Learning advanced statistics requires commitment and discipline. If you’re presently enrolled in a college-level statistics course, you’ll need to maintain a high degree of focus and motivation in order to succeed. Although the topics covered in class will vary slightly depending on your professor’s experience or interests, they will generally include the following:
- Confidence Intervals: definitions, a duality with hypothesis tests
- Hypothesis testing: significance level and power, Neyman-Pearson lemma, Likelihood ratio tests
- Convergence of random variables
- Nonparametric statistical techniques
- Discrete parametric probability distributions
- Common discrete and continuous distributions
- Descriptive statistical techniques
- Bivariate probability distributions
- Tests of parametric statistical hypotheses
- Testing goodness of fit
- Conditional probability
- Testing goodness of fit: Contingency tables
- Sampling and the sampling distribution of a statistic
- Estimation: Bias, MSE, consistency, sufficiency, maximum likelihood, method of moments, UMVUE, Rao-Blackwell Theorem, Fisher Information
- Univariate and bivariate transformations
- Random variables, expectations, and variance
- Probability theory
- Interval estimation and confidence interval estimates
- Probability definitions and properties
- Point estimation and properties of point estimators
- Continuous parametric probability distributions
- Bivariate distributions
- Bivariate linear regression and correlation
- Random variables and probability distributions
- The chi-square, student’s t, and Snedecor’s F distributions
- Combinatorics and basic set theory notation
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