Basic Statistics Formulas, Cheat Sheet of Statistics

Download Basic Statistics Formulas and more Cheat Sheet Statistics in PDF only on Docsity! Basic Statistics Formulas Population Measures Mean µ = 1 n ∑ xi (1) Variance σ2 = 1 n ∑ (xi − x)2 (2) Standard Deviation σ = √ 1 n ∑ (xi − x)2 (3) Sampling Sample mean x = 1 n ∑ xi (4) Sample variance s2x = 1 n− 1 ∑ (xi − x)2 (5) Std. Deviation sx = √ 1 n− 1 ∑ (xi − x)2 (6) z-score z = x− µ σ (7) Correlation r = 1 n− 1 n∑ i=1 ( (xi − x) sx )( (yi − y) sy ) (8) Linear Regression Line ŷ = a+ bx (9) b = r sy sx , a = y − bx (10) s = √√√√ 1 n− 2 n∑ i=1 (yi − ŷ)2 (11) SEb = s√√√√ n∑ i=1 (xi − x)2 (12) To test H0 : b = 0, use t = b SEb (13) CI = b± t∗SEb (14) Probability P (A or B) = P (A) + P (B)− P (A and B) (15) P (not A) = 1− P (A) (16) P (A and B) = P (A)P (B) (independent) (17) P (B|A) = P (A and B)/P (A) (18) 0! = 1;n! = 1× 2× 3 · · · × (n− 1)× n (19)( n k ) = n! k!(n− k)! (20) Binomial Distribution : P (X = k) = ( n k ) pk(1− p)n−k (21) µ = np, σ = √ np(1− p) (22) One-Sample z-statistic To test H0 : µ = µ0 usez = z − µ0 σ/ √ n (23) Confidence Interval for µ = x± z∗ σ√ n (24) Margin of Error ME = z∗ σ√ n (25) Minimum sample size n ≥ [ z∗σ ME ]2 (26) One-Sample t-statistic SEM = sx√ n , t = x− µ sx/ √ n (27) Confidence Interval = x± t∗ sx√ n (28) Two-Sample t-statistic t = x1 − x2√ s21 n1 + s22 n2 (29) Conf. Interval = (x1 − x2)± t∗ √ s21 n1 + s22 n2 (30) Sample Proportions µp̂ = p, σp̂ = √ p(1− p) n (31) Conf. Int. = p̂± z∗(SE) (32) SE = √ p̂(1− p̂) n (33) sample size n > [ z∗ ME ]2 p∗(1− p∗) (34) To test H0 : p = p0, use z = p̂− p0√ p0(1− p0) n (35) Two-Sample Proportions SE = √ p̂1(1− p̂1) n1 + p̂2(1− p̂2) n2 (36) CI = (p̂1 − p̂2)± z∗(SE) (37) To test H0 : p1 = p2, use (38) z = p̂1 − p̂2√ p̂(1− p̂) ( 1 n1 + 1 n2 ) (39) p̂ = X1 +X2 n1 + n2 , Xi = successes (40) Chi-Square Statistic χ2 = n∑ i=1 (oi − ei)2 ei (41) oi = observed, ei = expected Central Limit Theorem sx → σ√ n as n→∞ (42) 2013 B.E. Shapiro. This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License (BY-NC-SA 3.0). Last revised May 9, 2016.