A fancier method of imputation would be multiple imputation using, for example, the R library mice (Multivariate Imputation by Chained Equations) (guide), which will try to impute all missing values in a way which mimicks the internal structure of the data and provide several possible datasets to give us an idea of what the underlying data might have looked like, so we can see how our estimates improve with no missingness & how much of the estimate is now due to the imputation:

Increase your memory, alertness, energy and focus with the most revolutionary “limitless” pill ever created. As we age, our brains start to slow down both in reaction time and in the recalling of memories. That’s why we need to not only regain our mental capacity, we need to enhance it to such heights that we go well beyond where we started. When you use the dietary supplement Addium, you can total replenish and revitalize your mental alertness in a safe, all-natural way. Made of some of the most powerful brain enhancing ingredients on the market, Addium can be used each day to increase memory function, enhance brain power, increase physical energy and stay sharper and more focused. Don’t just settle for feeling like everyone else; it’s time to take your mind to a limitless state of mental preparedness. Addium Brain Enhancing Dietary Supplement also contains the following benefits: • Boosts your capacity for learning • Increases your alertness and focus • Safe and all natural • Promotes strong brain function • Enhances memory and performance Addium contains: Vitamin B6 - An economical source for cardio health and energy metabolism. Addium contains a Proprietary Blend of: Acetyl L-Carnitine - Energizes the mind and promotes concentration. L-Theanine - Enhances endocrine function, stimulating some brain waves and leaving others unaffected. Caffeine - Increase mental alertness. Rhodiola Rosea Extract - Fights the physical and mental effects of stress. Bacopa Monnieri Extract – This ingredient increases cerebral blood flow and cognitive function at the same time.
These pills don’t work. The reality is that MOST of these products don’t work effectively. Maybe we’re cynical, but if you simply review the published studies on memory pills, you can quickly eliminate many of the products that don’t have “the right stuff.” The active ingredients in brain and memory health pills are expensive and most companies sell a watered down version that is not effective for memory and focus. The more brands we reviewed, the more we realized that many of these marketers are slapping slick labels on low-grade ingredients.
I don’t believe there’s any need to control for training with repeated within-subject sampling, since there will be as many samples on both control and active days drawn from the later trained period as with the initial untrained period. But yes, my D5B scores seem to have plateaued pretty much and only very slowly increase; you can look at the stats file yourself.

Interesting however, that there’s no mention of the power of cocoa (chocolate extract) or green tea. I’ve reviewed dozens of studies from Harvard Science as well as internation publications that discuss cocoa in particular. We already know the value of antioxidants in green tea but chocolate seems to be up and coming. I’ve been taking a product called vavalert that combines cocoa and green tea and it’s been working like a miracle.
It goes without saying that ensuring your brain performs at its top capacity levels is every person’s priority. However, the trouble is this is something easier said than done. We live in the extremely competitive and demanding modern world. That’s a fact. We aren’t getting any younger. That’s also a fact. The inevitable aging process takes a toll on our mental capacity and brain itself, as well. So, what can you do about it? Natural supplements can boost your brain power in an efficient and harmless way. This is how one of these supplements named Brain Pill caught our attention.
"In an era of confusion about what we should eat, Brain Food is a shining light. This is the straight story about 'neuro-nutrition' firmly rooted in research by a neuroscientist who has a deep understanding of how food affects our cognitive health. Dr. Mosconi gives us advice we can easily implement into our lives and a story about the science behind it that is both delightful and accessible. A must read!"
(As I was doing this, I reflected how modafinil is such a pure example of the money-time tradeoff. It’s not that you pay someone else to do something for you, which necessarily they will do in a way different from you; nor is it that you have exchanged money to free yourself of a burden of some future time-investment; nor have you paid money for a speculative return of time later in life like with many medical expenses or supplements. Rather, you have paid for 8 hours today of your own time.)
"Instead of messing it up, we should be appreciating something that nature has taken years to optimize," Dr. Lisa mentions. But, we aren't messing it up voluntarily or, at the very least, on any conscious or malicious level. She attributes our disregard for neuro-nutrition to a series of factors, which include the portion size of meals, how parents don't have the time to cook or teach children how to eat healthily, the big influence of cafeteria food, and our "always on the go" culture. According to her, this leads us to unconsciously choose meals which are poor quality and high in sugars, a deathly combination for our brains.
Price discrimination is aided by barriers such as ignorance and oligopolies. An example of the former would be when I went to a Food Lion grocery store in search of spices, and noticed that there was a second selection of spices in the Hispanic/Latino ethnic food aisle, with unit prices perhaps a fourth of the regular McCormick-brand spices; I rather doubt that regular cinnamon varies that much in quality. An example of the latter would be using veterinary drugs on humans - any doctor to do so would probably be guilty of medical malpractice even if the drugs were manufactured in the same factories (as well they might be, considering economies of scale). Similarly, we can predict that whenever there is a veterinary drug which is chemically identical to a human drug, the veterinary drug will be much cheaper, regardless of actual manufacturing cost, than the human drug because pet owners do not value their pets more than themselves. Human drugs are ostensibly held to a higher standard than veterinary drugs; so if veterinary prices are higher, then there will be an arbitrage incentive to simply buy the cheaper human version and downgrade them to veterinary drugs.
Lisa Mosconi has a web and media presence and a book Brain Food: The Surprising Science of Eating for Cognitive Power. She claims, “There is increasing evidence that implementing the lifestyle changes described in this book has the potential to prevent Alzheimer’s from developing and also to help slow down or even halt progression of the disease.” What’s more, “eating for your brain…actually helps you achieve peak performance in every part of your life.”
The use of prescription stimulants is especially prevalent among students.[9] Surveys suggest that 0.7–4.5% of German students have used cognitive enhancers in their lifetime.[10][11][12] Stimulants such as dimethylamylamine and methylphenidate are used on college campuses and by younger groups.[13] Based upon studies of self-reported illicit stimulant use, 5–35% of college students use diverted ADHD stimulants, which are primarily intended for performance enhancement rather than as recreational drugs.[14][15][16] Several factors positively and negatively influence an individual's willingness to use a drug for the purpose of enhancing cognitive performance. Among them are personal characteristics, drug characteristics, and characteristics of the social context.[10][11][17][18]
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