Statistics Theory L3 = Experimental D Flashcards
Experimental design equation?
Experimental design = design structure + treatment structure + randomization
In environmental science studies, because we’re not designing a study in a carefully-controlled environment, what difficulties could arise? (3)
- Identifying the target population (statistical population), or matching the true statistical population to the intended statistical population.
- Using randomisation (assigning treatments to experimental units/random sampling).
- Using control or comparison areas or units.
Because we deal with a “treatment” (intervention/impact) that we can’t always control/manipulate, what consequences arise? (2)
- Might include long or broad time or spatial scales.
- Therefore, our only practical approach is to use observational studies (go to lesson 5).
To begin, do we have a clear definition/delineation of the target population?
No.
Why do we need a clear definition/delineation of the target population? (2)
It allows us to:
- Make easier decisions about the study design & sampling protocols.
- Easily apply results appropriately to the population of interest (intended popoulation).
Thing to note on Experimental designs?
There are various study types and the design of each study type will determine the inferences one can make from resulting the data.
Classification scheme/Classifications of research studies? (2)
- Studies of controlled events.
- Studies of uncontrolled events.
Types of Studies of controlled events? (3)
- Replicated experiments.
- Unreplicated experiments.
- Sampling for modelling (mu, beta, etc).
Types of Studies of uncontrolled events? (2)
- Perturbation (Intervention analysis - EIA).
- No perturbation.
Kinds of No perturbation studies? (2)
- Restricted domain of study (eg, particular age group).
- Sample over the entire domain of interest (complete population).
Philosophies for conducting research & making inferences? (3)
- Design-based/Data-based analysis.
- Model-based analysis.
- The two philosophies can be mixed, and rely on both approaches.
Design-based/Data-based analysis attributes? (2)
- Inferences are justified by the design of the study & the data collected.
- Inferences are dependent on several things.
What are the inferences of Design-based/Data-based analysis dependent on? (3)
- Appropriate y-variable.
- Methods to measure variables.
- A design protocol for sampling of the experimental set-up.
Model-based analysis attributes? (2)
- Rely on statistical models to make conclusions (eg, study of survival of cancer patients).
- Assumes that a valid inference depends on upholding model assumptions.
Even though we’ve already encountered tools such as randomisation, replication & control, how do we increase precision when dealing with limited replicates/absence of sufficient replication? (2)
- Blocking.
- Analysis of covariance (ANCOVA).
Blocking?
= randomly allocating treatments within homogenous groups (eg, sex).
Blocking attribute?
Is a categorical variable.
Analysis of covariance?
= includes covariates that might have an effect on the relationship of interest (eg, age in drug-cancer experiment).
Analysis of covarince attribute?
Is a continuous variable.
What is the goal of these additional methods, blocking & ANCOVA?
To help reduce the variability of the study.
Practical considerations? (7)
- Area of interest?
- Time of interest?
- Species/System of interest?
- Potential confounding/disturbing variables?
- Enough time to conduct the study?
- Budget?
- Magnitude of the anticipated effect?
Area of interest?
= what is the target/statistical population?
Time of interest?
= will it occur during day or night? different seasons? >1 year?
Species/System of interest?
= is it good for answering your question/solving the problem you want to solve?
Potential confounding/disturbing variables?
= how to grapple with variables you can’t control?
Enough time to conduct the study?
= do we have control over that?
Budget?
= major driver of all research & design consideration?
Magnitude of the anticipated effect?
= how does this affect sample size?
- Requires a power analysis to determine the magnitude.
Experimental designs?
= defined by the number of treatment types that are applied to the experimental units.
Experimental designs attributes? (3)
- Can get complicated very quickly, depending on the number & arrangements of treatments.
- The method chosen to analyse such experimental data links directly to the design that generated/produced it.
- Analyses like ANOVA were originally developed with such experimental designs in mind.
How do we allocate a limited number of experimental units in a way that gives us the best possible outcome from the experiment?
We use one of the types of experimental designs.
Types of experimental designs? (3)
- Single-factor experimental designs.
- Multiple-factor experimental designs.
- Hierarchical experimental designs.
Single-factor experimental designs?
