author: niplav, created: 2023-01-06, modified: 2024-07-06, language: english, status: maintenance, importance: 3, confidence: likely
Modeled after Gwern 2018 I've decided to log my nootropics usage and its effects.
You could put randomized substances in your body and find out what they do by recording the outcomes. That's what I did.
Value tracked | Effect size d (λ, p, σ change) | Effect size d (λ, p, σ change) |
---|---|---|
200 mg Caffeine (n=1, m=50) | 500 mg L-theanine (n=1, m=50) | |
Log-score substance prediction^{1} | -0.6 | -0.7 |
Absorption | 0.61 (λ≈13.3, p≈0.00017, -0.072) | 0.04 (λ≈1.38, p≈0.77, -0.07) |
Mindfulness | 0.58 (λ≈11.8, p≈0.0007, 0.021) | 0.12 (λ≈0.72, p≈0.89, -0.018) |
Productivity | 0.58 (λ≈28.9, p≈1.3^{-12}, 0.11) | -0.28 (λ≈5.51, p≈0.109, 0.03) |
Creativity | 0.45 (λ≈51, p≈4.6^{-27}, 0.09) | -0.12 (λ≈5.05, p≈0.14, -0.04) |
Happiness | 0.27 (λ≈10.6, p≈0.002, 0.3) | 0.16 (λ≈3.98, p≈0.27, -0.155) |
Contentment | 0.13 (λ≈7.66, p≈0.02, 0.47) | 0.25 (λ≈6.83, p≈0.04, -0.04) |
Relaxation | -0.11 (λ≈5, p≈0.15, 0.42) | 0.12 (λ≈1.5, p≈0.74, 0.02) |
Chastity^{2} | -0.14 (λ≈1.9, p≈0.64, 0.11) | -0.03 (λ≈1.15, p≈0.8, 0.25) |
Subjective length of day | Not collected | -0.015 (λ≈0.35, p≈0.95, -0.015)^{3} |
Flashcard ease | 0.003 (λ≈∞, p≈0, -0.009) | -0.072 (λ≈∞, p≈0, -0.01) |
Flashcard ease factor | -0.039 (λ≈∞, p≈0, -32.7) | 0.0026 (λ≈∞, p≈0, -18.9) |
Flashcard new interval | 0.011 (λ≈∞, p≈0, -1.88) | -0.016 (λ≈∞, p≈0, 3.1) |
Time per flashcard^{4} | 0.006 (λ≈∞, p≈0, 273.4) | 0.003 (λ≈∞, p≈0, 13.66) |
I am especially interested in testing many different substances for their effect on meditation, while avoiding negative side effects. The benefits from high meditational attainments valuable to me, and seem especially likely to benefit from chemical intervention, since the Algernon argument likely doesn't apply: Meditative attainments might've not led to a fitness advantage (even, by opportunity cost, to a fitness disadvantage), and so were likely selected against, but most of us don't care that much about inclusive genetic fitness and more about psychological well-being. Evolutionary dynamics favor being like Ghengis Khan (dozens to hundreds of offspring) over Siddharta Gautama (one son), but I'd rather attain sotāpanna than pillage and murder.
And meditative attainments are costly: they take tens to hundreds to thousands of hours to reach, which would make simple psychopharmacological interventions worthwhile. I also don't buy that they miss the point of meditation—most people already struggle enough, so some help doesn't make it a cakewalk; "reach heaven through fraud". One must be careful not to fall into the trap of taking substances that feel good but lessen sensory clarity (which I believe was the original intent behind the fifth precept, and so I'll exclude e.g. opiates from the substances to test).
I won't dig too deep into the effects of caffeine, as other people have done that already (Examine, Gwern, Wikipedia).
Variables tracked (see more here):
The total cost of the experiment is at least 21.5€:
$\frac{0.0825€}{\text{200mg caffeine pill}} \cdot \text{ 200mg caffeine pills}=2.0625€$
$\frac{0.03€}{\text{capsule}} \cdot 25 \text{ capsules}=0.75€$
200mg caffeine pills, placebo pills filled with sugar, of each 25.
Put each pill with a corresponding piece of paper ("C" for caffeine,
"P" for placebo) into an unlabeled envelope. Used seq 1 50 | shuf
to number the envelopes, and sorted them accordingly.
