NOTE (edited): I'm running this experiment with n1.tools, which is now a fully functional MVP! The tool is free to use, so feel free to register and try it out.
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I have been conducting a blinded trial to see whether 1.5mg of melatonin decreases the amount of time it takes me to get to sleep, as measured by my Oura ring (sleep latency).

1. Take 1.5mg melatonin or a placebo (blinded) before going to bed.

2. Sleep, check what I took the next morning.
3. Check the sleep latency metric in the Oura app and record alongside whether I took the placebo/supplement.

3. Repeat for 20 days.

Resolution criteria: Resolves YES if a naive model (i.e. that doesn't include confounders etc.) suggests at least an 80% probability that 1.5mg melatonin reduces my sleep latency at all.

Here's an example experiment that shows a 81% chance of a reduction in my post-coffee anxiety from L-Theanine - P(decrease) 0.81

Extra notes:
- I've actually already done this experiment (last day was today, March 27th), but I haven't released the results.
- I won't bet on this market.
- I haven't done the experiment on days when I stayed out later than usual, or consumed alcohol.

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Model details (for those interested)

I'll model the posterior distribution of sleep latency with the placebo and with 1.5mg melatonin, and then merge those to create a posterior distribution for the absolute difference in sleep latency between the two.

I'll be using a Bayesian model for this, with the assumptions laid out below. Importantly, I assume that the prior and posterior sleep latency observations are normally distributed. Skipping this assumption would mean I have to use a sampling algorithm like MCMC, which would take too long to be feasible in the n1.tools app (I could assume other forms for the distributions and use the corresponding equation to update, but for now I'm sticking to the above).

Priors:

• Mean Melatonin ~ Normal(mean_supplement_data, var_supplement_data)

• Mean Placebo ~ Normal(mean_placebo_data, var_placebo_data)

• Variance Melatonin ~ Variance of supplement_data

• Variance Placebo ~ Variance of placebo_data
  

Likelihoods:

• Data Melatonin ~ Normal(Mean Melatonin, sqrt(5))

• Data Placebo ~ Normal(Mean Placebo, sqrt(5))

Posterior Inference:

• Probability(Absolute Difference ≤ 0) ≥ 0.80