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

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

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

Pie chart: Good for relative data and comparing.

Daniel Campos

Statistics is deep and often manipulated, we need to be careful when translating raw data into decisions/conclusions.

Daniel Campos

If the probability of P(H) = 0.5, then P(H, H) would be: P(H) * P(H) = 0.25

Daniel Campos

For simple probability problems, a truth table helps finding the answer.

Daniel Campos

Probability of an event (P), an opposite event (1-P) and a composite event (P*P...*P) are independent.

Daniel Campos

Conditional Probability is where one event depends on another e.g. P(test | disease).

Daniel Campos

Bayes Rule: P(A|B) = P(B|A) * P(A) / P(B) Pior Probability (Cancer) * Test Evidence (Pos|Neg) = Posterior Probability

Daniel Campos

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

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

Studies and news often confuse correlation and causation.

Daniel Campos

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

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

Maximum Likelihood Estimator: 1/n * Sum(Appearances), e.g.: HHHT => 1/4 * Sum(H) => 1/4 * 3 = 0.75

Daniel Campos

When there isn't much data... fake it!

Daniel Campos

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

Variance measures how far the data is from the mean value, in other words, it show how spread the data is.

Daniel Campos

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

You can think of variance as a measure of how wide the tree is from which the apples fell down.

Daniel Campos

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

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

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

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

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

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

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

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

The more data we have and the more we trust the data the smaller the Confidence Interval will be.

Daniel Campos

Standard Deviation is not affected by the sample size whereas the Confidence Interval is.

Daniel Campos

Confidence Interval can be calculated by 1.96 * sqrt(σ²/N) 1.96 is a constant that depends on the sample size.

Daniel Campos

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

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

If the Null Hypothesis falls down into the Confidence Interval, we accept it, otherwise we reject it.

Daniel Campos

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

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

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

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

Correlation formula is: r = Σ((x-μx)*(y-μy)) / sqrt(Σ(x-μx)² * Σ(y-μy)²)

Daniel Campos

The truly happy man is the one who has everything money can’t buy.

Shraga Silverstein

I don't hide. I never have. I stay at home because I like to stay at home, and at home I work.

Oriana Fallaci

President Reagan always gave the credit to the American people and American ideals. He treated his job as a valuable temporary loan from the American people, a loan that should be respected and returned with dutiful appreciation.

William L. Jenkins

He who does not know how to create should not know.

Antonio Porchia

Good things take time.

Unknown

Hold those things that tell your history and protect them. During slavery, who was able to read or write or keep anything? The ability to have somebody to tell your story to is so important. It says: 'I was here. I may be sold tomorrow. But you know I was here.'

Maya Angelou

The brain is like a muscle. When it is in use we feel very good. Understanding is joyous.

Carl Sagan

We were playing, not for the drunks, but for the musicians, because it was more intellectually challenging. We needed somewhere to put our energy to show that we were growing, and as we started to achieve this, people came to hear us musically.

Ronnie Hawkins