Biostatistics for Health Sciences Review Sheet

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1 Biostatistics for Health Sciences Review Sheet June 1, 2017 Contents 1 Descriptive Statistics Variables Qualitative Quantitative Chart Boxplot Number Summary Outlier Thresholds Linear Transformation Type Effects On Coefficient of Variation Probability Combinatorics Laws Real-Life Example: Diagnostic Tests Distributions Discrete Binomial Distribution Sample Proportion Geometric Distribution Negative Binomial Distribution Hypergeometric Distribution Poisson Distribution Continuous CONTENTS 1

2 3.2.1 Uniform Distribution Normal Distribution Parametric Inferential Statistics Theory Hypotheses Testing One-Sample Mean Two-Independent-Sample Means Paired Differences One-Sample Proportion Two-Sample Proportions One-Sample χ 2 (Goodness-of-Fit) R C Contingency Table Correlation Confidence Interval One-Sample Mean Two-Independent-Sample Means Paired Differences One-Sample Proportion Two-Sample Proportions Correlation Non-Parametric Methods Sign Test (One-Sample Median) Signed-Rank Test (Paired Differences) Rank-Sum Test (Two Independent Samples) Confidence Interval for One-Sample Median Spearman s Rank Correlation Simple Regression Model Theory Descriptive Statistics 1.1 Variables Qualitative Nominal Ordinal Quantitative Discrete Continuous 1.2 Chart Pie Chart 1 DESCRIPTIVE STATISTICS 2

3 (Stacked) Bar Chart Histogram (Cumulative) Frequency Polygon Stemplot 1.3 Boxplot Number Summary Central Box (Q1, Q2, Q3) Max and Min Invariant under change of units 2 Probability 2.1 Combinatorics Multiplication Rule Permutation Rule Combination Rule (Binomial Coefficient) Partition Rule (Multinomial Coefficient) Outlier Thresholds 1.5 IQR away from the central box 1.4 Linear Transformation Type Shifting Rescaling Effects On Mean Median Quartiles IQR Range Standard Deviation Coefficient of Variation s X in % Variability with respect to X 2.2 Laws Union Complement Intersection General Formula Formula for Independent Events Law of Total Probability Conditional Probability 2.3 Real-Life Example: Diagnostic Tests # of True Positive False Positive True Negative False Negative Sensitivity (i.e., P (Diagnosed Disease) ) Specificity (i.e., P (U ndiagnosed N o Disease) ) Gold Standard Prevalence 2 PROBABILITY 3

4 3 Distributions 3.1 Discrete Binomial Distribution Distribution of the # of successes among n Sample Proportion 4 Parametric Inferential Statistics 4.1 Theory Unbiased Estimator Central Limit Theorem Standard Error Relationship between α and β Power Geometric Distribution Distribution of the first-success trial Negative Binomial Distribution Distribution of the k th -success trial Hypergeometric Distribution Poisson Distribution 4.2 Hypotheses Testing One-Sample Mean Two-Independent-Sample Means (Pooled Variance, Total Degree of Freedom) 3.2 Continuous Uniform Distribution Normal Distribution X Normal(µ, σ) = X µ σ Assessing Normality Mound-Shape Histogram Rule = Z Normal Probability Plot (Z-Score vs. Variable) Paired Differences One-Sample Proportion Two-Sample Proportions Pooled Proportion One-Sample χ 2 (Goodness-of-Fit) R C Contingency Table Multi-Sample χ 2 Yate Correction (2 2) 4 PARAMETRIC INFERENTIAL STATISTICS 4

5 Fisher s Exact Test (2 2) X = # of successes in Group Correlation (Normal Approximation) 5.2 Signed-Rank Test (Paired Differences) Exact Statistic : Confidence Interval One-Sample Mean ( 1+r ln 1 r N 1 1+ρ 2 ln 1 ρ, 1 n 3 Exact Statistic (R + = df Total Rank of Positive Data) ) ( : R + n(n+1) N 4, 5.3 Rank-Sum Test (Two Independent Samples) Exact Statistic (R 1 def = Total Rank of Sample 1) ) n(n+1)(2n+1) Two-Independent-Sample Means Paired Differences One-Sample Proportion Two-Sample Proportions Correlation 5 Non-Parametric Methods 5.1 Sign Test (One-Sample Median) Exact Statistic (X = df # of data > ) 5.4 Confidence Interval for One- Sample Median 5.5 Spearman s Rank Correlation 6 Simple Regression 6.1 Model Y = α + βx + ɛ β estimated by b = SS xy SS x α estimated by a = Ȳ b X ɛ N(0, σ), σ estimated by 6.2 Theory SSresidual SS T otal = SS Residual + SS Regression r 2 = SS Regression SS T otal N 2 6 SIMPLE REGRESSION 5

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