This individual's REM Sleep Duration is generally highest after a daily total of 500 grams of Spinach Raw intake over the previous 7 days.
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Blue represents the sum of Spinach Raw intake over the previous 7 days
An increase in 7 days cumulative Spinach Raw intake is usually followed by an decrease in REM Sleep Duration. (R = -0.117)
Typical values for REM Sleep Duration following a given amount of Spinach Raw intake over the previous 7 days.
Typical Spinach Raw intake seen over the previous 7 days preceding the given REM 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 your Spinach Raw changes over time.
Each column represents the number of days this value occurred.
This chart shows the typical value recorded for Spinach Raw on each day of the week.
This chart shows the typical value recorded for Spinach Raw for each month of the year.
This chart shows how your REM Sleep Duration changes over time.
Each column represents the number of days this value occurred.
This chart shows the typical value recorded for REM Sleep Duration on each day of the week.
This chart shows the typical value recorded for REM Sleep Duration for each month of the year.

Abstract

This individual's REM Sleep Duration is generally 5% higher than normal after a total of 504 grams Spinach Raw intake over the previous 7 days. This individual's data suggests with a medium degree of confidence (p=0.10081710098173, 95% CI -6.603 to 6.369) that Spinach Raw has a weakly negative predictive relationship (R=-0.12) with REM Sleep Duration. The highest quartile of REM Sleep Duration measurements were observed following an average 508.84 grams Spinach Raw per day. The lowest quartile of REM Sleep Duration measurements were observed following an average 579.42857142857 g Spinach Raw per day.REM Sleep Duration is generally 3% lower than normal after a total of 579.42857142857 grams of Spinach Raw intake over the previous 7 days. REM Sleep Duration is generally 5% higher after a total of 508.84 grams of Spinach Raw intake over the previous 7 days.

Objective

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

Participant Instructions

Record your Spinach Raw daily in the reminder inbox or using the interactive web or mobile notifications.
Get Fitbit here and use it to record your REM 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

Spinach Raw Pre-Processing
Spinach Raw measurement values below 0 grams were assumed erroneous and removed. No maximum allowed measurement value was defined for Spinach Raw. It was assumed that any gaps in Spinach Raw data were unrecorded 0 grams measurement values.
Spinach Raw Analysis Settings

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

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

Data Quantity
1222 raw Spinach Raw measurements with 297 changes spanning 1255 days from 2016-01-19 to 2019-06-27 were used in this analysis. 322 raw REM Sleep Duration measurements with 290 changes spanning 344 days from 2018-05-06 to 2019-04-15 were used in this analysis.

Data Sources

Spinach Raw 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.

REM 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 negative relationship between Spinach Raw intake and REM 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. 322 paired data points were used in this analysis. Assuming that the relationship is merely coincidental, as the participant independently modifies their Spinach Raw intake 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 Spinach Raw intake and REM 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 Spinach Raw intake
Effect Variable Name REM Sleep Duration
Sinn Predictive Coefficient 0.1151
Confidence Level medium
Confidence Interval 6.4858804696293
Forward Pearson Correlation Coefficient -0.117
Critical T Value 1.646
Total Spinach Raw intake Over Previous 7 days Before ABOVE Average REM Sleep Duration 508.84 grams
Total Spinach Raw intake Over Previous 7 days Before BELOW Average REM Sleep Duration 579.429 grams
Duration of Action 7 days
Effect Size weakly negative
Number of Paired Measurements 322
Optimal Pearson Product 0.03893409207797
P Value 0.10081710098173
Statistical Significance 0.9834
Strength of Relationship 6.4858804696293
Study Type individual
Analysis Performed At 2019-06-27

Spinach Raw Statistics

Property Value
Variable Name Spinach Raw
Aggregation Method SUM
Analysis Performed At 2019-06-28
Duration of Action 7 days
Kurtosis 1269.8263797806
Mean 89.606 grams
Median 100 grams
Minimum Allowed Value 0 grams
Number of Changes 298
Number of Correlations 196
Number of Measurements 1222
Onset Delay 30 minutes
Standard Deviation 789.61685342351
Unit Grams
UPC 865568000011
Variable ID 86616
Variance 623494.77521044

REM Sleep Duration Statistics

Property Value
Variable Name REM Sleep Duration
Aggregation Method SUM
Analysis Performed At 2019-04-18
Duration of Action 24 hours
Kurtosis 3.1877848056985
Maximum Allowed Value 7 days
Mean 78 minutes
Median 74 minutes
Minimum Allowed Value 60 seconds
Number of Changes 290
Number of Correlations 1
Number of Measurements 322
Onset Delay 0 seconds
Standard Deviation 33.196219964213
Unit Minutes
Variable ID 6054281
Variance 1101.9890199124

Tracking Spinach Raw

Record your Spinach Raw daily in the reminder inbox or using the interactive web or mobile notifications.

Tracking REM Sleep Duration

Get Fitbit here and use it to record your REM 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