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.
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