Statistics Formulas
Descriptive Statistics
Sample mean formula = x = ( Σ xi ) / n Sample standard deviation formula = s = sqrt [ Σ ( xi – x )2 / ( n – 1 ) ] Pooled sample standard error formula (two samples) = SEpooled = sqrt [ (n1 – 1) s12 + (n2 – 1) s22 ] / (n1 + n2 – 2) ]
Probability (Addition and Multiplication Rules, Expected Value and Variance of Random Variables)
Addition Rule: P(A ∪ B) = P(A) + P(B)- P(A ∩ B) Multiplication Rule: P(A ∩ B) = P(A) P(B|A) Expected value formula = E(X) = μx = Σ [ xi * P(xi) ] Formula for Variance of X (discrete random variable) = σ2 = Σ(xi-μ)2
Linear Regression equations, slope and correlation coefficients
Linear regression equation: ŷ = b0 + b1x Regression coefficient = b1 = Σ [ (xi – x)(yi – y) ] / Σ [ (xi – x)2] or b1 = r (sy / sx) Regression slope intercept = b0 = y – b1 x Sample correlation coefficient = r = [ 1 / (n – 1) ] Σ { [ (xi – x) / sx ] [ (yi – y) / sy ] } Standard error of regression slope = sb1 = sqrt [ Σ(yi – ŷi)2 / (n – 2) ] / sqrt [ Σ(xi – x)2 ]
Binomial Distributions and Proportions
Binomial distribution formula: P(X = x) = b(x; n, P) = nCx Px (1 – P)n – x = nCx Px Qn – x Formula for binomial distribution Mean = μx = n P Standard deviation of binomial distribution formula = σx = sqrt[ n P ( 1 – P ) ] Mean of sampling distribution of the proportion = μp = P Standard deviation of sampling distribution of the proportion = σp = sqrt[pq) / n ]
Inferential Statistics (Confidence Intervals, Chi-Square)
Standardized test statistic general formula = (Statistic – Parameter) / (Standard deviation of statistic)
Confidence interval general formula: Sample statistic + Critical value * Standard error of statistic
Chi-square statistic = Χ2 = Σ[ (Observed – Expected)2 / Expected ]