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Experimental design
A structured approach to planning and conducting manipulative or 'natural' experiments, intended to investigate relationships between variables.
Set of treatments
The set of treatments included in a research study.
Set of experimental units
The set of experimental units included in the study.
Rules and procedures
The rules and procedures by which the treatments are assigned to the experimental units (or vice versa).
Measurements
The measurements made on the experimental units after the treatments have been applied.
Experimental treatment
Any specific intervention or manipulation of an independent variable (IV) that is applied to experimental units.
Control treatment
Designed to eliminate alternate explanations of experimental results, specifically focusing on mitigating experimenter bias and experimental errors.
Negative control treatment
A basis of comparison that is identical to the experimental treatment except that the specific manipulation or intervention is not applied.
Positive control treatment
Used to verify that an experimental procedure is functioning as expected, where experimental units are treated in a way that is known to show an expected result.
Sham control treatment
An additional negative control treatment in which the experimental procedure is used, but the actual specific treatment is not applied.
Placebo
An inactive substance or treatment, often used in clinical trials, to compare against an active treatment.
No control treatment
A design that compares two or more levels of the experimental treatment against each other to test for a treatment effect.
Treatment
Any specific intervention or manipulation of an IV applied to units.
Levels
The different forms or quantities of the manipulation (e.g., different levels of hunger on aggressive behavior).
Experimental unit
The smallest entity to which a treatment is randomly applied and on which a response measurement is taken.
Replicate
Each experimental unit belonging to one treatment group.
Sample size (N)
Determined by the number of replicates per treatment group; research designs are considered legitimate only if they provide adequate replication.
Pseudoreplication
A statistical error that occurs when a researcher's analysis mistakenly treats non-independent samples as if they are independent replicates.
Spatial pseudoreplication
Taking multiple samples from within the same experimental unit.
Temporal pseudoreplication
Taking multiple measurements over time from the same experimental unit.
Type I statistical error
A false positive error where a true null hypothesis is incorrectly rejected.
Type II statistical error
A false negative error where a false null hypothesis is incorrectly accepted.
Blind designs
Participants do not know if they are in the treatment group or the control group.
Double-blind designs
Neither the participants nor the researchers who evaluate them know who is in the treatment group or the control group.
Triple blinding
An approach where patients, doctors, and statisticians are all kept unaware of which group is the control group until the analysis is complete.
Randomization
The technique of assigning experimental units to a particular treatment without any particular pattern.
Importance of randomization
Eliminates or reduces bias in the research design, preventing systematic biases between test groups.
Regression to the mean
The observation that subjects who stand out on an initial measurement will, on average, show measurements closer to their true mean on subsequent measurements.
How regression to the mean arises
Occurs when subjects are selected based on extreme scores, representing both true ability and temporary factors.
Example of regression to the mean
If a researcher selects patients specifically for high blood pressure, their initial high reading may be due to temporary factors, leading to improvement regardless of treatment.
Effect of pseudoreplication
Increases the likelihood of a Type I error.
Fisher's justification of randomization
Not provided in detail regarding his hypothetical tea-tasting experiment.
Lady Tasting Coffee case study
No comparative explanation of which error is 'worse' in that context is provided.
Confounding factors
Factors that can systematically affect the results if randomization is not successful.
Statistical significance
Indicates that the intervention is the only possible cause if randomization is successful.
Inflation of Type I error rate
Occurs when randomization is not used, leading to regression to the mean.
Temporary factors
Elements like a particularly stressful week or measurement error that can affect initial measurements.
Independent samples
Samples that are not influenced by each other, which is necessary for valid statistical analysis.
Experimental units
The subjects or items to which treatments are assigned in an experiment.
Control group
The group in an experiment that does not receive the treatment, used for comparison.
Treatment group
The group in an experiment that receives the treatment being tested.
Simple random sampling
Individuals are assigned randomly to specific treatments.
Cluster sampling
Arbitrary groups or clusters of individuals are assigned randomly to specific treatments.
Stratified random sampling
Individuals belonging to particular categories or strata are assigned randomly to specific treatments in proportion to the size of each category.
