This individual's Deep Sleep is generally highest after a daily total of 30 minutes of Active Time over the previous 7 days.
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Blue represents the sum of Active Time over the previous 7 days
An increase in 7 days cumulative Active Time is usually followed by an increase in Deep Sleep. (R = 0.11)
Typical values for Deep Sleep following a given amount of Active Time over the previous 7 days.
Typical Active Time seen over the previous 7 days preceding the given Deep Sleep 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 your Active Time changes over time.
Each column represents the number of days this value occurred.
This chart shows the typical value recorded for Active Time on each day of the week.
This chart shows the typical value recorded for Active Time 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 0.72% higher than normal after a total of 29 minutes Active Time over the previous 7 days. This individual's data suggests with a low degree of confidence (p=0.37907687523023, 95% CI 0.059 to 0.161) that Active Time has a weakly positive predictive relationship (R=0.11) with Deep Sleep. The highest quartile of Deep Sleep measurements were observed following an average 9 minutes Active Time per day. The lowest quartile of Deep Sleep measurements were observed following an average 712 s Active Time per day.Deep Sleep is generally 0.96% lower than normal after a total of 12 minutes of Active Time over the previous 7 days. Deep Sleep is generally 0.72% higher after a total of 9 minutes of Active Time over the previous 7 days.

Objective

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

Participant Instructions

Record your Active Time daily in the reminder inbox or using the interactive web or mobile notifications.
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

Active Time Pre-Processing
Active Time measurement values below 0 microseconds were assumed erroneous and removed. Active Time measurement values above 24 hours were assumed erroneous and removed. No missing data filling value was defined for Active Time so any gaps in data were just not analyzed instead of assuming zero values for those times.
Active Time 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 Active Time would produce an observable change in Deep Sleep. It was assumed that Active Time could produce an observable change in Deep Sleep for as much as 7 days after the stimulus event.
Predictive Analysis Settings

Data Quantity
107 raw Active Time measurements with 56 changes spanning 283 days from 2013-08-30 to 2014-06-09 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

Active Time 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.

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 positive relationship between Active Time 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. 7 paired data points were used in this analysis. Assuming that the relationship is merely coincidental, as the participant independently modifies their Active 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.

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 Active Time 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 Active Time
Effect Variable Name Deep Sleep
Sinn Predictive Coefficient 0.0026
Confidence Level low
Confidence Interval 0.050856848771966
Forward Pearson Correlation Coefficient 0.11
Critical T Value 1.895
Total Active Time Over Previous 7 days Before ABOVE Average Deep Sleep 9 minutes
Total Active Time Over Previous 7 days Before BELOW Average Deep Sleep 12 minutes
Duration of Action 7 days
Effect Size weakly positive
Number of Paired Measurements 7
Optimal Pearson Product -0.028155128494838
P Value 0.37907687523023
Statistical Significance 0.023639635029583
Strength of Relationship 0.050856848771966
Study Type individual
Analysis Performed At 2019-06-29

Active Time Statistics

Property Value
Variable Name Active Time
Aggregation Method SUM
Analysis Performed At 2019-05-26
Duration of Action 7 days
Kurtosis 489.96725788803
Maximum Allowed Value 24 hours
Mean 12 seconds
Median 0 microseconds
Minimum Allowed Value 0 microseconds
Number of Changes 56
Number of Correlations 390
Number of Measurements 107
Onset Delay 0 seconds
Standard Deviation 178.41526055149
Unit Seconds
Variable ID 1872
Variance 31832.005197656

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 Active Time

Record your Active Time daily in the reminder inbox or using the interactive web or mobile notifications.

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