1. Experimental design

2. Experiments vs. observational studies
Manipulative experiments: The only way to proof the causal relationships
BUT
Spatial and temporal limitation of manipulations
Side effects of manipulations

3. Laboratory, field, natural trajectory (NTE), and natural snapshot experiments (Diamond 1986)
NTE/NSE - Natural Trajectory/Snapshot Experiment

4. Observational studies (e. g
Observational studies (e.g. for correlation between environment and species, or estimates of plot characteristics)
Random vs. regular sampling plan

5. Regular design - biased results, when there is some regular structure in the plot (e.g. regular furrows), with the same period as is the distance in the grid - otherwise, better design providing better coverage of the area, and also enables use of special permutation tests.

6. Manipulative experiments
frequent trade-off between feasibility and requirements of correct statistical design and power of the tests
To maximize power of the test, you need to maximize number of independent experimental units
For the feasibility and realism, you need plots of some size, to avoid the edge effect

7. Important - treatments randomly assigned to plots
Completely randomized design
Typical analysis: One way ANOVA
often, chessboard arrangement or similar regular pattern

8. Randomized complete blocks

9. ANOVA, TREAT x BLOCK interaction is error term

10. If the block has strong explanatory power, the RCB design is stronger

11. If the block has no explanatory power, the RCB design is weak

12. Latin square design

13. Most frequent errors - pseudoreplications

16. Fertilization experiment in three countries
COUNTRY FERTIL NOSPEC
1 CZ
2 CZ
3 CZ
4 CZ
5 CZ
6 CZ
7 UK
8 UK
9 UK
10 UK
11 UK
12 UK
13 NL
14 NL
15 NL
16 NL
17 NL
18 NL

17. Country is a fixed factor (i. e
Country is a fixed factor (i.e., we are interested in the three plots only)
Summary of all Effects; design: (new.sta)
1-COUNTRY, 2-FERTIL
df MS df MS
Effect Effect Error Error F p-level
Country is a random factor (i.e., the three plots arew considered as random selection of all plots of this type in Europe - [to make Brussels happy])
Summary of all Effects; design: (new.sta)
1-COUNTRY, 2-FERTIL
df MS df MS
Effect Effect Error Error F p-level

18. Nested designs („split-plot“)

19. Two explanatory variables, Treatment and Plot,
Plot is random factor nested in Treatment.
Accordingly, there are two error terms, effect of Treatment is tested against Plot, effect of Plot against residual variability:
F(Treat)=MS(Treat)/MS(Plot)
F(Plot)=MS(Plot)/MS(Resid) [often not of interest]

20. Split plot (main plots and split plots - two error levels)

21. ROCK is the MAIN PLOT factor, PLOT is random factor nested in ROCK, TREATMENT is the within plot (split-plot) factor.
Two error levels:
F(ROCK)=MS(ROCK)/MS(PLOT)
F(TREA)=MS(TREA)/MS(PLOT*TREA)

22. Following changes in time
Non-replicated BACI (Before-after-control-impact)

23. Analysed by two-way ANOVA
factors: Time (before/after) and Location (control/impact)
Of the main interest: Time*Location interaction (i.e., the temporal change is different in control and impact locations)

24. In fact, in non-replicated BACI, the test is based on pseudoreplications.
Should NOT be used in experimental setups
In impact assessments, often the best possibility
(The best need not be always good enough.)

25. Replicated BACI - repeated measurements
Usually analysed by “univariate repeated measures ANOVA”. This is in fact split-plot, where TREATment is the main-plot effect, time is the within-plot effect, individuals (or experimental units) and nested within a treatment.
Of the main interest is interaction TIME*TREAT