What is meant by statistical independence?
Statistical independence is a concept in probability theory. Two events A and B are statistical independent if and only if their joint probability can be factorized into their marginal probabilities, i.e., P(A ∩ B) = P(A)P(B). The concept can be generalized to more than two events.
What does it mean if two variables are statistically independent?
The first component is the definition: Two variables are independent when the distribution of one does not depend on the the other. If the probabilities of one variable remains fixed, regardless of whether we condition on another variable, then the two variables are independent.
How do you demonstrate statistical independence?
Events A and B are independent if the equation P(A∩B) = P(A) · P(B) holds true. You can use the equation to check if events are independent; multiply the probabilities of the two events together to see if they equal the probability of them both happening together.
How do you know if a variable is statistically independent?
You can tell if two random variables are independent by looking at their individual probabilities. If those probabilities don’t change when the events meet, then those variables are independent. Another way of saying this is that if the two variables are correlated, then they are not independent.
What is the difference between statistical independence and correlation?
Correlation can be used to quantify the linear dependency of two variables. It cannot capture non-linear relationship between variables. Independent variables has NIL correlation, r=0. In other words variables which are perfectly dependent on each other, can also give you a zero Correlation.
Why is statistical independence important?
The assumption of independence is used for T Tests, in ANOVA tests, and in several other statistical tests. It’s essential to getting results from your sample that reflect what you would find in a population. Independence means there isn’t a connection.
How do you know if data is dependent or independent?
Therefore, it’s important to know whether your samples are dependent or independent:
- If the values in one sample affect the values in the other sample, then the samples are dependent.
- If the values in one sample reveal no information about those of the other sample, then the samples are independent.
How do you know if probability is dependent or independent?
Two events A and B are said to be independent if the fact that one event has occurred does not affect the probability that the other event will occur. If whether or not one event occurs does affect the probability that the other event will occur, then the two events are said to be dependent.
What is the meaning of independent and dependent variables?
The variables in a study of a cause-and-effect relationship are called the independent and dependent variables. The independent variable is the cause. Its value is independent of other variables in your study. The dependent variable is the effect. Its value depends on changes in the independent variable.
Does mean independence imply independence?
As the direction of the arrows in the image below indicates, independence implies mean independence, which in turn implies zero correlation. The converse statements are not true: zero correlation does not imply mean independence, which in turn doesn’t imply independence.
What does statistically dependent mean?
n. (Statistics) a condition in which two random variables are not independent. X and Y are positively dependent if the conditional probability, P(X|Y), of X given Y is greater than the probability, P(X), of X, or equivalently if P(X&Y) > P(X).P(Y).
How do you define an independent observation?
Independent Observations Two observations are independent if the occurrence of one observation provides no information about the occurrence of the other observation. A simple example is measuring the height of everyone in your sample at a single point in time. These should be unrelated observations.