How it works

The standard score is the signed number of standard deviations by which the value of an observation or data point is above the mean value of what is being observed or measured. Observed values above the mean have positive standard scores, while values below the mean have negative standard scores. z = (x - μ)/σ

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Intro to Statistics

These thoughts were extracted from Udacity online course and cover topics such as: Visualizing relationships in data, Probability, Estimation, Outliers and Normal Distribution, Inference and Regression.
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Bar chart: Useful to see global trend where individual points have too much noise.
Daniel Campos
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Difference between Bar Chart and Histograms: Bar Charts can show 2D whereas Histograms show only 1D, which is the frequency of data between ranges.
Daniel Campos
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Pie chart: Good for relative data and comparing.
Daniel Campos
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Statistics is deep and often manipulated, we need to be careful when translating raw data into decisions/conclusions.
Daniel Campos
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If the probability of P(H) = 0.5, then P(H, H) would be: P(H) * P(H) = 0.25
Daniel Campos
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For simple probability problems, a truth table helps finding the answer.
Daniel Campos
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Probability of an event (P), an opposite event (1-P) and a composite event (P*P...*P) are independent.
Daniel Campos
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Conditional Probability is where one event depends on another e.g. P(test | disease).
Daniel Campos
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Bayes Rule: P(A|B) = P(B|A) * P(A) / P(B) Pior Probability (Cancer) * Test Evidence (Pos|Neg) = Posterior Probability
Daniel Campos
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Bayes Rule describes the probability of an event, based on prior knowledge of conditions that might be related to the event e.g. if cancer is related to age, then, using Bayes Rule, a person’s age can be used to more accurately assess the probability that they have cancer.
Daniel Campos
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In continuous distributions, every outcome has a probability of 0 e.g. spin a bottle in a 360 panel to hit an exact angle.
Daniel Campos
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Data is correlated if knowledge about one variable tells you something about another variable.
Daniel Campos
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Studies and news often confuse correlation and causation.
Daniel Campos
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A correlation between variables does not automatically mean that the change in one variable is the cause of the change in the values of the other variable.
Daniel Campos
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Causation indicates that one event is the result of the occurrence of the other event; i.e. there is a causal relationship between the two events.
Daniel Campos
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Maximum Likelihood Estimator: 1/n * Sum(Appearances), e.g.: HHHT => 1/4 * Sum(H) => 1/4 * 3 = 0.75
Daniel Campos
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When there isn't much data... fake it!
Daniel Campos
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Mean: 1/n * Σ(x). Median: sort(x) and gets the value in the middle. Mode: Most frequent value. Useful for Bimodal or Multimodal (several bumps in a chart) data.
Daniel Campos
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Variance measures how far the data is from the mean value, in other words, it show how spread the data is.
Daniel Campos
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Variance can be calculated as the average of the squared difference for each element from the mean.: σ² = i/n * Σ(x-μ)²
Daniel Campos
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You can think of variance as a measure of how wide the tree is from which the apples fell down.
Daniel Campos
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Standard Deviation (SD) is also a measure of spread and it is the σ = sqrt(σ²). The scale of SD is the same as the mean.
Daniel Campos
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Quartiles are the three points that divide the data set into four equal groups, each group comprising a quarter of the data. We could remove the lower and higher quartiles in order to get rid of outliers.
Daniel Campos
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A percentile is a measure used in statistics indicating the value below which given percentage of observations in a group of observations fall. For example, the 20th percentile is the value (or score) below which 20% of the observations may be found.
Daniel Campos
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The binomial distribution is used when there are exactly two mutually exclusive outcomes of a trial. The binomial distribution is used to obtain the probability of observing k successes in N trials, with the probability of success on a single trial denoted by P.
Daniel Campos
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The Central Limit Theorem establishes that, in most situations, when independent random variables are added, their properly normalized sum tends toward a normal distribution (informally a "bell curve" or Gaussian) even if the original variables themselves are not normally distributed.
Daniel Campos
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The Central Limit Theorem is a key concept in probability theory because it implies that probabilistic and statistical methods that work for normal distributions can be applicable to many problems involving other types of distributions.
Daniel Campos
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Email:daniel felicissimo@gmail com63329 h1ujmg.y6xkw0o1or
The normal (or Gaussian) distribution is a very common continuous probability distribution. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known.
Daniel Campos
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If you're a doctor and you have 1 patient, use simple probability like a coin flip, if you have few patients use Binomial Distribution, if you have hundreds of thousand of patients (such as in testing a new drug) use Normal Distribution.
Daniel Campos
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The more data we have and the more we trust the data the smaller the Confidence Interval will be.
Daniel Campos
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Standard Deviation is not affected by the sample size whereas the Confidence Interval is.
Daniel Campos
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Confidence Interval can be calculated by 1.96 * sqrt(σ²/N) 1.96 is a constant that depends on the sample size.
Daniel Campos
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Hypothesis Test: Given a hypothesis H0 (or null hypothesis) (P = 0.8), we test if it is plausible or not. First, we define the Alternate Hypothesis H1 (P < 0.8), calculate the critical region, then we check if the sample result falls into the critical region.
Daniel Campos
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Hypothesis Test: Checking the critical region -- one-side tail goes until 5% is reached, two-sided tail goes until 2.5% is reached on both ends. If yes, the we can reject H0 with a 95% confidence.
Daniel Campos
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If the Null Hypothesis falls down into the Confidence Interval, we accept it, otherwise we reject it.
Daniel Campos
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In order to calculate the Confidence Interval we need: 1) calculate the mean μ, 2) calculate the variance σ², 3) get the probability constant according to the number of samples, 4) calculate the CI: constant * sqrt(σ²/N).
Daniel Campos
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In Linear Regression, we try to find a linear equation (y = bx + a) that best fits the given data. Where b = Σ((x-μx)*(y-μy))/Σ(x-μx) and a = μy - b*μx
Daniel Campos
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Linear Regression: "b" is also known as Slope and "a" as Intercept. b = cov(x, y)/var(x) and a = μy - b*μx
Daniel Campos
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Correlation coefficient is a value between -1 and 1 and it tells us how "related" 2 variables are. Both -1 and 1 stand for perfectly linear data.
Daniel Campos
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Correlation formula is: r = Σ((x-μx)*(y-μy)) / sqrt(Σ(x-μx)² * Σ(y-μy)²)
Daniel Campos
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Beyond any question, the way the American founders consistently linked faith and freedom, republicanism and religion, was not only deliberate and thoughtful, it was also surprising and anything but routine.
Os Guinness
Challenge yourself, its fine not to be a totally finished person.
Leigh Steinberg
Time invested in improving ourselves cuts down on time wasted in disapproving of others.
Unknown
There is a disconnect between the film Bond and the literary Bond which is their contemporaneity. I don't suffer from that.
William Boyd
I believe that shows should be shot where they take place.
Gabriel Macht
Sundance took me on my first film and from there sort of launched my career.
Cary Fukunaga
A man can be short and dumpy and getting bald but if he has fire women will like him.
Mae West
In terms of the arguments, I think the pro-Leave campaign is winning them all.
Nigel Lawson