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December 31, 2019 - May 22, 2020
you study the biographies of successful people, you will notice a pattern: luck plays a significant role in success. However, if you look deeper, you will notice that most also had a broad luck surface area. Yes, they were in the right place at...
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many aspects of life have inherent variability and cannot be predicted with certainty.
“The most important questions of life are indeed, for the most part, really only problems of probability.”
anecdotal evidence, informally collected evidence from personal anecdotes.
You run into trouble when you make generalizations based on anecdotal evidence or weigh it more heavily than scientific evidence.
“Anecdotal thinking comes naturally, science requires training.”
One issue with anecdotal evidence is that it is often not representative of a full range of experiences.
Just because two events happened in succession, or are correlated, doesn’t mean that the first actually caused the second. Statisticians use the phrase correlation does not imply causation to describe this fallacy.
a confounding factor, a third, possibly non-obvious factor that influences both the assumed cause and the observed effect, confounding the ability to draw a correct conclusion.
confounding the ability to draw a correct conclusion.
randomized controlled experiment, where participants are randomly assigned to two groups, and then results from the experimental group (who receive a treatment) are compared with the results from the control group
A popular version of this experimental design is A/B testing, where user behavior is compared between version A (the experimental group) and version B (the control group) of a site or product, which may differ in page flow, wording, imagery, colors, etc. Such experiments must be carefully designed to isolate the one factor you are studying. The simplest way to do this is to change just one thing between the two groups.
additional blinding helps reduce the impact of observer-expectancy bias (also called experimenter bias), where the cognitive biases of the researchers, or observers, may cause them to influence the outcome in the direction they expected.
Interestingly, just the act of receiving something that you expect to have a positive effect can actually create one, called the placebo effect.
While placebos have little effect on some things, like healing a broken bone, the placebo effect can bring about observed benefits for numerous ailments.
anticipation of side effects can also result in real negative effects, even with fake treatments, a phenomenon known as the nocebo effect.
One of the hardest things about designing a solid experiment is defining its endpoint, the metric that is used to evaluate the hypothesis.
Selection bias can also occur when a sample is selected that is not representative of the broader population of interest, as with online reviews.
Results are therefore biased based on measuring just the population that survived, in this case the employees remaining at the company.
law of large numbers, which states that the larger the sample, the closer your average result is expected to be to the true average.
sample is too small. First, consider the gambler’s fallacy, named after roulette players who believe that a streak of reds or blacks from a roulette wheel is more likely to end than to continue with the next spin. Suppose you see ten blacks in a row. Those who fall victim to this fallacy expect the next spin to have a higher chance of coming up red, when in fact the underlying probability of each spin hasn’t changed.
Streaks like this are often erroneously interpreted as evidence of nonrandom behavior, a failure of intuition called the clustering illusion.
The improbable should not be confused with the impossible. If enough chances are taken, even rare events are expected to happen.
gambler’s fallacy, you shouldn’t always expect short-term results to match long-term expectations. The inverse is also true: you shouldn’t base long-term expectations on a small set of short-term results.
you shouldn’t base long-term expectations on a small set of short-term results.
regression to the mean.
regression to the mean explains why extreme events are usually followed by something more typical, regressing closer to the expected mean.
The takeaway is that you should never assume that a result based on a small set of observations is typical. It may not be representative of either another small set of observations or a much larger set of observations.
data. The mean (average or expected value) measures central tendency, or where the values tend to be centered.
median (middle value that splits the data into two halves) and the mode (the most frequent result).
minimum to maximum reported values from healthy people, as in the graph below (called a histogram).
The most common statistical measures of dispersion, though, are the variance and the standard deviation (the latter usually denoted by the Greek letter σ, sigma). They are both measures of how far the numbers in a dataset tend to vary from its mean.
They are both measures of how far the numbers in a dataset tend to
vary from its mean. The following figure shows how you calculate th...
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The normal distribution is a special type of probability distribution, a mathematical function that describes how the probabilities for all possible outcomes of a random phenomenon are distributed.
central limit theorem. This theorem states that when numbers are drawn from the same distribution and then are averaged, this resulting average approximately follows a normal distribution.
This type of data looks nothing like a normal distribution, as each data point can take only one of two possible values. Binary data like this is often analyzed using a different probability distribution, called the Bernoulli distribution,
This is an example of a model called conditional probability, the probability of one thing happening under the condition that something else also happened. Conditional probability allows us to better estimate probabilities by using this additional information.
conditional probability, the probability of one thing happening under the condition that something else also happened.
Some people find conditional probabilities confusing. They mix up the probability that an event A will happen given a condition that event B happened—P(A|B)—with the probability that an event B will happen given the condition that event A happened—P(B|A). This is known as the inverse fallacy, whereby people think that P(A|B) and P(B|A) must have similar probabilities. While you just saw that P(breast cancer by ninety | woman with BRCA mutation) is about 80 percent, by contrast P(woman with BRCA mutation | breast cancer by ninety) is only 5 to 10 percent, because many other people develop
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When a probability calculation fails to account for the base rate (like the base rate of drunk drivers), the mistake
that is made is called the base rate
P(A|B) does not equal P(B|A), but how are they related? There is a very useful result in probability called Bayes’ theorem,
There is a very useful result in probability called Bayes’ theorem, which tells us the relationship between these two conditional probabilities.
The basic principle of Bayes’ Theorem is to take a set of “prior beliefs" and see how they change in the face of given evidence
Bayesians, by contrast, allow probabilistic judgments about any situation, regardless of whether any observations have yet occurred. To do this, Bayesians begin by bringing related evidence to statistical determinations.
far you have learned that you shouldn’t base your decisions on anecdotes and that small samples cannot reliably tell you what will happen in larger populations.
p-value, which is formally defined as the probability of obtaining a result equal to or more extreme than what was observed,
The absence of evidence is not the evidence of absence.
In order to be sure a study result isn’t a fluke, it needs to be replicated.
Some but not all systematic reviews include meta-analyses, which use statistical techniques to combine data from several studies into one analysis.
