Statistics Theory L2 = Study Design Basics

Question 1

How do we design & execute a study to collect data and draw inferences as reliably as possible?

Answer 1

Through using a Population-sample-direction-of-inference diagram.

Question 2

What is a Population-sample-direction-of-inference diagram?

Answer 2

= it is diagram used by scientists to direct how/what kind of inference to apply to their study.

Question 3

Population-sample-direction-of-inference diagram attributes? (4)

Answer 3

• 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).

Question 4

Goal of the Population-sample-direction-of-inference diagram?

Answer 4

To help us think in terms of estimating one or more parameters from our designated statistical population.

Question 5

How could we do this, i.e., what could we be estimating? (2)

Answer 5

Could be:

• Estimating more than 1 parameter in a model.
• Estimating a difference between treatments in a randomised experiment.

Question 6

So, what do we have to do to achieve our goal?

Answer 6

We have to fit a model with parameters using data that we have collected (and the data are measured in terms of variables).

Question 7

Types of variables?

Answer 7

= the function they serve in answering our question or what effect they have on the outcome or conclusion.

Question 8

Use of the types of variables?

Answer 8

They inform the type of analysis we choose.

Question 9

Types of variables in terms of their function? (4)

Answer 9

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.

Question 10

Explanatory variables?

Answer 10

= variables we need to answer the questions we are interested in.

Question 11

Explanatory variables attributes? (4)

Answer 11

• 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.

Question 12

Predictor variable?

Answer 12

= variable that is purported by the hypothesis to cause the behaviour of the response variable.

Question 13

Predictor variable attributes? (4)

Answer 13

• 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.

Question 14

Response variable?

Answer 14

= variable of interest whose behaviour we want to predict (on the basis of our research hypothesis).

Question 15

What choices does an investigator have in dealing with disturbing variables? (3)

Answer 15

• Provide control for them.
• Randomise them to remove/minimise their effect.
• Ignore them.

Question 16

Goals when using explanatory variables? (3)

Answer 16

• 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.

Question 17

Disturbing/Extraneous variables?

Answer 17

= the things we need to control for or accommodate to get at the things we are interested in.

Question 18

Disturbing varibales attributes? (2)

Answer 18

• Represent extraneous influences that can affect the estimated relationship between explanatory variables, or our ability to measure them.
• Can introduce bias into the study.

Question 19

Eg of Disturbing variables?

Answer 19

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.

Question 20

Types of Disturbing variables? (2)

Answer 20

• Controlling.
• Randomising.

Question 21

Controlling variables?

Answer 21

= the subset of disturbing variables that we measure so that we can assess their effect on the variables & relationships of interest.

Question 22

Controlling variables attributes? (4)

Answer 22

• Best way to deal with disturbing variables.
• We control for variability explained by a “nuissance”.
• “Nuissance” removes bias, and
• Improves precision.

Question 23

Eg of Controlling variables?

Answer 23

Snake mass vs length, without & with sex variable.

Question 24

Explain the Controlling variables example? (4)

Answer 24

• Mass & length are the explanatory variables.
• We know that the sex will affect the relationship between mass & length.
• With controlling variable.
• Without controlling variable.

Question 25

With controlling variable in Controlling variable example effects? (3)

Answer 25

- Included sex (male & female) as a controlling variable. - Less bias for male & female. - End up with more precision (lower variability around each line).

Question 26

Without controlling variable in Controlling variable example effects? (3)

Answer 26

- Combined data. - Biased slopes (too low for males; too high for females). - Less precise (higher variability).

Question 27

Randomised variables?

Answer 27

= the subset of disturbing variables that represent the factors whose influence we are aiming to reduce through the randomisation process.

Question 28

Randomising/Randomised variables attribute?

Answer 28

Cannot be controlled through design or measurement of controlling variable.

Question 29

Why do we use randomising? (3)

Answer 29

- 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.

Question 30

Example of Randomised variables? (6)

Answer 30

- 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.

Question 31

What are our goals in using Randomisation & Replication? (3)

Answer 31

- 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.

Question 32

Randomisation attributes? (4)

Answer 32

- Incorporates a "chance mechanism". - Aims for representation. - Random assignment of treatments to experimental units. - Consists of 2 facets, namely, random sampling & randomised experiment.

Question 33

What will happen if there's no randomisation? (3)

Answer 33

- 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).

Question 34

Replication attributes? (3)

Answer 34

- 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).

Question 35

Conditions/Criteria that experimental units should meet for Replication? (2)

Answer 35

Experimental units should be: - Physically separate from each other (temporally or spatially). - Independent applications of a treatment.

Question 36

Consequence of experimental units not meeting the conditions/criteria?

Answer 36

We're at risk of pseudo-replication.

Question 37

Pseudo-replication?

Answer 37

= involves treating non-independent experimental units as independent.

Question 38

Eg of Replication?

Answer 38

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?

Question 39

Why is Replication important?

Answer 39

To enable researchers to detect an effect in the experimental units.

Question 40

Types of study designs? (4)

Answer 40

- Manipulative experiment. - Quasi-experiment. - Mensurative study. - Descriptive study.

Question 41

Manipulative experiment?

Answer 41

= the predictor (explanatory) variable is under the control of the researchers.

Question 42

Manipulative experiment attributes? (3)

Answer 42

- Not necessarily in a lab. - Have random allocation of treatments & controls to experimental units. - Has replication.

Question 43

Quasi-experiment?

Answer 43

= environmental science studies where replicated, manipulative experiments are not feasible.

Question 44

Quasi-experiment attributes? (4)

Answer 44

- 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.

Question 45

Mensurative study?

Answer 45

= observational study where no researcher-controlled manipulation occurs.

Question 46

Mensurative study attributes? (5)

Answer 46

- 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.

Question 47

Descriptive study attributes? (4)

Answer 47

- 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.

Question 48

Know the differences between what terms? (3)

Answer 48

- Accuracy. - Precision. - Bias.

Question 49

Accuracy?

Answer 49

= a function of bias & precision.

Question 50

Precision?

Answer 50

= how close repeated estimates of the same parameter are to each other.

Question 51

Bias?

Answer 51

= the distance between an estimate of a parameter & the true value of that parameter.

Question 52

What is it that we want/aim for for our study design? (2)

Answer 52

- High precision. - Low bias.

Question 53

High precision, low bias?

Answer 53

= repeated estimates are close together & close to the true value (to the truth).

Question 54

High precision, high bias?

Answer 54

= repeated estimates are close together & far from the true value.

Question 55

Low precision, low bias?

Answer 55

= repeated estimates are far from each other & close to the true value.

Question 56

Low precision, high bias?

Answer 56

= repeated estimates are far from each other & far from the true value.

Question 57

Control?

Answer 57

= an unmanipulated experimental unit.

Question 58

Control atributes? (2)

Answer 58

- Are also treatments. - Benchmarks used to evaluate the impacts of treatments on the system response.

Question 59

Experimental unit VS Observational unit?

Answer 59

An experimental unit differs from an observational unit in that observational units can be samples taken from the experimental unit.