Statistical Formula
Statistical formula can be defined as the group of statistical symbols used to make a statistical statement.
The expected value of a random variable X is E(X) = μₓ = ∑. In this statistical formula, the symbol ‘μx’ represents the expected value of some random variable X. The symbol ‘P (xi)’ represents the probability that the random variable will have an outcome ‘i.’ Compute the expected value of X using the above method if X is discrete.
The variance of a random variable X is Var(X) = σ² = Σ [(Xᵢ – μₓ)² * P(xᵢ)]. The symbol ‘σ2’ represents the variance of that random variable.
The chi-square statistic is X² = [(n – 1) * s²] / σ², where X² represents the chi-square statistic. ‘n’ represents the size of the sample. ‘s2’ represents the sample variance.
The F-statistic is given by F = / . Here, s₁² is the variance of sample 1, and s₂² is the variance of sample 2.
The expected value of the sum of two random variables, X and Y, is E(X + Y) = E(X) + E(Y). The term E(X) and E(Y) in the statistical formula is nothing but the same as described above.
The expected value of the difference between two random variables is E(X – Y) = E(X) – E(Y). The term ‘E(X-Y)’ is nothing but the expected value of the difference between the random variables.
The variance of the sum of independent variables is Var(X + Y) = Var(X) + Var(Y). Ideally, the covariance between the two variables should also exist, but since the two variables are independent in nature, the covariance will not exist.
The statistical formula represents the standard error of the difference for proportion:
SEp = sqrt [ p(1 – p) * (1/n₁ + 1/n₂) ]
Here, SEp refers to the standard error for difference proportion. Additionally, p represents the pooled sample variance. Furthermore, n₁ is the first sample size, while n₂ is the second, combined with the first.
Similarly, the binomial formula is given by:
P(X = x) = b(x; n, p) = nCx * pˣ(1 – p)ⁿ⁻ˣ
In this equation, n represents the number of trials, whereas x stands for the number of successes within those trials. Moreover, p signifies the probability of success in each binomial trial.
Likewise, the Poisson formula expresses as:
P(x; µ) = (e⁻ᵘ * µˣ) / x!
Here, µ represents the mean number of successes occurring in a specific region. Additionally, x refers to the actual number of successes observed. Finally, e is the base of the natural logarithmic system, with an approximate value of 2.71828.