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# Statistics

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### Statistics

1. 1. Kelly Chan | Nov 20 2013 Statistics Z-test (1 var) T-test (2 vars) Correlation Regression Parametric Tests (numeric: mean/stddev) F-test (AVONA) (3 vars) X-test (Chi Squared) Non-Parametric Tests (n vars) (category: frequency/proportions)
2. 2. Kelly Chan | Nov 20 2013 Statistics (X)-Tests Z-test T-test Dependent F-test (AVONA) Independent One item Goodness-of-Fit Test for Independent Two items Pre/Post Longitudinal Two-Condition X-test (Chi Squared) Observation Experiential 1 variable 2 variables 3 variables N categories Normal distribution Large sample size Population StdDev Normal distribution Small sample size (15~30) Population StdDev unknown Normal distribution Non-directional (+/-) Non-directional (+/-) One-directional (>0) One-directional (>0) Numeric (mean/stdev) Numeric (mean/stdev) Numeric (mean/stdev) Category (frequencies/proportions)
3. 3. Kelly Chan | Nov 20 2013 Statistics Calculations Formulas Process Alpha: significance level X −Table 1 X-CriticalValue df: degree of freedom Hypothesis Mean ( distances)DifferenceBetweenMeans ( stdDev)StandardError Difference Mean 2 X-Statistic StdDev Decision Standard Error n 3 P-Value CI =mean(X )±MarginOfError CI =mean(X )±CriticalValue( X )∗SE( StandardError) ( distances)DifferenceBetweenMeans SD pooled 4 Significance CI: Confidence Intervals Effect Size (%) The proportion of a difference in means
4. 4. Kelly Chan | Nov 20 2013 Statistics Formulas Z-test T-test Dependent x F-test (AVONA) Independent x df =n X-test (Chi Squared) Goodness-of-Fit A/B n−1 A/ B/C n(A)+n(B)−2 Test for Independent A/ B/C/.../N df between =k −1 (NumberOfRows−1)∗(NumberOfColumns−1) df within =N −k ∑ (x −m (x )) ∑ (x −m (x )) n n−1 2 2 2 S p= 2 S p= √ stdDev √ (n) x −mean (x ) StdDev ( √ variance(x1 −x2) ( ) n−1 df ( A)+df (B) √ variance (x1−x2) ) n−1 mean (x1)−mean (x2) SS ( A)+ SS (B) df ( A)+ df (B) ∑ (x i −m(x))2 + ∑ ( y i −m( y))2 2 SE= ( t= Sp 2 Sp + ) n (A) n( B) m (A)−m (B)−(u (A)−u (B)) ∑ (n k∗(m (x k )−m(G))2 )/(k −1) F= S2 S2 p p ∑ (x i −m(x k ))2 /(N −k ) ( + ) n(A) n (B) √ √ Tukey' sHSD=q∗ ( Cohen' sD= r2 = t m (x A )−m( x B ) √ (S p ) Cohen' sD= n ( f o − f e)2 fe ) ) m (x A )−m( x B ) √ (MS within ) 2 t2 +df MS within x =∑ ( 2 EtaSquare(n 2)= SS between SS total √ x 2 Statistic Cramer' sV = ( ) n( k −1)
5. 5. Kelly Chan | Nov 20 2013 Statistics Correlation Correlation? r= cov ( X , Y) S x∗S y Regression Hypothesis? (X)-Test? t= r∗√ (N −2) √ (1−r ) 2 Regression slope= ∑ ((x i −mean(x))∗( yi −mean ( y))) ∑ (x i −mean (x )2 ) slope=r∗( 2 r <− coefficient of determination Sy Sx ) Y −intercept =mean( y)−slope∗mean(x )