For most, Attentiveness is generally highest after a daily total of 1200 milliliters of Water intake over the previous 7 days.


Abstract
Aggregated data from 8 study participants suggests with a low degree of confidence (p=0.18585846207855, 95% CI 0.209 to 0.731) that Water (mL) has a weakly positive predictive relationship (R=0.26) with Attentiveness. The highest quartile of Attentiveness measurements were observed following an average 920.2 milliliters Water (mL) per day. The lowest quartile of Attentiveness measurements were observed following an average 823.57893987346 mL Water (mL) per day.
Objective
The objective of this study is to determine the nature of the relationship (if any) between Water (mL) and Attentiveness. Additionally, we attempt to determine the Water (mL) values most likely to produce optimal Attentiveness values.
Participant Instructions
Get Fitbit here and use it to record your Water. 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.
Record your Attentiveness daily in the reminder inbox or using the interactive web or mobile notifications.
Record your Attentiveness daily in the reminder inbox or using the interactive web or mobile notifications.
Design
This study is based on data donated by 8 participants. Thus, the study design is equivalent to the aggregation of 8 separate n=1 observational natural experiments.
Data Analysis
Water PreProcessing
Water measurement values below 0 milliliters were assumed erroneous and removed. No maximum allowed measurement value was defined for Water. It was assumed that any gaps in Water data were unrecorded 0 milliliters measurement values.
Attentiveness PreProcessing
Attentiveness measurement values below 1 out of 5 were assumed erroneous and removed. Attentiveness measurement values above 5 out of 5 were assumed erroneous and removed. No missing data filling value was defined for Attentiveness so any gaps in data were just not analyzed instead of assuming zero values for those times.
Predictive Analytics
It was assumed that 0.5 hours would pass before a change in Water (mL) would produce an observable change in Attentiveness. It was assumed that Water (mL) could produce an observable change in Attentiveness for as much as 7 days after the stimulus event.
Water measurement values below 0 milliliters were assumed erroneous and removed. No maximum allowed measurement value was defined for Water. It was assumed that any gaps in Water data were unrecorded 0 milliliters measurement values.

Attentiveness PreProcessing
Attentiveness measurement values below 1 out of 5 were assumed erroneous and removed. Attentiveness measurement values above 5 out of 5 were assumed erroneous and removed. No missing data filling value was defined for Attentiveness so any gaps in data were just not analyzed instead of assuming zero values for those times.

Predictive Analytics
It was assumed that 0.5 hours would pass before a change in Water (mL) would produce an observable change in Attentiveness. It was assumed that Water (mL) could produce an observable change in Attentiveness for as much as 7 days after the stimulus event.

Data Sources
Water (mL) data was primarily collected using Fitbit. Fitbit makes activity tracking easy and automatic.
Attentiveness 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.
Attentiveness 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.
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 nonexistent 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 Water intake and Attentiveness
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. 64 paired data points were used in this analysis. Assuming that the relationship is merely coincidental, as the participant independently modifies their Water 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 timeprecedence 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 biochemical 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 Water intake and Attentiveness 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.
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 Water intake and Attentiveness
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. 64 paired data points were used in this analysis. Assuming that the relationship is merely coincidental, as the participant independently modifies their Water 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 timeprecedence 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 biochemical 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 Water intake and Attentiveness 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  Water intake 
Effect Variable Name  Attentiveness 
Sinn Predictive Coefficient  0.062813867531007 
Confidence Level  low 
Confidence Interval  0.47012207789031 
Forward Pearson Correlation Coefficient  0.261 
Critical T Value  1.726625 
Total Water intake Over Previous 7 days Before ABOVE Average Attentiveness  920.2 milliliters 
Total Water intake Over Previous 7 days Before BELOW Average Attentiveness  823.57893987346 milliliters 
Duration of Action  7 days 
Effect Size  weakly positive 
Number of Paired Measurements  64 
Optimal Pearson Product  0.20515636791686 
P Value  0.18585846207855 
Statistical Significance  0.2769624977791 
Strength of Relationship  0.47012207789031 
Study Type  population 
Analysis Performed At  20190203 
Number of Participants  8 
Water Statistics
Property  Value 

Variable Name  Water (mL) 
Aggregation Method  SUM 
Analysis Performed At  20190128 
Duration of Action  7 days 
Kurtosis  204.60955518589 
Mean  246.55070571942 milliliters 
Median  208.90107913669 milliliters 
Minimum Allowed Value  0 milliliters 
Number of Correlations  135 
Number of Measurements  16539 
Onset Delay  30 minutes 
Standard Deviation  192.76251202553 
Unit  Milliliters 
UPC  075720004096 
Variable ID  109592 
Variance  143304.44930319 
Attentiveness Statistics
Property  Value 

Variable Name  Attentiveness 
Aggregation Method  MEAN 
Analysis Performed At  20190202 
Duration of Action  24 hours 
Kurtosis  2.9010308452766 
Maximum Allowed Value  5 out of 5 
Mean  2.6094145789101 out of 5 
Median  2.6030904693325 out of 5 
Minimum Allowed Value  1 out of 5 
Number of Correlations  302 
Number of Measurements  20496 
Onset Delay  0 seconds 
Standard Deviation  0.4502096987717 
Unit  1 to 5 Rating 
Variable ID  1267 
Variance  0.45353341406611 
Principal Investigator  Mike Sinn