3. causality , simpson's paradox, random variable and baye's rule

what is a causality or causation

• the influence by which one event or process contributes to another

• the cause is partly responsible for the effect, and the effect is partly dependent on the cause

why in most cases they only say that it is “probably causal”

because the researcher can never be completely certain that there are no other factors influencing the causal relationship

what is one popular way to causal data analysis

randomized controlled trial

what is a randomized controlled trial

• a study design that randomly assigns participants into an experimental group or a control group

• as the study is conducted, the only expected difference between 2 grips is the outcome variable being studied

what is correlation

• correlation is any statistical relationship, whether causal or not, between 2 random variables

• correlations are useful because they can indicate a predictive relationship that can be exploited in practice

what is simpson’s paradox

simpson’s paradox is a phenomenon in probability and statistics, in which a trend appears in several different groups of data but disappears or reverses when these groups are combined

what is a random experiment

we describe a random experiment by describing its procedure and observations of its outcome

what are outcomes

outcomes are mutually exclusive in the sense that only one outcome occurs in specific trial of the random experiment

• this also means an outcome is not decomposable

• all unique outcomes from a sample space

what are the 2 types of random variables

1. discrete

2. continuous

what are the 2 types of notations for probability of the different variables

• P(*): probability is discrete random variables

• p(*): probability of continuous random variables

what is a probability distribution of a discrete random variable

it is described by a list of probabilities associated with each of its possible values. the list of probabilities is called a probability mass function. the probabilities sum to 1

what is the probability distribution of a continuous random variable

the probability density function

expectation formula

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variance formula

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what is the sum rule

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what is the product rule

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what is bayes’ rule

the conditional probability Pr(Y = y|X = x) is the probability of the random variable Y to have a specific value y, given that another random variable X has a specific value of x

what is the bayes’ rule (also known as the bayes’ theorem)

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