experimental design
DESCRIPTION
Experimental design. 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. - PowerPoint PPT PresentationTRANSCRIPT
Experimental design
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
Example of side effects – exclosures for grazing
Exclosures have significantly higher density of small rodents
????????????
The poles of fencing are perfect perching sites for birds of pray
Laboratory, field, natural trajectory (NTE), and natural snapshot experiments (Diamond 1986)
Lab Field NTE NSERegulation ofindep. variables
Highest Medium/low None None
Site matching Highest Medium Medium/low LowestAbility to followtrajectory
Yes Yes Yes No
Maximumtemporal scale
Lowest Lowest Highest Highest
Maximumspatial scale
Lowest Low Highest Highest
Scope (range ofmanipulations)
Lowest Medium/low Medium/high
Highest
Realism None/low High Highest HighestGenerality None Low High High
NTE/NSE - Natural Trajectory/Snapshot Experiment
Observational studies(e.g. for correlation between environment and species, or
estimates of plot characteristics)Random vs. regular sampling plan
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
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.
Manipulative experimentsfrequent 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
Completely randomized design
Typical analysis: One way ANOVA
Important - treatments randomly assigned to plots
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
When randomizing, your treatment allocation could be also e.g.:
Regular pattern helps to avoid possible “clumping” of the same treatment plots
E N V I R O N M E N T A L G R A D I E N T
Block 1 Block 2 Block 3 Block 4
Randomized complete blocks
For repeated measurements - adjust the blocks (and even the randomization) after the baseline measurement
ANOVA, TREAT x BLOCK interaction is the error term
TREAT BLOCK RESPO1 RESPO21 1 5 52 1 6 63 1 4 41 2 7 52 2 9 53 2 8 41 3 3 52 3 5 73 3 2 41 4 6 42 4 7 63 4 5 51 5 8 42 5 11 53 5 9 6
TREAT:G_1:1
TREAT:G_2:2
TREAT:G_3:3
BLOCK
RE
SP
O1
0
2
4
6
8
10
12
G_1:1 G_2:2 G_3:3 G_4:4 G_5:5
If the block has a strong explanatory power, the RCB design is stronger than completely randomized one
df MS df MSEffect Effect Error Error F p-level
TREAT 2 6.066667 8 0.4 15.16667 0.001897BLOCK 4 17 8 0.4 42.5 1.97E-05
TREAT 2 6.066667 12 5.933333 1.022472 0.389016
TREAT:G_1:1
TREAT:G_2:2
TREAT:G_3:3
BLOCK
RE
SP
O2
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
G_1:1 G_2:2 G_3:3 G_4:4 G_5:5
df MS df MSEffect Effect Error Error F p-level
TREAT 2 2.4 8 0.816667 2.938776 0.110435BLOCK 4 0.166667 8 0.816667 0.204082 0.929067
TREAT 2 2.4 12 0.6 4 0.046656
If the block has no explanatory power, the RCB design is weak
Latin square designIn 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
Most frequent errors - pseudoreplications
Cited 4000+ times
Note, B. is in fact not a pseudoreplication, if the analysis reflects correctly the hierarchical design of the data
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.
Oksanen, LLogic of experiments in ecology: is pseudoreplication a pseudoissue? OIKOS 94 : 27-38
Factorial designs
Completely randomised
F for testing effects in variouscombination of fixed and randomfactors in two-way ANOVA
Testedeffect
Both fixed A-fixed,B-random
Both random
A MSA/MSerror MSA/MSAxB MSA/MSAxB
B MSB/MSerror MSB/MSerror MSB/MSAxB
A x B MSAxB/MSerror MSAxB/MSerror MSAxB/MSerror
COUNTRY FERTIL NOSPEC1 CZ 0.000 9.0002 CZ 0.000 8.0003 CZ 0.000 6.0004 CZ 1.000 4.0005 CZ 1.000 5.0006 CZ 1.000 4.0007 UK 0.000 11.0008 UK 0.000 12.0009 UK 0.000 10.00010 UK 1.000 3.00011 UK 1.000 4.00012 UK 1.000 3.00013 NL 0.000 5.00014 NL 0.000 6.00015 NL 0.000 7.00016 NL 1.000 6.00017 NL 1.000 6.00018 NL 1.000 8.000
Fertilization experiment in three countries
Difference of meaning of the test, depending on whether the country is factor with fixed or random effect
Summary of all Effects; design: (new.sta)1-COUNTRY, 2-FERTIL
df MS df MS Effect Effect Error Error F p-level
1 2 2.16667 12 1.05556 2.05263 .1711122 1 53.38889 2 26.05556 2.04904 .28862412 2 26.05556 12 1.05556 24.68421 .000056
Summary of all Effects; design: (new.sta)1-COUNTRY, 2-FERTIL
df MS df MS Effect Effect Error Error F p-level
1 2 2.16667 12 1.055556 2.05263 .1711122 1 53.38889 12 1.055556 50.57895 .00001212 2 26.05556 12 1.055556 24.68421 .000056
Country is a fixed factor (i.e., we are interested in the three plots only)
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])
Nested design („split-plot“)
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]
Plot 1 Plot 2 Plot 3
Plot 4 Plot 5 Plot 6
C
P
N
N
P
C
C
N
P
N
CP C
N
P N
P
C
Split plot (main plots and split plots - two error levels)
df MS df MSEffect Effect Error Error F p-level
ROCK 1 0.055556 4 8.944445 0.006211 0.940968PLOT 4 8.944445 0 0TREA 2 3.166667 8 0.611111 5.181818 0.036018ROCK*PLOTROCK*TREA 2 0.722222 8 0.611111 1.181818 0.355068PLOT*TREA 8 0.611111 0 03way
ROCK PLOT TREA RESP1 1 1 51 1 2 81 1 3 61 2 1 61 2 2 81 2 3 61 3 1 21 3 2 31 3 3 32 1 1 52 1 2 62 1 3 52 2 1 52 2 2 42 2 3 32 3 1 52 3 2 72 3 3 6
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)
Following changes in time
Non-replicated BACI (Before-after-control-impact)
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)
TIME:BEFORE
TIME:AFTER
LOCATION
CD
6
7
8
9
10
11
12
13
CONTR IMPACT
TIME:BEFORE
TIME:AFTER
LOCATION
PB
6
7
8
9
10
11
12
13
CONTR IMPACT
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.)
T0 Treatment T1 T2
Control
Control
Control
Impact
Impact
Impact
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
df MS df MSEffect Effect Error Error F p-level
1 1 24.5 4 2.111111 11.60526 0.0271112 2 35.72222 8 0.944444 37.82353 8.37E-0512 2 12.16667 8 0.944444 12.88235 0.003151
TRE T1 T2 T31 5 6 71 6 5 81 5 7 72 4 7 112 6 8 122 5 9 15
TRE:G_1:1
TRE:G_2:2
TIME
He
igh
t
4
5
6
7
8
9
10
11
12
13
14
T1 T2 T3