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HCAD Advanced Statistics

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.

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HCAD Advanced Statistics

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  1. HCAD Advanced Statistics Dr. Mary Whiteside

  2. Review • Concepts of statistics • Data & sources • Graphs • Numeric descriptions of data • Probability • Random variables • Discrete – binomial • Continuous – normal • Sampling distributions • Inferences • Estimation • Hypothesis testing

  3. Concepts of statistics • Variability • Randomness • Significance • Uncertainty • Probability

  4. 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

  5. Graphs • Time series • Line • Bar • Cross sectional • Categorical • Pie • Bar • Numeric • Histogram • Box and whiskers • Stem and leaf • Ogive

  6. 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

  7. Probability • Five laws • Conditional probabilities • Prior and posterior probabilities • Approaches to probability • Equal likelihood • Relative frequency • Mathematical • Problem of false positives

  8. 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

  9. Sampling distributions • Frequently normal due to the Central Limit Theorem • Based on an assumption of underlying normality • t • F • C2 • Binomial • Exact

  10. 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

  11. 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

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