Notes on the experiment:
In general, I'll be working with the likelihood ratio
test (encouraged by
this article). For
this, let $\mathbf{v}_P$
be the distribution of values of a
variable for the placebo arm, and $\mathbf{v}_C$
the distribution
of values for a variable of the caffeine arm. (I apologise for the
$C$
being ambiguous, since it could also refer to the control
arm).
Then let $\theta_0=(\mu_0, \sigma_0)=MLE_{\mathcal{N}}(\mathbf{v}_P)$
be the Gaussian maximum likelihood
estimator
for our placebo values, and
$\theta=(\mu, \sigma)=MLE_{\mathcal{N}}(\mathbf{v}_C)$
be the MLE for our caffeine values.
Then the likelihood ratio statistic $\lambda$
is defined as
where $\mathcal{L}_C(\theta)$
is the likelihood the caffeine
distribution assigns to the parameters $\theta$
. This test is useful
here because we fix all values of $\theta_0$
. See Wasserman 2003
ch. 10.6
for more.
If $\lambda \approx 0$
, then the MLE for the placebo arm is very close
to the MLE for the caffeine arm, the distributions are similar. If
$\lambda>0$
, then the MLE for the placebo arm is quite different from
the caffeine arm (though there is no statement about which has higher
values). $\lambda<0$
is not possible, since that would mean that
the MLE of the placebo distribution has a higher likelihood for the
caffeine data than the MLE of the caffeine distribution itself—not
very likely.
Note that I'm not a statistician, this is my first serious statistical analysis, so please correct me if I'm making some important mistakes. Sorry.
After collecting the data, but before analysing it, I want to make some predictions about the outcome of the experiment, similar to another attempt here.
Moved here.
We start by setting everything up and loading the data.
import math
import numpy as np
import pandas as pd
import scipy.stats as scistat
substances=pd.read_csv('../..//data/substances.csv')
meditations=pd.read_csv('../../data/meditations.csv')
meditations['meditation_start']=pd.to_datetime(meditations['meditation_start'], unit='ms', utc=True)
meditations['meditation_end']=pd.to_datetime(meditations['meditation_end'], unit='ms', utc=True)
creativity=pd.read_csv('../../data/creativity.csv')
creativity['datetime']=pd.to_datetime(creativity['datetime'], utc=True)
productivity=pd.read_csv('../../data/productivity.csv')
productivity['datetime']=pd.to_datetime(productivity['datetime'], utc=True)
expa=substances.loc[substances['experiment']=='A'].copy()
expa['datetime']=pd.to_datetime(expa['datetime'], utc=True)
The mood data is a bit special, since it doesn't have timezone info, but that is easily remedied.
mood=pd.read_csv('../../data/mood.csv')
alarms=pd.to_datetime(pd.Series(mood['alarm']), format='mixed')
mood['alarm']=pd.DatetimeIndex(alarms.dt.tz_localize('CET', ambiguous='infer')).tz_convert(tz='UTC')
dates=pd.to_datetime(pd.Series(mood['date']), format='mixed')
mood['date']=pd.DatetimeIndex(dates.dt.tz_localize('CET', ambiguous='infer')).tz_convert(tz='UTC')
This data can now be plotted unwieldly:
We can first test how well my predictions fared:
probs=np.array(expa['prediction'])
substances=np.array(expa['substance'])
outcomes=np.array([0 if i=='sugar' else 1 for i in substances])
drumroll
>>> np.mean(list(map(lambda x: math.log(x[0]) if x[1]==1 else math.log(1-x[0]), zip(probs, outcomes))))
-0.5991670759554912
At least this time I was better than chance:
>>> np.mean(list(map(lambda x: math.log(x[0]) if x[1]==1 else math.log(1-x[0]), zip([0.5]*40, outcomes))))
-0.6931471805599453
After finishing the coding for this
experiment,
I decided it'd be easier if for the future I could call a single
function to analyze all my data for me. The result can be found
here, the function is
analyze(experiment, substance, placebo)
.
