Applied Statistics – A Practical Course
2025-09-16
\(\Rightarrow\) Practical understanding and “statistical feeling”,
\(\rightarrow\) More important than facts learned by heart.
\(\rightarrow\) Slides and exercises are regularly updated, depending on the progress of the course. Comments are welcome.
Written exam at the end of the semester
\(\rightarrow\) > 50% practical questions
\(\rightarrow\) Attend the labs!
Questions?
\(\rightarrow\) a few examples before we begin
Daily average discharge of River Elbe, pegel Dresden, river km 55.6
date, discharge
1806-01-01, 472
1806-01-02, 1050
1806-01-03, 1310
1806-01-04, 1020
1806-01-05, 767
1806-01-06, 616
...
2020-10-11, 216
2020-10-12, 204
2020-10-13, 217
2020-10-14, 288
2020-10-15, 440
2020-10-16, 601
2020-10-17, 570
2020-10-18, 516
2020-10-19, 450
2020-10-20, 422
2020-10-21, 396
2020-10-22, 372
2020-10-23, 356
2020-10-24, 357
2020-10-25, 332
2020-10-26, 303
2020-10-27, 302
2020-10-28, 316
2020-10-29, 321
2020-10-30, 331
2020-10-31, 353
2020-11-01, 395
\(>\) 70,000 measurements. How can we analyse this and what does it mean?
Data Source: Bundesanstalt für Gewässerkunde
Discharge of the Elbe River, gauge station Dresden, data source BfG
Which of these parameters are most appropriate?
Descriptive statistics and graphics
Hypothesis testing
Statistical modelling
How likely is it, that our hypothesis is true?
Examples
Fit a statistical model to the data
Examples
Wide format
station | 2021 | 2022 | 2023 |
---|---|---|---|
A | 4 | 20 | 13 |
B | 4 | 4 | 3 |
C | 18 | 7 | 6 |
D | 12 | 17 | 10 |
E | 2 | 19 | 11 |
Long format
year | station | value |
---|---|---|
2021 | A | 4 |
2021 | B | 4 |
2021 | C | 18 |
2021 | D | 12 |
2021 | E | 2 |
2022 | A | 20 |
2022 | B | 4 |
2022 | C | 7 |
2022 | D | 17 |
2022 | E | 19 |
2023 | A | 13 |
2023 | B | 3 |
2023 | C | 6 |
2023 | D | 10 |
2023 | E | 11 |
treat | replicate 1 | replicate 2 | replicate 3 |
---|---|---|---|
Fertilizer | 0.020 | -0.217 | -0.273 |
F. open | 0.940 | 0.780 | 0.555 |
F.+sugar | 0.188 | -0.100 | 0.020 |
F.+CaCO3 | 0.245 | 0.236 | 0.456 |
Bas.med. | 0.699 | 0.727 | 0.656 |
A.dest | -0.010 | 0.000 | -0.010 |
Tap water | 0.030 | -0.070 | NA |
growth ~ treat
treat | rep | growth |
---|---|---|
Fertilizer | 1 | 0.020 |
Fertilizer | 2 | -0.217 |
Fertilizer | 3 | -0.273 |
F. open | 1 | 0.940 |
F. open | 2 | 0.780 |
F. open | 3 | 0.555 |
F.+sugar | 1 | 0.188 |
F.+sugar | 2 | -0.100 |
F.+sugar | 3 | 0.020 |
F.+CaCO3 | 1 | 0.245 |
F.+CaCO3 | 2 | 0.236 |
F.+CaCO3 | 3 | 0.456 |
Advantages
Therefore:
\(\rightarrow\) Lab-exercise with Elbe River time series.
\(\rightarrow\) Proper use of ready-made software packages requires fundamental understanding.
Required software
In contrast to other systems Copy & Paste is allowed! – just cite it.
Statistics
R Programming