Statistics Theory L2 = Study Design Basics Flashcards
How do we design & execute a study to collect data and draw inferences as reliably as possible?
Through using a Population-sample-direction-of-inference diagram.
What is a Population-sample-direction-of-inference diagram?
= it is diagram used by scientists to direct how/what kind of inference to apply to their study.
Population-sample-direction-of-inference diagram attributes? (4)
- Statistical population is a fluid concept (fluffy).
- Sample is a concrete concept (box).
- From sample to statistical population, you get statistics (induction).
- From statistical population to sample, you get probability (deduction).
Goal of the Population-sample-direction-of-inference diagram?
To help us think in terms of estimating one or more parameters from our designated statistical population.
How could we do this, i.e., what could we be estimating? (2)
Could be:
- Estimating more than 1 parameter in a model.
- Estimating a difference between treatments in a randomised experiment.
So, what do we have to do to achieve our goal?
We have to fit a model with parameters using data that we have collected (and the data are measured in terms of variables).
Types of variables?
= the function they serve in answering our question or what effect they have on the outcome or conclusion.
Use of the types of variables?
They inform the type of analysis we choose.
Types of variables in terms of their function? (4)
Primarily, you have Explanatory & Disturbing variables. Under disturbing variables you have 2 kinds of variables namely, controlling & randomising variables.
So, essentially you have:
- Explanatory variables.
- Disturbing variables.
- Controlling variables.
- Randomising variables.
Explanatory variables?
= variables we need to answer the questions we are interested in.
Explanatory variables attributes? (4)
- The focus of most scientific studies.
- Represent the things we are actually interested in knowing something about.
- Include x (predictor) and y (response) variables.
- Focus on the function of the variables.
Predictor variable?
= variable that is purported by the hypothesis to cause the behaviour of the response variable.
Predictor variable attributes? (4)
- Can be discrete or continuous.
- Can be ordered & disordered.
- If discrete, called a “factor”, as in the analysis of variance.
- If continuous, called a “covariate”, as in studies that use regression analysis.
Response variable?
= variable of interest whose behaviour we want to predict (on the basis of our research hypothesis).
What choices does an investigator have in dealing with disturbing variables? (3)
- Provide control for them.
- Randomise them to remove/minimise their effect.
- Ignore them.
Goals when using explanatory variables? (3)
- Identify relationships between predictor & response variables.
- Do this in the most unbiased & precise way as possible.
- Very difficult in environmental science (esp. observational studies) due to the many external influences that we can’t control.
Disturbing/Extraneous variables?
= the things we need to control for or accommodate to get at the things we are interested in.
Disturbing varibales attributes? (2)
- Represent extraneous influences that can affect the estimated relationship between explanatory variables, or our ability to measure them.
- Can introduce bias into the study.
Eg of Disturbing variables?
Aerial game counts: we might be interested in animal abundance or distribution, but other factors get in the way of our ability to estimate those things accurately such as, detection probability of animals we count, observer experience & weather conditions on the day of the survey.
Types of Disturbing variables? (2)
- Controlling.
- Randomising.
Controlling variables?
= the subset of disturbing variables that we measure so that we can assess their effect on the variables & relationships of interest.
Controlling variables attributes? (4)
- Best way to deal with disturbing variables.
- We control for variability explained by a “nuissance”.
- “Nuissance” removes bias, and
- Improves precision.
Eg of Controlling variables?
Snake mass vs length, without & with sex variable.
Explain the Controlling variables example? (4)
- Mass & length are the explanatory variables.
- We know that the sex will affect the relationship between mass & length.
- With controlling variable.
- Without controlling variable.
With controlling variable in Controlling variable example effects? (3)
- Included sex (male & female) as a controlling variable.
- Less bias for male & female.
- End up with more precision (lower variability around each line).
Without controlling variable in Controlling variable example effects? (3)
- Combined data.
- Biased slopes (too low for males; too high for females).
- Less precise (higher variability).
Randomised variables?
= the subset of disturbing variables that represent the factors whose influence we are aiming to reduce through the randomisation process.
Randomising/Randomised variables attribute?
Cannot be controlled through design or measurement of controlling variable.
Why do we use randomising? (3)
- To reduce the effect of unknown influences on our study.