To analyze this specific experiment, I simply call
caffeine_results=analyze('A', 'caffeine', 'sugar')
and get this nice
DataFrame:
absorption mindfulness productivity creativity happy content relaxed horny ease factor ivl time
d 0.611936 0.575982 5.784144e-01 4.544300e-01 0.270813 0.129624 -0.114858 -0.140795 -0.009327 -0.068599 -0.046602 0.021811
λ 13.309889 11.791000 2.889791e+01 5.103201e+01 10.644193 7.660893 5.007775 1.964261 inf inf inf inf
p 0.000167 0.000724 1.348364e-12 4.609786e-27 0.002074 0.024625 0.150156 0.639840 0.000000 0.000000 0.000000 0.000000
dσ -0.072088 0.021868 1.139222e-01 9.659407e-02 0.295592 0.473630 0.415262 0.108356 -0.011060 -0.679137 -0.567543 697.624130
Caffeine appears helpful for everything except relaxation (and it maybe makes me hornier, which I'm neutral about). I'd call this experiment a success and will be running more in the future, while in the meantime taking caffeine before morning meditations.
Examine. I follow the loading procedure detailed here:
Creatine is a supplement that is known for having a 'loading' phase followed by a 'maintenance' phase. A typical creatine cycle has three parts to it.
- Take 20-25g (or 0.3g/kg) for 5-7 days (Loading)
- Then take 5g daily for 3-4 weeks (Maintenance)
- Take a week or two off creatine, and then repeat (Wash-out)
First dose was taken on 2023-01-06.
I'm especially interested in the effects of creatine on my cognition (it might increase IQ in vegetarians (or it might not?), and I'm a lacto-vegetarian), my exercising performance and my meditation ability.
L-Theanine is synergistic with caffeine in regards to attention switching^{[318]} and alertness^{[319][320]} and reduces susceptibility to distractions (focus).^{[320][321]} However, alertness seems to be relatively subjective and may not be a reliable increase between these two compounds,^{[318]} and increases in mood are either present or absent.^{[322][318][323]} This may be due to theanine being a relatively subpar nootropic in and of itself pertaining to the above parameters, but augmenting caffeine's effects; some studies do note that theanine does not affect the above parameters in and of itself.^{[324]} Due to this, any insensitivity or habituation to caffeine would reduce the effects of the combination as L-theanine may work through caffeine.
L-Theanine does not appear to be synergistic with caffeine in regards to attention to a prolonged and monotonous task.^{[325]}
—Kamal Patel, “Caffeine”, 2023
See again Examine, Wikipedia and Gwern.
Sitiprapaporn et al. 2018 test the effect of an unspecified quantity of L-theanine via Oolong tea on meditation on 10 university students (non-randomized, it seems). Data collected via EEG and indicates statistically significantly more alpha waves during meditation (although it is unclear how long the meditation was).
This paper is bad. The english is so horrendous it feels like I'm having a stroke while I'm reading it, but that would be fine if they were good at reporting methods, which they are not (missing amounts of L-theanine and duration of meditation, they also mention reading earlier in the article, which I assumed was the control activity, but it doesn't come up again?). Also they report differences between scores, not effect sizes, and some figures are screenshotted images from a Windows Vista clustering application.
Examine agrees on the cognitive effects of l-theanine (if not on meditation specifically):
L-Theanine supplementation in the standard dosages (50-250mg) has been repeatedly noted to increase α-waves in otherwise healthy persons. This may only occur in persons with somewhat higher baseline anxiety^{[25][26]} or under periods of stress (positive^{[14]} and negative^{[27]} results), but has been noted to occur during closed eye rest^{[5]} as well as during visuospatial tasks^{[16]} around 30-45 minutes after ingestion.^{[5][4]} It appears that only the α-1 wave (8-10Hz) is affected, with no influence on α-2 wave (11-13Hz).^{[4]}
Bill Willis, “Theanine”, 2022
Although I'm confused about the increased α-waves in "otherwise healthy patients"‽
Additionally, it notes that memory was slightly increased:
One study using a supplement called LGNC-07 (360mg of green tea extract and 60mg theanine; thrice daily dosing for 16 weeks) in persons with mild cognitive impairment based on MMSE scores, supplementation was associated with improved delayed recognition and immediate recall scores with no effect on verbal and visuospatial memory (Rey-Kim test).^{[17]}
Bill Willis, “Theanine”, 2022
This time I explicitely divided my meditation into a concentration part (first 15 minutes) and a mindfulness part (last 30 minutes).
