The course gives the students a detailed overview of statistical inference and basic applications. The basic applications are implemented using Excel and SPSS. The course focuses on fundamental data science issues, on basic probability theory, the logic of hypothesis testing and confidence intervals, and the concept of a statistical model, illustrated via simple and multiple linear regression. A brief introduction to the design of experiments, randomization, and data gathering is given.
- Univariate descriptive statistics and plots, the normal distribution.
- Bivariate descriptive statistics and plots, correlation and least squares estimation. Tables for categorical data, Simpson’s paradox.
- Causation, randomization, sampling, bias and variability.
- Basic probability rules, random variables, population means and variances, the law of large numbers.
- The sampling distribution of a sample mean, the central limit theorem.
- Confidence intervals and testing under exact normality with a known . Potential problems with tests. Power and inference as a decision.
- Inference for a mean under more realistic conditions.
- The simple linear regression model, and inference.
- The multiple linear regression model, inference and data examples.
- One way ANOVA.
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