1. Experimental design

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

3. Example of side effects – exclosures for grazing

4. Exclosures have significantly higher density of small rodents
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5. The poles of fencing are perfect perching sites for birds of pray

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

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

8. Take care
Even if the plots are located randomly, some of them are (in a finite area) close to each other, and so they might be “auto-correlated”
Regular pattern maximizes the distance between neighbouring plots

9. 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.

10. 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

12. Important - treatments randomly assigned to plots
Completely randomized design
Typical analysis: One way ANOVA

13. Regular patterns of individual treatment type location are often used, they usually maximize possible distance and so minimize the spatial dependence of plots getting the same treatment
Similar danger as for regular sampling pattern - i.e., when there is inherent periodicity in the environment – usually very unlikely

14. When randomizing, your treatment allocation could be also e.g.:
Regular pattern helps to avoid possible “clumping” of the same treatment plots

15. Randomized complete blocks
For repeated measurements - adjust the blocks (and even the randomization) after the baseline measurement

16. ANOVA, TREAT x BLOCK interaction is the error term

17. If the block has a strong explanatory power, the RCB design is stronger than completely randomized one

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

19. Reminder – Covariates
Use of covariates (covariables) and Analysis of Covariance – another possibility how to filter out „noise“ and decrease the unexplained variability

20. Latin square design
In most cases rather weak test if analyzed as Latin square (i.e. column and row taken as factors in incomplete three way ANOVA)
Again, useful to avoid clumping of the same treatment

21. Most frequent errors - pseudoreplications

22. Cited times

24. Note, B. is in fact not a pseudoreplication, if the analysis reflects correctly the hierarchical design of the data

25. Logic of experiments in ecology: is pseudoreplication a pseudoissue?
Oksanen, L
Logic of experiments in ecology: is pseudoreplication a pseudoissue?
OIKOS 94 : 27-38
Hurlbert divides experimental ecologist into 'those who do not see any need for dispersion (of replicated treatments and controls) and those who do recognize its importance and take whatever measures are necessary to achieve a good dose of it'. Experimental ecologists could also be divided into those who do not see any problems with sacrificing spatial and temporal scales in order to obtain replication, and those who understand that appropriate scale must always have priority over replication.

29. Reminder Type I and Type III SS
If the design is balanced, you don’t need to care
In non-balanced designs –
Type I – sequential – the order of predictors IS important
Type III, Type VI

30. What is the interaction?

31. Log transformation and the interaction
If the interaction = 0 - we expect the pure additivity
Effect of A+B = Effect of A + Effect of B
Null model for interaction: Xijk = m + ai + bj + eijk
(fertilization increases height by 5cm)
Model with interaction: Xijk = m + ai + bj + gij + eijk
Often biologically more feasible null model: pure multiplicativity (fertilization increases height by 20%)
Null model for interaction: Xijk = m . ai . bj . eijk
Then: log(Xijk) = log(m . ai . bj . eijk) = log m + log ai + log bj + log eijk

32. If you log-transform in a factorial ANOVA
Think more about the meaning of the interaction, the distributional properties of response variable are (usually) less important

33. Fixed and random factors

35. Fertilization experiment in three countries
Difference of meaning of the test, depending on whether the country is factor with fixed or random effect
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

36. 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 are considered as a 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

37. Nested design („split-plot“)

38. 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]

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

40. 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)

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

42. 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)

43. 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.)

44. 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) are nested within a treatment.
Of the main interest is interaction TIME*TREAT