= focus on a single type of treatment.
Eg of a Single-factor experimental design?
Amount of drug in a drug trial.
Types of Single-factor experimental designs? (5)
- Paired & unpaired studies.
- Completely randomised design.
- Randomised complete block design.
- Incomplete block design.
- Latin squares design.
Paired studies?
= evaluate changes in study units paired for similarity (eg, twins; before-after).
Unpaired studies?
= have two independent samples from two groups/populations.
Goal of Paired & unpaired studies?
To compare the means of the two groups.
Completely randomised design attributes? (6)
- There is one pool of potential units (need to be homogeneous).
- A treatment is randomly assigned to a subset of the units.
- Each unit from the pool has the same chance of receiving the treatment.
- Analysed with a t-test or ANOVA.
- Useful for lab experiments where experimental units are carefully controlled.
- Situation is more difficult in the field.
Why is the situation more difficult in the field when using a Completely randomised design?
There is a lot of natural variation, measurement variation. & confounding factors that might affect conclusions.
Model equation of a Completely randomised design?
Observed outcome = overall mean + treatment effect + residual variation
Randomised complete block design attributes? (3)
- Uses blocking & stratification as a form of variation control.
- Then we randomly assign within blocks.
- Eg, Have the same amount of grazing treatments for each soil type (each block), just randomised.
Model equation for Randomised complete block design?
Observed outcome = overall mean + block effect + treatment effect + residual variation + block x treatment variation
Incomplete block design attributes? (3)
- Like randomised complete block design, but each block has less than the full complement of treatments.
- Each treatment occurs the same number of times (i.e., a balanced design).
- Eg, Not every treatment is represented for each soil type (possibly due to funding).
Latin squares design attributes? (2)
- A randomised block design that uses two blocking variables.
- Latin square must be symmetrical (same number of levels) so that each of the two blocking variables is a unique block.
Model equation for Latin squares design?
Observed outcome = block1 effect + block2 effect + treatment effect + residual variation
Multiple-factor experimental design?
We’re not focusing/touching on it.
Types of Hierarchical designs? (3)
- Nested design.
- Split-plot design.
- Repeated measures design.
Nested design?
= there are at least 2 levels of replication.
Eg of Nested design? (3)
- Random sample of schools (1, 2, 3).
- Random sample of students [A, B, C…(from school 1); A, B, C… (from school 2); A, B, C… (from school 3)].
- Replication of schools, but we also have a replication of students.
Split-plot design attributes? (2)
- Common in agricultural experiments.
- There are more than two levels of replication.
Steps to carry out a Split-plot design? (4)
1) Define blocks along the lines discussed previously.
2) Divide blocks into “main plots” (one factor within each block).
3) Divide main plots into “split plots” (a second factor within each split plot).
4) We randomly assign treatments to split plots.
What to do if one factor is spatially larger than another? (2)
- It might be necessary to apply some treatment to whole plots.
- The main goal is to compare the “smaller” factor.
Eg of Split-plot design?
- 2 levels of grazing (“split plot”).
- 2 levels of fire (“main plot”).
Repeated measures design attributes? (2)
- Repeated measures (over space or time) can lead to a lack of independence within experimental units.
- In longitudinal studies, the same units are measured repeatedly over time.
Kind of a Repeated measures design?
Change-over experiment.
Change-over experiment attributes? (5)
- With a pool of units & two treatments, half the units are randomly assigned treatment 1, the other half treatment 2.
- Partway through the experiment, the treatments are reversed (units exchange one treatment for the other).
- The outcome is measured as the difference between the two treatments.
- Commonly used in drug trials.
- Doing it this way is randomising, to see the effects of A & B. Compared to staring everyone off with A or B, and then switching them to B & A.
Analysis of covariance (ANCOVA)?
= a combination of ANOVA & linear regression, where linear models combine levels of a categorical variable with continuous covariates.
Why covariates?
Covariates are chosen to separate the treatment effects on the response variable from the effects of confounding variables.
Eg of ANCOVA? (3)
2-way ANOVA where:
- x: 2 levels of food; 2 levels of antibiotic.
- y: calf body mass growth.
- covariate is age.
