Statistical Consulting Blog

Statistical Formula

Posted May 25, 2009

Statistical formula can be defined as the group of statistical symbols used to make a statistical statement.

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The term called the expected value of some random variable X will be represented by the statistical formula as E(X)= μx=∑[xi * P(xi)]. In this statistical formula, the symbol ‘μx’ represents the expected value of some random variable X. In this statistical formula, the symbol ‘P (xi)’ represents the probability that the random variable will have an outcome ‘i.’ In this statistical formula, the expected value of the random variable X will be computed in the above described manner if the random variable is discreet in nature.

The term called the variance of some random variable X is represented by the statistical formula as Var(X) =σ2 = Σ [Xi – μx]2 * P(xi). In this statistical formula, the symbol ‘σ2’ represents the variance of that random variable.

The term called the chi square statistic will be represented by the statistical formula as X2=[(n-1)*s2]/ σ2. In this statistical formula, the X2 is being represented as the chi square statistic. In this statistical formula, ‘n’ represents the size of the sample. In this statistical formula, ‘s2’ represents the sample variance.

The term called the f statistic will be represented by the statistical formula f=[s12/ σ12]/ [s22/ σ22]. In this statistical formula, s12 represents the variance of the sample drawn from population 1 and s22 represents the variance of the sample drawn from population 2.

The expected value of the sum of two random variables, for example, random variable X and random variable Y, will be represented by the statistical formula as 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 the random variables will be represented by the statistical formula as E(X-Y) =E(X)-E(Y). The term ‘E(X-Y)’ in the statistical formula is nothing but the expected value of the difference between the random variables.

The variance of the sum of the independent variable is represented by the statistical formula as Var(X+Y) = Var(X)+Var(Y). Ideally, in this statistical formula, the covariance between the two variables should also exist, but since the two variables are independent in nature, the covariance in this statistical formula will not exist.

The standard error of the difference for proportion is represented by the statistical formula as SEp= sp = sqrt [ p*(1-p)*{1/n1 + 1/n2} ] . The term ‘SEp’ in the statistical formula represents the standard error for difference proportion. The term ‘p’ in the statistical formula is the pooled sample variance. The term ‘n1’ in the statistical formula represents the size of the first sample and the term ‘n2’ in the statistical formula represents the size of the second sample, which is pooled with the first sample.

The binomial formula is represented by the statistical formula as P(X=x)=b(x;n,P)= nCx * px(1-p)n-x. The term ‘n’ in this statistical formula represents the number of trials. The term ‘x’ in this statistical formula represents the number of successes in ‘n’ trials. The term ‘p’ in this statistical formula represents the probability of getting success from the ‘n’ binomial trials.
The poisson formula is represented by the statistical formula as P(x;µ)=(e-µ)(µx)/x!. The term ‘µ’ in the statistical formula represents the mean number of the successes that has occurred in a specific region. The term ‘x’ in the statistical formula represents the actual number of successes that has occurred in a specific region. The term ‘e’ in the statistical formula represents the base of the natural logarithmic system. Its value is approximately 2.71828.

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