$\frac{~0.25€}{\text{500mg L-theanine pill}} \cdot 25 \text{ 500mg L-theanine pills}=6.25€$
$0.75€$
Notes during consumption:
Ran the experiment from 2023-06-22 to 2023-09-28, sometimes with pauses inbetween samples.
I use the same statistical techniques as in the caffeine experiment, and start, as usual, with my predictions about the content of the pill:
>>> substances=pd.read_csv('../../data/substances.csv')
>>> experiment='B'
>>> substance='l-theanine'
>>> placebo='sugar'
>>> expa=substances.loc[substances['experiment']==experiment].copy()
>>> expa['datetime']=pd.to_datetime(expa['datetime'], utc=True)
>>> probs=np.array(expa['prediction'])
>>> substances=np.array(expa['substance'])
>>> outcomes=np.array([0 if i=='sugar' else 1 for i in substances])
>>> np.mean(list(map(lambda x: math.log(x[0]) if x[1]==1 else math.log(1-x[0]), zip(probs, outcomes))))
-0.705282842369643
This is not great. In fact, it's slightly worse than chance (which would be about -0.693). Not a great sign for L-theanine, and, in fact, it gets worse. I use the generalized and compacted code from the last experiments to get the other results, and they don't point a rosy picture for L-theanine:
>>> analyze('B', 'l-theanine', 'sugar')
absorption mindfulness productivity creativity happy content relaxed horny ease factor ivl time
d 0.040887 0.124170 -0.278448 -0.116001 0.164261 0.254040 0.119069 -0.031665 -0.072098 0.002561 -0.015955 0.003073
λ 1.378294 0.720780 5.517769 5.049838 3.983760 6.833004 1.496601 1.148131 inf inf inf inf
p 0.765758 0.894798 0.109735 0.146420 0.266491 0.045270 0.740705 0.813279 0.000000 0.000000 0.000000 0.000000
dσ -0.067847 -0.017736 0.039855 -0.043241 -0.155797 -0.046668 0.019655 0.251454 -0.016542 -18.901846 3.108518 13.660820
It worsens productivity and creativity (though not quite statistically significantly, but it's on the way there), but at least it improves my mood somewhat (though those results, besides contentment, might as well be due to random chance). No clear effect sizes with the flashcards either.
So a hard pass on L-theanine, I think. My current best guess is that as a night owl in the morning I'm still quite tired, and lack energy, with l-theanine just making me more sleepy than I already am. But then again, under Bonferroni correction none of the p-values are statistically significant, so it looks like l-theanine just doesn't do anything. Maybe it's better when combined with caffeine?
After being bullied into it by Gwern 2019 and reading more about dosage & administration in Scott Alexander 2018, I decided to tackle my irregular sleeping rhythm and my late bedtimes by taking Melatonin.
Getting enough high-quality sleep had been quite a problem for most of my life, I just could not find the willpower to actually go to bed early on most days. Most other advice relied on exactly bringing up this willpower (just read before going to bed/just stay away from screens/just do sports in the morning/just spend more time outside/just masturbate (actually counter-productive in my case!)); Gwern's framing as an enforcement mechanism appealed to me, and the cost-benefit analysis seemed sound.
I first tried buying Melatonin at a pharmacy, only to find out that it is prescription only in my country. A friend told me he had bought his from Ebay as a food supplement (laws have interesting loopholes), I ordered 100 3mg pills for ~30€ and they arrived, together with around 10g of protein powder.
I experimented around with administration time & dosage, finding out that 1/8th (≈0.375g) of a pill, administered at ~20:00, was usually sufficient to make me sleepy enough at 23:00 to actually go to bed (though the pills are kind of hard to cut well). I also realized that it was not necessary to take Melatonin every evening, once a good rhythm had been established, a dosage every 2 or 3 days was usually enough to keep the habit of going to bed early.
In the last couple of weeks I've felt like 1/8th of a pill is not enough, perhaps this is adaption to the substance (though I remember reading that adaption is negligible). Alternatively, the placebo effect might be wearing off.
While I haven't experiencde more vivid dreams from Melatonin (which I'd consider an advantage), sometimes my sleep on Melatonin is very light, bordering on dozing, and I also sometimes experience sleep paralysis while on melatonin. This is in stark contrast with my normal sleep on melatonin, which I'd guess is deeper than my normal sleep.
