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HCAD Advanced Statistics Dr. Mary Whiteside Review Concepts of statistics Data & sources Graphs Numeric descriptions of data Probability Random variables Discrete – binomial Continuous – normal Sampling distributions Inferences Estimation Hypothesis testing Concepts of statistics Variability Randomness Significance Uncertainty Probability Data and sources Data Times series vs. cross sectional Categorical (nominal, qualitative) vs. numeric For numeric: discrete vs. continuous; ordinal, vs. interval or ratio Sources Experiments Observational studies • • • • Random samples Convenience samples Self selected samples Samples from a process Graphs Time series Line Bar Cross sectional Categorical • Pie • Bar Numeric • • • • Histogram Box and whiskers Stem and leaf Ogive Numeric descriptions Symmetric distributions m = mu = Mean=median=mode Standard deviation = sigma = s Empirical rule for mound shaped • 95% in 2 standard deviations • 99.7% in 3 standard deviations Skewed distributions R mode < median < mean L mean < median < mode Five points: min Q1 Q2 Q3 max Probability Five laws Conditional probabilities Prior and posterior probabilities Approaches to probability Equal likelihood Relative frequency Mathematical Problem of false positives Random variables Discrete = counting numbers as values Continuous = measuring numbers as values Binomial as an example of a discrete distribution Normal as an example of a continuous distribution Sampling distributions Frequently normal due to the Central Limit Theorem Based on an assumption of underlying normality t F C2 Binomial Exact Inference Confidence interval estimation Precision Cost Confidence Hypothesis testing Reject H0 when evidence is sufficient at the given significance level Fail to reject H0 when evidence is insufficient • No evidence • Some evidence but not enough Inferences are for parameters p = the population proportion or the probability of success in a binomial process m = the population mean of the Expected Value of a random variable X