Descriptive and Inferential Statistics: Concepts and Applications - Prof. min, Schemes and Mind Maps of Law

Download Descriptive and Inferential Statistics: Concepts and Applications - Prof. min and more Schemes and Mind Maps Law in PDF only on Docsity! MATERIALS SB CHAPTER 1 ❖ Descriptive data and Inferential Data ❖ Critical thinking + Conclusion from small samples + Conclusion from non-random samples + Conclusion from rare event + Poor survey methods + Post-hoc fallacy CHAPTER 2 ❖ Level of measurement + Nominal measurement + Ordinal measurement + Interval measurement + Ratio measurement ❖ Sampling method + Simple random sample + Systematic sample + Stratified sample Random sampling method + Cluster sample + Judgment sample + Convenience sample Non-random sampling method + Focus group CHAPTER 3 ❖ Stem and leaf ❖ Dot plot ❖ Sturges’ Rule: k ¿1+3.3 log log (n) ❖ Bin width ❖ Histogram and shape ❖ Exponential Distribution CDP: P ( X ≤ x )=1−e− λx ❖ Normal Approximation to Binomial: μ=nπ; σ=√❑ for nπ ≥ 10 and n(1−π)≥ 10 ❖ Normal Approximation to Poisson: μ= λ; σ=√❑ for λ ≥ 10 ❖ Linear Transformation. Rule 1: μaX+b=a μX+b (mean of a transformed variable) ❖ Linear Transformation. Rule 2: σ aX+b=aσ X (standard deviation of transformed variable) ❖ Linear Transformation. Rule 3: μX+Y=μX +μY (mean of sum of tow random variables X and Y) ❖ Linear Transformation. Rule 4: σ X+ Y=√❑ (standard deviation of sum if X and Y are independent) ❖ Covariance: σ X+Y=√❑ . If X and Y are correlated. CHAPTER 8: Sampling Distributions and Estimation Commonly Used Formulas in Sampling Distributions ❖ Sample proportion: p = x n ❖ Standard error of the sample mean: σ x = σ √❑ ❖ Confidence interval for μ, known σ:x ± zα /2 σ √❑ ❖ Confidence interval for μ, unknown σ: x± t α /2 s √❑ with d . f .=n−1 ❖ Standard error of the sample proportion: σ p = √❑ ❖ Confidence interval for π: p ± zα /2 √❑ ❖ Sample size to estimate μ: n=( zσ E ) 2 ❖ Sample size to estimate π: n=( z E ) 2 π (1−π ) ❖ Interpretation: P - value Interpretation P > 0,05 No evidence against H0 P < 0.05 Moderate evidence against H0 P < 0.01 Strong evidence against H0 P < 0.001 Very strong evidence against H0 CHAPTER 9: One – Sample Hypothesis Test Commonly Used Formulas in One-Sample Hypothesis Tests ❖ Test statistic for a Mean (known σ): zcalc = x−μ0 σx = x−μ0 σ √❑ ❖ Test statistic for a Mean (unknown σ): tcalc = x−μ0 s √❑ ❖ Test statistic for a Proportion: zcalc = p−π0 σ p = p−π0 √❑ ❖ Test for one variance: CHI-SQUARE DISTRIBUTION compares the sample variance with a benchmark χcalc 2 = (n−1) s2 σ2 ; With n: sample size s2: sample variance σ2: population variance. CHAPTER 10: Two-sample Hypothesis Tests Commonly Used Formulas in Two-Sample Hypothesis Tests ❖ Test Statistic for Zero Difference of Means: ❖ Confidence interval for μ1−μ2: ( x1−x2 ) ±t α /2 √❑ *Note: for paired t test, n is number of pairs ❖ Paired t test: d = ∑i=1 n d i ❑ (mean of n differences) ❖ St. Dev of n differences: sd = √❑ ❖ Test statistic for paired samples: t calc = d−μd sd √❑ ❖ Degree of freedom: d . f .=n−1 ❖ The ith paired difference is: Di=X1i – X2 i ❖ Confidence interval for μD: D ±t α /2 sd √❑ ❖ Test statistic for equality of proportion: zcalc = ( p1−p2 )−(π1−π2) √❑ ; ❖ Test statistic for zero correlation: tcalc = r √❑ with d . f .=n−2, tα/2 ❖ Slope of fitted regression: b1 = ∑i=1 n (x i−x )( y i− y ) ❑ ❖ Intercept of fitted regression: b0= y−b1 x ❖ Sum of squared residuals: SSE=∑ i=1 n ( yi− ŷi) 2=∑ i=1 n ( y i−b0−b1 xi) 2 ❖ Coefficient of determination: R2 = 1 - ∑i=1 n ( y i− ŷ i) 2 ❑ = 1 - SSE SST = SSR SST ❖ Standard error of the estimate: s = √❑ = √❑ ❖ Standard error of the slope: sb1 = s √❑ , with d . f .=n−2, ❖ T test for zero slope: tcalc = b1−0 sb1 ❖ Confidence interval for true slope: b1−t α /2 . sb1 ≤ β1≤ b1+t α /2 . sb1, with d . f .=n−2 ❖ Confidence interval for conditional mean of Y: ŷ i ±t α /2 s. √❑ ❖ Prediction interval for Y: ŷ i ±t α /2 s. √❑ ❖ Excel Output: Regression Statistics R square R2 = SSR SST Standard Error se = √❑ ANOVA df SS MS F Regression k (SSR) MSR = SSR k MSR MSE Residual n-k-1 (SSE) MSE = SSE n−k−1 Total n-1 (SST) Coefficient Standard Error T Stat Intercept (b0) (b0) (sb0) Square feet (b1) (b1) (sb1) b1−β1 sb1