One large (potential) advantage of Melatonin would be a reduction in the
amount of time slept.
2½ months after getting a wearable tracker, I decided to analyze
my data on this. I'll spare you the details of data conversion (and
will just say that it's kind of annoying that pandas merge
doesn't
implement the antijoin)
and cut straight to the chase (of which the code can be found
here):
>>> melatonin_sleep['minutes_asleep'].mean()
395.5652173913044
>>> non_melatonin_sleep['minutes_asleep'].mean()
387.2142857142857
>>> non_melatonin_sleep['minutes_asleep'].var()
17452.53506493507
>>> melatonin_sleep['minutes_asleep'].var()
5158.620553359683
>>> len(non_melatonin_sleep)
56
>>> len(melatonin_sleep)
23
It doesn't look like Melatonin has a large effect on sleep durations, at least with the current (meagre) sample sizes).
Maybe it helps if we filter out sleep that starts later than 6:00 in the morning (which excludes naps)?
>>> non_nap_melatonin_sleep=melatonin_sleep.loc[(melatonin_sleep['start_time'].dt.hour<6) & (melatonin_sleep['start_time'].dt.hour<18)]
>>> non_nap_melatonin_sleep['minutes_asleep'].mean()
395.5652173913044
>>> non_nap_non_melatonin_sleep=non_melatonin_sleep.loc[(non_melatonin_sleep['start_time'].dt.hour<6) & (non_melatonin_sleep['start_time'].dt.hour<18)]
>>> non_nap_non_melatonin_sleep['minutes_asleep'].mean()
419.29545454545456
>>> len(non_nap_melatonin_sleep)
23
>>> len(non_nap_non_melatonin_sleep)
44
>>> lr=likelihood_ratio_test(placebo_likelihood_ratio(non_nap_melatonin_sleep['minutes_asleep'], non_nap_non_melatonin_sleep['minutes_asleep']))
6.363562898136653
>>> llrt_pval(lr)
0.06284859113951252
Here it looks like there is a medium-sized advantage to taking melatonin, with ~25 minutes shorter sleep (at the edge of 'statistical significance').
While Melatonin has been very useful at enforcing bedtimes, the advantage of sleeping less has been moderate, and potentially just caused by noise.
I am very glad that I've bought & tried Melatonin; it has to a large degree fixed a significant problem in my life. I am now happier in the morning when I wake up, less tired during the course of the day, and don't have to feel guilty at 04:00 because I stayed up too late.
At my current usage, my stash will last me
$95 \hbox{ pills } \cdot 8\frac{\hbox{dosages}}{\hbox{pill}} \cdot 2\frac{\hbox{days}}{\hbox{dosage}}=1520 \hbox{ days}$
:
more than 4 years! Even if the future effects are just half as good as
the past effects, this investment was completely worth it.
I started taking nicotine (in the form of nicotine chewing gum with 2mg of active ingredient) in high-pressure situations (e.g. I'm procrastinating on an important task and have anxiety around it, or during exams). So far, it seems especially useful to break me out of an akratic rut.
Predicting the outcomes of personal experiments give a useful way to train ones own calibration, I take it a step further and record the predictions for the world to observe my idiocy. The probabilities link to PredictionBook/Fatebook.
