At the end of the course the student is able to:
- Recall and explain basic terminology and concepts of statistics: Define standard descriptive statistics, recognize common parametric distributions, explain concepts such as random samples, estimation, confidence intervals, hypothesis testing, p-value and power of a test.
- Analyze a data set: Summarize and represent characteristics of the data using descriptive statistics, judge whether the given data set is well-modeled by a normal distribution, or another parametric distribution. Identify outliers and extreme observations in the data.
- Apply elementary statistical techniques (see ‘content description’ for the list): Choose an appropriate technique for a given problem, judge whether the assumptions of the model are satisfied, work out the necessary computations to obtain (correct) numerical results.
- Interpret the output of a statistical procedure (see ‘content description’ for the list): Translate the output of the model into an answer to the original problem, explain the results and quantify the uncertainty attached to these.
- Use statistical software: Input and manipulate data using statistical software package(s), apply statistical methods in statistical software package(s), interpret the output of statistical software package(s).
- Apply cognitive skills: Describe quantities and events using random variables, communicate in a clear way ideas and solutions to a problem, be critical about his/her own solutions as well as others', and identify when an answer is either impossible or extremely unlikely.
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Based on the knowledge of “Probability Theory” in M4, the Statistics course aims to introduce the basic topics in statistics: Descriptive statistics, Estimation (theory), Confidence intervals and Testing of hypotheses. Apart from applying the techniques correctly, we will focus on understanding: what is the meaning of the confidence level 95% of an interval and what do concepts as significance level, p-value and the power of a test mean?
After introducing the basics for one-sample-problems, where the normal or the binomial distribution applies, we will extend our techniques to two-sample-problems and cross tables. Assessing the assumption of a normal distribution with numerical and graphical methods, such as QQ-plots, is completed with a test on normality. For the case that the normal distribution does not apply we will discuss two non-parametric methods.
List of models and techniques:
- Confidence intervals for the population mean and population variance of normal (or binomial) distributions
- Tests on the population mean and population variance of a normal (or binomial) distribution
- Test on the difference of two population means (or proportions) for normally (or binomially) distributed populations
- Test on the equality of variance of two normal distributions
- Tests on independence or homogeneity of contingency tables
- Non-parametric alternatives, such as the sign test and Wilcoxon's rank-sum test
- Shapiro-Wilk's test on normality
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