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This individual's Sleep Quality is generally highest after a daily total of 11 serving of Protein Shake consumption over the previous 7 days.
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Blue represents the sum of Protein Shake consumption over the previous 7 days
An increase in 7 days cumulative Protein Shake consumption is usually followed by an increase in Sleep Quality. (R = 0.422)
Typical values for Sleep Quality following a given amount of Protein Shake consumption over the previous 7 days.
Typical Protein Shake consumption seen over the previous 7 days preceding the given Sleep Quality value.
This chart shows how your Protein Shake changes over time.
Each column represents the number of days this value occurred.
This chart shows the typical value recorded for Protein Shake on each day of the week.
This chart shows the typical value recorded for Protein Shake for each month of the year.
This chart shows how your Sleep Quality changes over time.
Each column represents the number of days this value occurred.
This chart shows the typical value recorded for Sleep Quality on each day of the week.
This chart shows the typical value recorded for Sleep Quality for each month of the year.

Abstract

This individual's Sleep Quality is generally 9% higher than normal after a total of 11 serving Protein Shake consumption over the previous 7 days. This individual's data suggests with a high degree of confidence (p=9.8202613400414E-8, 95% CI 0.25 to 0.594) that Protein Shake has a moderately positive predictive relationship (R=0.42) with Sleep Quality. The highest quartile of Sleep Quality measurements were observed following an average 10.02 serving Protein Shake per day. The lowest quartile of Sleep Quality measurements were observed following an average 4.7073170731707 serving Protein Shake per day.Sleep Quality is generally 7% lower than normal after a total of 4.7073170731707 serving of Protein Shake consumption over the previous 7 days. Sleep Quality is generally 9% higher after a total of 10.02 serving of Protein Shake consumption over the previous 7 days.

Objective

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

Participant Instructions

Get MyFitnessPal here and use it to record your Protein Shake. Once you have a MyFitnessPal 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 Sleep Quality. 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

Protein Shake Pre-Processing
Protein Shake measurement values below 0 serving were assumed erroneous and removed. Protein Shake measurement values above 30 serving were assumed erroneous and removed. It was assumed that any gaps in Protein Shake data were unrecorded 0 serving measurement values.
Protein Shake Analysis Settings

Sleep Quality Pre-Processing
Sleep Quality measurement values below 1 out of 5 were assumed erroneous and removed. Sleep Quality measurement values above 5 out of 5 were assumed erroneous and removed. No missing data filling value was defined for Sleep Quality so any gaps in data were just not analyzed instead of assuming zero values for those times.
Sleep Quality Analysis Settings

Predictive Analytics
It was assumed that 0.5 hours would pass before a change in Protein Shake would produce an observable change in Sleep Quality. It was assumed that Protein Shake could produce an observable change in Sleep Quality for as much as 7 days after the stimulus event.
Predictive Analysis Settings

Data Quantity
440 raw Protein Shake measurements with 172 changes spanning 418 days from 2013-01-13 to 2014-03-08 were used in this analysis. 635 raw Sleep Quality measurements with 312 changes spanning 2520 days from 2012-05-06 to 2019-04-01 were used in this analysis.

Data Sources

Protein Shake data was primarily collected using MyFitnessPal. Lose weight with MyFitnessPal, the fastest and easiest-to-use calorie counter for iPhone and iPad. With the largest food database of any iOS calorie counter (over 3,000,000 foods), and amazingly fast food and exercise entry.

Sleep Quality 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 moderately positive relationship between Protein Shake consumption and Sleep Quality

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. 225 paired data points were used in this analysis. Assuming that the relationship is merely coincidental, as the participant independently modifies their Protein Shake consumption 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 Protein Shake consumption and Sleep Quality 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 Protein Shake consumption
Effect Variable Name Sleep Quality
Sinn Predictive Coefficient 0.4597
Confidence Level high
Confidence Interval 0.17239163451457
Forward Pearson Correlation Coefficient 0.422
Critical T Value 1.646
Total Protein Shake consumption Over Previous 7 days Before ABOVE Average Sleep Quality 10.02 serving
Total Protein Shake consumption Over Previous 7 days Before BELOW Average Sleep Quality 4.707 serving
Duration of Action 7 days
Effect Size moderately positive
Number of Paired Measurements 225
Optimal Pearson Product 0.33298233954827
P Value 9.8202613400414E-8
Statistical Significance 0.9771
Strength of Relationship 0.17239163451457
Study Type individual
Analysis Performed At 2019-04-04

Protein Shake Statistics

Property Value
Variable Name Protein Shake
Aggregation Method SUM
Analysis Performed At 2018-12-21
Duration of Action 7 days
Kurtosis 30.156925187947
Maximum Allowed Value 30 serving
Mean 0.21913 serving
Median 0 serving
Minimum Allowed Value 0 serving
Number of Changes 172
Number of Correlations 207
Number of Measurements 440
Onset Delay 30 minutes
Standard Deviation 0.80838027730134
Unit Serving
Variable ID 1617
Variance 0.65347867272979

Sleep Quality Statistics

Property Value
Variable Name Sleep Quality
Aggregation Method MEAN
Analysis Performed At 2019-04-01
Duration of Action 7 days
Kurtosis 2.7819199718877
Maximum Allowed Value 5 out of 5
Mean 3.3303 out of 5
Median 3.2325582504272 out of 5
Minimum Allowed Value 1 out of 5
Number of Changes 312
Number of Correlations 924
Number of Measurements 635
Onset Delay 0 seconds
Standard Deviation 0.83531375879634
Unit 1 to 5 Rating
UPC 754185214911
Variable ID 1448
Variance 0.69774907563447

Tracking Protein Shake

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

Tracking Sleep Quality

Get Sleep as Android here and use it to record your Sleep Quality. 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