Question | Caffeine probability | Caffeine outcome | L-Theanine probability | L-Theanine outcome |
---|---|---|---|---|
Prediction of Arm | ||||
My prediction about the content of the pill is more accurate than random guesses | 80% | Yes | 65% | No |
My prediction about the content of the pill has a log score of more than -0.5 | 60% | No | 40% | No |
Meditation | ||||
On interventional days, my average mindfulness during meditation was higher than days with placebo | 60% | Yes | 45% | Yes |
On interventional days, my average absorption during meditation was higher than days with placebo | 40% | No | 55% | Yes |
On interventional days, the variance of values for mindfulness during meditation was lower than on placebo days | 55% | No | 60% | No |
On interventional days, the variance of values for absorption during meditation was lower than on placebo days | 35% | Yes | 65% | No |
$\lambda<1$ for the mindfulness values |
20% | No | 7% | Yes |
$\lambda<1$ for the absorption values |
25% | No | 5% | No |
$\lambda<4$ for the mindfulness values |
82% | No | 15% | Yes |
$\lambda<4$ for the absorption values |
88% | No | 20% | Yes |
$\lambda<10$ for the mindfulness values |
65% | Yes | ||
$\lambda<10$ for the absorption values |
60% | Yes | ||
Mood | ||||
On interventional days, my average happiness during the day was higher than days with placebo | 65% | Yes | 55% | Yes |
On interventional days, my average contentment during the day was higher than days with placebo | 45% | Yes | 60% | Yes |
On interventional days, my average relaxation during the day was higher than days with placebo | 35% | No | 65% | Yes |
On interventional days, my average chastity during the day was higher than days with placebo | 50% | No | 50% | No |
On interventional days, the variance of values for happiness during the day was lower than on placebo days | 55% | No | 60% | Yes |
On interventional days, the variance of values for contentment during the day was lower than on placebo days | 30% | No | 65% | Yes |
On interventional days, the variance of values for relaxation during the day was lower than on placebo days | 30% | No | 65% | No |
On interventional days, the variance of values for chastity during the day was lower than on placebo days | 50% | No | 50% | No |
$\lambda<1$ for the happiness values |
45% | No | 8% | No |
$\lambda<1$ for the contentment values |
40% | No | 5% | No |
$\lambda<1$ for the relaxation values |
37% | No | 5% | No |
$\lambda<1$ for the chastity values |
60% | No | 10% | No |
$\lambda<4$ for the happiness values |
85% | No | 18% | No |
$\lambda<4$ for the contentment values |
90% | No | 12% | No |
$\lambda<4$ for the relaxation values |
90% | No | 12% | Yes |
$\lambda<4$ for the chastity values |
95% | Yes | 20% | Yes |
$\lambda<10$ for the happiness values |
75% | Yes | ||
$\lambda<10$ for the contentment values |
70% | Yes | ||
$\lambda<10$ for the relaxation values |
70% | Yes | ||
$\lambda<10$ for the chastity values |
85% | Yes | ||
Productivity and Creativity | ||||
On interventional days, my average productivity during the day was higher than days with placebo | 52% | Yes | 65% | No |
On interventional days, my average creativity during the day was higher than days with placebo | 55% | Yes | 55% | No |
On interventional days, the variance of values for productivity during the day was lower than on placebo days | 40% | No | 70% | No |
On interventional days, the variance of values for creativity during the day was lower than on placebo days | 65% | No | 50% | Yes |
$\lambda<1$ for the productivity values |
40% | No | 7% | No |
$\lambda<1$ for the creativity values |
45% | No | 9% | No |
$\lambda<4$ for the productivity values |
75% | No | 20% | No |
$\lambda<4$ for the creativity values |
80% | No | 25% | No |
$\lambda<10$ for the productivity values |
60% | Yes | ||
$\lambda<10$ for the creativity values |
70% | Yes |
I also recorded my predictions about the content of the pill on PredictionBook (Caffeine: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50) and Fatebook (L-theanine: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50).
I continue to be worse than chance in my predictions on the outcomes of my own experiments:
>>> import math
>>> import numpy as np
>>> probs=np.array([0.8, 0.6, 0.6, 0.4, 0.55, 0.35, 0.2, 0.25, 0.82, 0.88, 0.65, 0.45, 0.35, 0.5, 0.55, 0.3, 0.3, 0.5, 0.45, 0.4, 0.37, 0.6, 0.85, 0.9, 0.9, 0.95, 0.52, 0.55, 0.4, 0.65, 0.4, 0.45, 0.75, 0.8])
>>> outcomes=np.array([1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0])
>>> np.mean(list(map(lambda x: math.log(x[0]) if x[1]==1 else math.log(1-x[0]), zip(probs, outcomes))))
-0.8610697622640346
>>> np.mean(list(map(lambda x: math.log(x[0]) if x[1]==1 else math.log(1-x[0]), zip([0.5]*50, outcomes))))
-0.6931471805599452
Die Welt gibt dir viel falsche Zeichen,
dem tückischen Geist zu vergleichen,
Du bist, alle Zeichen verachtend,
zu dem ohne Zeichen gegangen.
