This individual's Deep Sleep is generally highest after an average of 160 meters of Walk Or Run Distance over the previous 7 days.
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Blue represents the mean of Walk Or Run Distance over the previous 7 days
An increase in 7 days cumulative Walk Or Run Distance is usually followed by an decrease in Deep Sleep. (R = -0.103)
Typical values for Deep Sleep following a given amount of Walk Or Run Distance over the previous 7 days.
Typical Walk Or Run Distance seen over the previous 7 days preceding the given Deep Sleep value.
This chart shows how your Walk Or Run Distance changes over time.
Each column represents the number of days this value occurred.
This chart shows the typical value recorded for Walk Or Run Distance on each day of the week.
This chart shows the typical value recorded for Walk Or Run Distance for each month of the year.
This chart shows how your Deep Sleep changes over time.
Each column represents the number of days this value occurred.
This chart shows the typical value recorded for Deep Sleep on each day of the week.
This chart shows the typical value recorded for Deep Sleep for each month of the year.

Abstract

This individual's Deep Sleep is generally 1.48% higher than normal after an average of 163.8 meters Walk Or Run Distance over the previous 7 days. This individual's data suggests with a high degree of confidence (p=0.070090731432517, 95% CI -0.117 to -0.089) that Walk Or Run Distance has a weakly negative predictive relationship (R=-0.1) with Deep Sleep. The highest quartile of Deep Sleep measurements were observed following an average 6 meters Walk Or Run Distance. The lowest quartile of Deep Sleep measurements were observed following an average 7044.7583583043 m Walk Or Run Distance.Deep Sleep is generally 1.64% lower than normal after an average of 7044.7583583043 meters of Walk Or Run Distance over the previous 7 days. Deep Sleep is generally 1.48% higher after an average of 6 meters of Walk Or Run Distance over the previous 7 days.

Objective

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

Participant Instructions

Get Withings here and use it to record your Walk Or Run Distance. Once you have a Withings account, you can import your data from the Import Data page. This individual's data will automatically be imported and analyzed.
Get Sleep as Android here and use it to record your Deep Sleep. Once you have a Sleep as Android 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

Walk Or Run Distance Pre-Processing
Walk Or Run Distance measurement values below 0 meters were assumed erroneous and removed. No maximum allowed measurement value was defined for Walk Or Run Distance. No missing data filling value was defined for Walk Or Run Distance so any gaps in data were just not analyzed instead of assuming zero values for those times.
Walk Or Run Distance Analysis Settings

Deep Sleep Pre-Processing
Deep Sleep measurement values below 0 out of 1 were assumed erroneous and removed. Deep Sleep measurement values above 1 out of 1 were assumed erroneous and removed. No missing data filling value was defined for Deep Sleep so any gaps in data were just not analyzed instead of assuming zero values for those times.
Deep Sleep Analysis Settings

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

Data Quantity
2105 raw Walk Or Run Distance measurements with 2043 changes spanning 2568 days from 2012-04-18 to 2019-04-29 were used in this analysis. 632 raw Deep Sleep measurements with 359 changes spanning 1225 days from 2013-11-23 to 2017-04-01 were used in this analysis.

Data Sources

Walk Or Run Distance data was primarily collected using Withings. Withings creates smart products and apps to take care of yourself and your loved ones in a new and easy way. Discover the Withings Pulse, Wi-Fi Body Scale, and Blood Pressure Monitor.

Deep Sleep data was primarily collected using Sleep as Android. Smart alarm clock with sleep cycle tracking. Wakes you gently in optimal moment for pleasant mornings.

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 negative relationship between Walk Or Run Distance and Deep Sleep

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. 639 paired data points were used in this analysis. Assuming that the relationship is merely coincidental, as the participant independently modifies their Walk Or Run Distance 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 Walk Or Run Distance and Deep Sleep 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 Walk Or Run Distance
Effect Variable Name Deep Sleep
Sinn Predictive Coefficient 0.1493
Confidence Level high
Confidence Interval 0.014175001822168
Forward Pearson Correlation Coefficient -0.103
Critical T Value 1.646
Average Walk Or Run Distance Over Previous 7 days Before ABOVE Average Deep Sleep 6 meters
Average Walk Or Run Distance Over Previous 7 days Before BELOW Average Deep Sleep 7 meters
Duration of Action 7 days
Effect Size weakly negative
Number of Paired Measurements 639
Optimal Pearson Product 0.0021653613935381
P Value 0.070090731432517
Statistical Significance 0.99999999810811
Strength of Relationship 0.014175001822168
Study Type individual
Analysis Performed At 2019-06-24

Walk Or Run Distance Statistics

Property Value
Variable Name Walk Or Run Distance
Aggregation Method MEAN
Analysis Performed At 2019-05-23
Duration of Action 7 days
Kurtosis 44.987597187604
Mean 6593.2 meters
Median 6259.5 meters
Minimum Allowed Value 0 meters
Number of Changes 2043
Number of Correlations 2881
Number of Measurements 2105
Onset Delay 0 seconds
Standard Deviation 4839.624321724
Unit Meters
UPC 744960759935
Variable ID 1304
Variance 23421963.575422

Deep Sleep Statistics

Property Value
Variable Name Deep Sleep
Aggregation Method MEAN
Analysis Performed At 2019-03-14
Duration of Action 7 days
Kurtosis 4.4611235779915
Maximum Allowed Value 1 out of 1
Mean 0.52175 out of 1
Median 0.53571426868439 out of 1
Minimum Allowed Value 0 out of 1
Number of Changes 359
Number of Correlations 2711
Number of Measurements 632
Onset Delay 0 seconds
Standard Deviation 0.1316962526704
Unit 0 to 1 Rating
UPC 884904543333
Variable ID 53709
Variance 0.017343902967425

Tracking Walk Or Run Distance

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

Tracking Deep Sleep

Get Sleep as Android here and use it to record your Deep Sleep. Once you have a Sleep as Android 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