Method SUM
Analysis Performed At 2019-04-16
Duration of Action 24 hours
Kurtosis 3.0359623344059
Maximum Allowed Value 7 days
Mean 70 minutes
Median 72 minutes
Minimum Allowed Value 60 seconds
Number of Changes 307
Number of Measurements 323
Onset Delay 0 seconds
Standard Deviation 31.262599866283
Unit Minutes
Variable ID 6054282
Variance 977.35015039934

Tracking Calories Burned

Get Fitbit here and use it to record your Calories Burned. Once you have a Fitbit account, you can import your data from the Import Data page. This individual's data will automatically be imported and analyzed.

Tracking Deep Sleep Duration

Get Fitbit here and use it to record your Deep Sleep Duration. Once you have a Fitbit account, you can import your data from the Import Data page. This individual's data will automatically be imported and analyzed.
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https://lh6.googleusercontent.com/-BHr4hyUWqZU/AAAAAAAAAAI/AAAAAAAIG28/2Lv0en738II/photo.jpg Principal Investigator - Mike Sinn