This individual's Sleep Duration is generally highest after an average of 0.33 capsules of Digestive Advantage Daily Probiotic over the previous 7 days.
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Blue represents the mean of Digestive Advantage Daily Probiotic over the previous 7 days
An increase in 7 days cumulative Digestive Advantage Daily Probiotic is usually followed by an increase in Sleep Duration. (R = 0.029)
Typical values for Sleep Duration following a given amount of Digestive Advantage Daily Probiotic over the previous 7 days.
Typical Digestive Advantage Daily Probiotic seen over the previous 7 days preceding the given 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 Digestive Advantage Daily Probiotic changes over time.
Each column represents the number of days this value occurred.
This chart shows the typical value recorded for Digestive Advantage Daily Probiotic on each day of the week.
This chart shows the typical value recorded for Digestive Advantage Daily Probiotic for each month of the year.
This chart shows how Sleep Duration changes over time.
Each column represents the number of days this value occurred.
This chart shows the typical value recorded for Sleep Duration on each day of the week.
This chart shows the typical value recorded for Sleep Duration for each month of the year.

Abstract

This individual's Sleep Duration is generally 3% higher than normal after an average of 0.3333 capsules Digestive Advantage Daily Probiotic over the previous 7 days. This individual's data suggests with a medium degree of confidence (p=0.097756725919832, 95% CI -0.319 to 0.377) that Digestive Advantage Daily Probiotic has a very weakly positive predictive relationship (R=0.03) with Sleep Duration. The highest quartile of Sleep Duration measurements were observed following an average 0.32 capsules Digestive Advantage Daily Probiotic. The lowest quartile of Sleep Duration measurements were observed following an average 0.29835004177109 capsules Digestive Advantage Daily Probiotic.Sleep Duration is generally 2% lower than normal after an average of 0.29835004177109 capsules of Digestive Advantage Daily Probiotic over the previous 7 days. Sleep Duration is generally 3% higher after an average of 0.32 capsules of Digestive Advantage Daily Probiotic over the previous 7 days.

Objective

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

Participant Instructions

Record your Digestive Advantage Daily Probiotic daily in the reminder inbox or using the interactive web or mobile notifications.
Get Fitbit here and use it to record your 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

Digestive Advantage Daily Probiotic Pre-Processing
Digestive Advantage Daily Probiotic measurement values below 0 capsules were assumed erroneous and removed. Digestive Advantage Daily Probiotic measurement values above 20 capsules were assumed erroneous and removed. It was assumed that any gaps in Digestive Advantage Daily Probiotic data were unrecorded 0 capsules measurement values.
Digestive Advantage Daily Probiotic Analysis Settings

Sleep Duration Pre-Processing
Sleep Duration measurement values below 3 hours were assumed erroneous and removed. Sleep Duration measurement values above 7 days were assumed erroneous and removed. No missing data filling value was defined for Sleep Duration so any gaps in data were just not analyzed instead of assuming zero values for those times.
Sleep Duration Analysis Settings

Predictive Analytics
It was assumed that 0.5 hours would pass before a change in Digestive Advantage Daily Probiotic would produce an observable change in Sleep Duration. It was assumed that Digestive Advantage Daily Probiotic could produce an observable change in Sleep Duration for as much as 7 days after the stimulus event.
Predictive Analysis Settings

Data Quantity
99 raw Digestive Advantage Daily Probiotic measurements with 34 changes spanning 231 days from 2013-07-22 to 2014-03-10 were used in this analysis. 2127 raw Sleep Duration measurements with 2043 changes spanning 2533 days from 2012-04-28 to 2019-04-05 were used in this analysis.

Data Sources

Digestive Advantage Daily Probiotic 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.

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 very weakly positive relationship between Digestive Advantage Daily Probiotic and 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. 247 paired data points were used in this analysis. Assuming that the relationship is merely coincidental, as the participant independently modifies their Digestive Advantage Daily Probiotic 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 Digestive Advantage Daily Probiotic and 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 Digestive Advantage Daily Probiotic
Effect Variable Name Sleep Duration
Sinn Predictive Coefficient 0.0254
Confidence Level medium
Confidence Interval 0.34758546624636
Forward Pearson Correlation Coefficient 0.029
Critical T Value 1.646
Average Digestive Advantage Daily Probiotic Over Previous 7 days Before ABOVE Average Sleep Duration 0.32 capsules
Average Digestive Advantage Daily Probiotic Over Previous 7 days Before BELOW Average Sleep Duration 0.298 capsules
Duration of Action 7 days
Effect Size very weakly positive
Number of Paired Measurements 247
Optimal Pearson Product 0.0012438490160756
P Value 0.097756725919832
Statistical Significance 0.8755
Strength of Relationship 0.34758546624636
Study Type individual
Analysis Performed At 2019-07-01

Digestive Advantage Daily Probiotic Statistics

Property Value
Variable Name Digestive Advantage Daily Probiotic
Aggregation Method MEAN
Analysis Performed At 2019-04-05
Duration of Action 7 days
Kurtosis 1.1386276404136
Maximum Allowed Value 20 capsules
Mean 0.40693 capsules
Median 0 capsules
Minimum Allowed Value 0 capsules
Number of Changes 34
Number of Correlations 83
Number of Measurements 99
Onset Delay 30 minutes
Standard Deviation 0.49232773526213
Unit Capsules
UPC 680474664269
Variable ID 1302
Variance 0.24238659890834

Sleep Duration Statistics

Property Value
Variable Name Sleep Duration
Aggregation Method MEAN
Analysis Performed At 2019-06-30
Duration of Action 7 days
Kurtosis 2.9523224471114
Maximum Allowed Value 7 days
Mean 7 hours
Median 7 hours
Minimum Allowed Value 3 hours
Number of Changes 2043
Number of Correlations 5768
Number of Measurements 2127
Onset Delay 0 seconds
Standard Deviation 1.5205517506778
Unit Hours
UPC 067981966602
Variable ID 1867
Variance 2.3120776264892

Tracking Digestive Advantage Daily Probiotic

Record your Digestive Advantage Daily Probiotic daily in the reminder inbox or using the interactive web or mobile notifications.

Tracking Sleep Duration

Get Fitbit here and use it to record your 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