—Dschelāladdīn Rūmī, “Am Ende bist du entschwunden”, 1256
I realised the code for this wasn't interesting to probably anyone, but if you want details, here it is:
Merging the meditations closest (on the right) to the consumption and selecting the individual variables of interest:
meditations.sort_values("meditation_start", inplace=True)
meditations_a=pd.merge_asof(expa, meditations, left_on='datetime', right_on='meditation_start', direction='forward')
caffeine_concentration=meditations_a.loc[meditations_a['substance']=='caffeine']['concentration_rating']
placebo_concentration=meditations_a.loc[meditations_a['substance']=='sugar']['concentration_rating']
caffeine_mindfulness=meditations_a.loc[meditations_a['substance']=='caffeine']['mindfulness_rating']
placebo_mindfulness=meditations_a.loc[meditations_a['substance']=='sugar']['mindfulness_rating']
So, does it help?
>>> (caffeine_concentration.mean()-placebo_concentration.mean())/meditations['concentration_rating'].std()
0.6119357868347828
>>> (caffeine_mindfulness.mean()-placebo_mindfulness.mean())/meditations['mindfulness_rating'].std()
0.575981762563846
Indeed! Cohen's d here looks pretty good. Taking caffeine also reduces the variance of both variables:
>>> caffeine_concentration.std()-placebo_concentration.std()
-0.0720877290884765
>>> caffeine_mindfulness.std()-placebo_mindfulness.std()
0.02186797288826836
We repeat the same procedure for the productivity and creativity data:
prod_a=pd.merge_asof(expa, productivity, left_on='datetime', right_on='datetime', direction='forward')
creat_a=pd.merge_asof(expa, creativity, left_on='datetime', right_on='datetime', direction='forward')
caffeine_productivity=prod_a.loc[meditations_a['substance']=='caffeine']['productivity']
placebo_productivity=prod_a.loc[meditations_a['substance']=='sugar']['productivity']
caffeine_creativity=creat_a.loc[meditations_a['substance']=='caffeine']['creativity']
placebo_creativity=creat_a.loc[meditations_a['substance']=='sugar']['creativity']
And the result is…
>>> (caffeine_productivity.mean()-placebo_productivity.mean())/prod_a['productivity'].std()
0.5784143673702401
>>> (caffeine_creativity.mean()-placebo_creativity.mean())/creat_a['creativity'].std()
0.38432393552829164
Again surprisingly good! The creativity values are small enough to be a fluke, but the productivity values seem cool.
In this case, though, caffeine increases variance in the variables (not by very much):
>>> caffeine_productivity.std()-placebo_productivity.std()
0.1139221931098384
>>> caffeine_creativity.std()-placebo_creativity.std()
0.08619686235791152
Some unimportant pre-processing, in which we filter
for mood recordings 0-10 hours after caffeine intake, since
pd.merge_asof
doesn't do cartesian product:
mood_a=expa.join(mood, how='cross')
mood_a=mood_a.loc[(mood_a['alarm']-mood_a['datetime']<pd.Timedelta('10h'))&(mood_a['alarm']-mood_a['datetime']>pd.Timedelta('0h'))]
caffeine_mood=mood_a.loc[mood_a['substance']=='caffeine']
placebo_mood=mood_a.loc[mood_a['substance']=='sugar']
And now the analysis:
>>> caffeine_mood[['happy', 'content', 'relaxed', 'horny']].describe()
happy content relaxed horny
count 88.000000 88.000000 88.000000 88.000000
mean 52.193182 51.227273 50.704545 46.568182
std 2.396635 2.911441 3.115254 3.117601
[…]
>>> placebo_mood[['happy', 'content', 'relaxed', 'horny']].describe()
happy content relaxed horny
count 73.000000 73.000000 73.000000 73.000000
mean 51.575342 50.876712 51.041096 47.000000
std 2.101043 2.437811 2.699992 3.009245
[…]
Which leads to d of ~0.27 for happiness, ~0.13 for contentment, ~-0.11 for relaxation and ~-0.14 for horniness.