- To deal with factors that are not practical to measure, or we don’t know how to measure them.
- To accommodate limits imposed by sample size.
Example of Randomised variables? (6)
- Let’s say we’re studying the amount of weight loss in fat Americans as a result of the diet they are given (diet A, diet B, diet C).
- X variable = Diet A, Diet B, Diet C.
- Y variable = Amount of weight loss.
- Possible influences on amount of weight loss is genetics.
- So, we distribute the fat Americans in each diet group in the hopes that genetics (or other possible uncontrollable factors) will have a low influence over the results.
- By doing this you’re randomising the variables.
What are our goals in using Randomisation & Replication? (3)
- To be objective/unbiased in the selection of the population subset to study.
- To ensure that our inferences can be applied to the intended target population (i.e., the sample is representative of the statistical population).
- To control confounding variables.
Randomisation attributes? (4)
- Incorporates a “chance mechanism”.
- Aims for representation.
- Random assignment of treatments to experimental units.
- Consists of 2 facets, namely, random sampling & randomised experiment.
What will happen if there’s no randomisation? (3)
- Can’t claim that results apply to the statistical population/entire target population.
- Can’t infer cause-and-effect.
- Research is vulnerable to disturbing variables (due to the lack of probabilistic design that accompanies randomisation).
Replication attributes? (3)
- We want to measure >1 experimental unit.
- Or, we want to apply treatment to >1 experimental unit.
- More experimental units, more ability to detect an effect (& make inferences about the population studied).
Conditions/Criteria that experimental units should meet for Replication? (2)
Experimental units should be:
- Physically separate from each other (temporally or spatially).
- Independent applications of a treatment.
Consequence of experimental units not meeting the conditions/criteria?
We’re at risk of pseudo-replication.
Pseudo-replication?
= involves treating non-independent experimental units as independent.
Eg of Replication?
Imagine we have 2 lakes containing fish. We treat 1 lake with some chemical, and take a sample of 30 fish from each lake. How many replicates do we have?
Why is Replication important?
To enable researchers to detect an effect in the experimental units.
Types of study designs? (4)
- Manipulative experiment.
- Quasi-experiment.
- Mensurative study.
- Descriptive study.
Manipulative experiment?
= the predictor (explanatory) variable is under the control of the researchers.
Manipulative experiment attributes? (3)
- Not necessarily in a lab.
- Have random allocation of treatments & controls to experimental units.
- Has replication.
Quasi-experiment?
= environmental science studies where replicated, manipulative experiments are not feasible.
Quasi-experiment attributes? (4)
- Circumstances might require a sacrifice in terms of randomisation or replication.
- Compromise our ability to make statistical inferences.
- “Manipulation” is not necessarily under the control of researchers.
- Impact assessments of development projects.
Mensurative study?
= observational study where no researcher-controlled manipulation occurs.
Mensurative study attributes? (5)
- Random sampling is possible.
- Generally no allocation of experimental units.
- Comparisons take the place of experiments.
- Findings are correlative.
- Useful for evaluating patterns & processes within the population of interest.
Descriptive study attributes? (4)
- Provide description of a system of interest.
- Not designed to answer “how” or “why” questions.
- No replication, randomisation & comparison.
- Increase our knowledge about the system of interest.
Know the differences between what terms? (3)
- Accuracy.
- Precision.
- Bias.
Accuracy?
= a function of bias & precision.
Precision?
= how close repeated estimates of the same parameter are to each other.
Bias?
= the distance between an estimate of a parameter & the true value of that parameter.
What is it that we want/aim for for our study design? (2)
- High precision.
- Low bias.
High precision, low bias?
= repeated estimates are close together & close to the true value (to the truth).
High precision, high bias?
= repeated estimates are close together & far from the true value.
Low precision, low bias?
= repeated estimates are far from each other & close to the true value.
Low precision, high bias?
= repeated estimates are far from each other & far from the true value.
Control?
= an unmanipulated experimental unit.
Control atributes? (2)
- Are also treatments.
- Benchmarks used to evaluate the impacts of treatments on the system response.
Experimental unit VS Observational unit?
An experimental unit differs from an observational unit in that observational units can be samples taken from the experimental unit.
