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Comprehensive Review of Advanced Statistics Concepts by Dr. Mary Whiteside

This detailed review by Dr. Mary Whiteside covers essential concepts in advanced statistics, including data types, sources, and representations using graphs along with a variety of numeric descriptors. It delves into probability principles, random variables (discrete and continuous distributions), sampling distributions, and statistical inferences such as estimation and hypothesis testing. Key topics explored include variability, significance, uncertainty, and the implications of the Central Limit Theorem, all crucial for understanding statistical analysis in real-world applications.

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Comprehensive Review of Advanced Statistics Concepts by Dr. Mary Whiteside

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Presentation Transcript

  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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