Because Anki stores the intervals of learning flashcards (that is, ones that have been answered incorrectly too many times), we have to adjust the numbers to reflect that a negative second is not equal to a day.
flashcards_a=flashcards.loc[(flashcards['id']>expa['datetime'].min()) & (flashcards['id']<expa['datetime'].max()+pd.Timedelta('10h'))]
flashcards_a=expa.join(flashcards_a, how='cross', rsuffix='r')
flashcards_a=flashcards_a.loc[(flashcards_a['idr']-flashcards_a['datetime']<pd.Timedelta('10h'))&(flashcards_a['idr']-flashcards_a['datetime']
>pd.Timedelta('0h'))]
flashcards_a.loc[flashcards_a['ivl']>0,'ivl']=-flashcards_a.loc[flashcards_a['ivl']>0,'ivl']/86400
We then again separate into placebo and caffeine:
placebo_flashcards=flashcards_a.loc[flashcards_a['substance']==placebo]
substance_flashcards=flashcards_a.loc[flashcards_a['substance']==substance]
We assume (at first) that the data is distributed normally. Then we can define a function for the gaussian likelihood of a distribution given some parameters:
def normal_likelihood(data, mu, std):
return np.product(scistat.norm.pdf(data, loc=mu, scale=std))
And now we can compute the likelihood ratio
$\frac{\mathcal{L}{θ}}{\mathcal{L}{θ_0}}$
for the null hypothesis
$θ_0=\text{MLE}(\mathbf{v}_P)$
for the placebo data $\mathbf{v}_P$
,
and also the result of the likelihood ratio test:
def placebo_likelihood(active, placebo):
placebo_mle_lh=normal_likelihood(active, placebo.mean(), placebo.std())
active_mle_lh=normal_likelihood(active, active.mean(), active.std())
return active_mle_lh/placebo_mle_lh
def likelihood_ratio_test(lr):
return 2*np.log(lr)
And this gives us surprisingly large values:
>>> placebo_likelihood_ratio(caffeine_concentration, placebo_concentration)
776.6147119766716
>>> likelihood_ratio_test(placebo_likelihood_ratio(caffeine_concentration, placebo_concentration))
13.309888722406932
>> placebo_likelihood_ratio(caffeine_mindfulness, placebo_mindfulness)
363.3984201164464
>>> likelihood_ratio_test(placebo_likelihood_ratio(caffeine_mindfulness, placebo_mindfulness))
11.790999616893938
>>> placebo_likelihood_ratio(caffeine_productivity, placebo_productivity)
1884090.6347491818
>>> likelihood_ratio_test(placebo_likelihood_ratio(caffeine_productivity, placebo_productivity))
28.8979116811553
>>> placebo_likelihood_ratio(caffeine_creativity, placebo_creativity)
14009015.173307568
>>> likelihood_ratio_test(placebo_likelihood_ratio(caffeine_creativity, placebo_creativity))
32.910423242578126
And, if one is interested in p-values, those correspond to (with 2 degrees of freedom each):
def llrt_pval(lmbda, df=2):
return scistat.chi2.cdf(df, lmbda)
>>> llrt_pval([13.309888722406932,11.790999616893938, 28.8979116811553, 32.910423242578126])
array([1.66559304e-04, 7.23739116e-04 ,1.34836408e-12, 5.17222209e-15])
I find these results surprisingly strong, and am still kind of mystified why. Surely caffeine isn't that reliable!
And, the same, for mood:
>>> placebo_likelihood_ratio(caffeine_mood['happy'], placebo_mood['happy'])
204.81283712162838
>>> likelihood_ratio_test(placebo_likelihood_ratio(caffeine_mood['happy'], placebo_mood['happy']))
10.644193144917832
>>> placebo_likelihood_ratio(caffeine_mood['content'], placebo_mood['content'])
46.08310645632934
>>> likelihood_ratio_test(placebo_likelihood_ratio(caffeine_mood['content'], placebo_mood['content']))
7.6608928570645105
>>> placebo_likelihood_ratio(caffeine_mood['relaxed'], placebo_mood['relaxed'])
12.229945616108525
>>> likelihood_ratio_test(placebo_likelihood_ratio(caffeine_mood['relaxed'], placebo_mood['relaxed']))
5.007775005855661
>>> placebo_likelihood_ratio(caffeine_mood['horny'], placebo_mood['horny'])
2.670139324155222
>>> likelihood_ratio_test(placebo_likelihood_ratio(caffeine_mood['horny'], placebo_mood['horny']))
1.9642613047646074
And the p-values of those are:
>>> llrt_pval([10.644193144917832, 7.6608928570645105, 5.007775005855661, 1.9642613047646074])
array([0.0020736 , 0.02462515, 0.15015613, 0.63984027])