Basic Statistical Analysis
Work Page

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This is a work page to the course 'Basic Statistical Analysis in Life and Environmental Sciences", a course at PhD level under the PhD school at Faculty of Science and Technology, offered by the Applied Statistics Laboratory, Aarhus University. Here the material for the daily work in the course will be placed. The page is dynamic in the sense that it will be updated along the course. Please, click in the table of contents below to navigate in the page. Remember to refresh the page to be sure that you are using an updated version of the page.


Page contents:

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Material related to each module:
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Lecture notes and texts:
  • Chapter 01 - Basic Notions of Probability Theory (click here)

  • Chapter 02 - Basic Notions of Statistical inference (click here)

  • Chapter 03 - Binomial models (click here)

  • Chapter 04 - Poisson models (click here)

  • Additional text on the corner point parametrization (click here)

  • Remarks on Model Definition (click here)
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Exercises and R-tutorials:
  • Tutorial-01- Generation of caos from a deterministic sequence (random?) (click here)

  • Tutorial-02- Some (key) probability distributions (click here)

  • Tutorial-03- Expectations and Variances (click here)

  • Tutorial-04-The Normal Distribution (click here)

  • Tutorial-05- Demonstration of the Law of Large Numbers (click here)

  • Tutorial-06-Demonstration of the Central Limit Theorem (click here)

  • Tutorial-07-The Failure Of the Central Limit Theorem (click here)

  • Tutorial-08-Confidence intervals based on the normal distribution (click here)

  • Tutorial-09- Simple hypotheses tests based on the normal distribution(z- and t-tests) (click here)

  • Tutorial-10- Construction of a range of examples of pairs of random variables that are non-correlated yet dependent (click here)

  • Tutorial-11- The Anscombe Quartet and some variations demonstrating that the determination coefficient (r2) fails to characterize reasonable linear regressions (click here)

  • Tutorial-12- Binomial Regression (to be revised) (click here)

  • Tutorial 14 - Poisson distribution and law of rare events (click here)

  • Tutorial 15 - The Poisson distribution arises from the Poisson process (click here)

  • Solution of exercise 3.1 (to be revised) (click here)

  • Solution of exercise 3.2 (to be revised) (click here)

  • Solution of exercise 3.3 (to be revised) (click here)

  • Solution of exercise 3.4 (to be revised) (click here)

  • Solution of exercise 3.5 (to be revised) (click here)

  • Solution of exercise 3.6 (to be revised) (click here)

  • Solution of exercise 4.1 (to be revised) (click here)

  • Solution of exercise 4.2 (to be revised) (click here)

  • Solution of exercise 4.3 (to be revised) (click here)

  • Solution of exercise 4.4 (REVISED) (click here)
    Correction of the description of the exercise 4.4 (click here)

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Programs:
  • Lecture 3 (first part) - Binomial one-way models (to be revised) (click here)

  • Lecture 3 (second part) - Binomial two-ways models (to be revised) (click here)

  • Lecture 4 - Binomial regression models (to be revised) (click here)

  • Lecture 5 - Poisson Regression Models (to be revised) (click here)

  • Lecture 6* - Poisson Classification Models (to be revised) (click here)

  • Lecture 7 - Gaussian Models Models (click here)

    * The itens marked with * might be (slightly) changed.
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Datasets:
    Collection of data frames (to be updated) (click here)

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Software

The Software R will be used in the course. I recommend you to install the version of R and the software RStudio (both are freeware) indicated in the links below:


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2 - (cos(x + T*y) + cos(x - T*y) + cos(y + T*z) + cos(y - T*z) + cos(z - T*x) + cos(z + T*x))


Examination:

Final version.