Haphazard sampling
Selects items without a plan, attempting to avoid bias but still relying on convenience and personal judgment.
Random sampling
Uses a statistical method where every item has an equal chance of selection, making it more reliable and unbiased.
Constants
Potentially confounding variables that are maintained consistent or uniform across all replicates.
Independent Variable (IV)
A variable that is manipulated (as a 'treatment') in some way to test if it has an effect.
Dependent Variable (DV)
What is measured in response to the manipulation of the IV.
Categorical Variable
Variables whose levels are discrete categories (i.e., non-continuous).
Quantitative Variable
Variables whose levels represent numerical measurements on a continuous scale.
Ordinal Scale
Numerical measurements represent a ranked order, but the intervals between ranks may be unequal.
Interval Scale
Numerical measurements represent equal distances between intervals, but there is no true zero.
Ratio Scale
Numerical measurements represent equal distances between intervals, and zero represents 'none' of the variable being measured.
Column graph (Bar graph)
Recommended visualization for categorical IV and categorical DV.
Line graph
Recommended visualization for categorical IV and quantitative DV.
Box plot
Recommended visualization for quantitative IV and categorical DV.
Scatterplot
Recommended visualization for quantitative IV and quantitative DV.
Correlation
Neither variable is dependent on the other; IV/DV cannot be defined.
Regression
One variable is identified as the IV and one as the DV, often based on temporal precedence.
Association
Deals with an association or a non-causal relationship.
Causation
Deals with a causal link based on design.
Interpretation/Limitations of Correlation
An association is not the same as a causal link; associations are limited because they can be influenced by uncontrolled confounding variables.
Interpretation/Limitations of Regression
Requires three criteria to establish cause and effect: (1) purported cause precedes the effect, (2) cause and effect vary together, and (3) the research design eliminates alternative explanations.
Cohort Study
Good for studying the consequences of rare exposures. Can directly establish the relative risk of developing a disease.
Cohort Study Limitations
Expensive (especially prospective designs), requires a large sample size, takes a long time to complete, and is prone to attrition bias.
Cohort Study Data Collection
Starts in the past (retrospective) or present (prospective) and collects data moving forward in time. Compares the future incidence rate of developing an outcome between an exposed group and an unexposed group.
Case-Control Study
Good for studying the causes of rare outcomes. Can determine odds ratios associated with increased or decreased risk.
Case-Control Study Data Collection
Starts in the present and collects data moving backward in time. Compares the exposure history of a group with a disease/condition (case group) to a control group without the disease/condition.
Case-Control Study Limitations
Difficult to obtain a comparatively appropriate control group. Historical data may be incomplete or of limited quality. Highly susceptible to confounding variables.
Internal Validity
The degree to which a research study successfully establishes a causal relationship between the independent and dependent variables.
Factors Affecting Internal Validity
High internal validity depends on the proper application of research design principles, such as legitimate control, randomization, and the identification of confounds.
Criteria for Establishing Causality
The purported cause must precede the effect, the cause and effect must vary together, and the design must eliminate alternative explanations.
External Validity
The degree to which the study results can be generalized across different times, populations, settings, and so on.
Enhancing External Validity
Conducting experiments in natural settings (e.g., in the field vs. a lab) and by having replicability in different settings.
Relationship Between Validities
Internal and external validity are not mutually inclusive. A study might have high internal validity but be irrelevant to the real world, or it might have high relevance but results that are not trustworthy (low internal validity).
Base Rate Fallacy
The error of misinterpreting the p value (the probability of observing data assuming there is no effect) as the probability that the finding itself is a fluke or that the hypothesis is true.
Misinterpretation of p-value
People often wrongly assume a low p-value means the chance of error is similarly low (e.g., that p<0.05 implies a 95% chance the result is true).
Importance of Base Rate
To calculate the actual probability that a result is true, one must factor in the base rate (the prior probability that the hypothesis is correct).
False Positives in Research
In fields where the base rate of true associations is low (e.g., early drug trials), the base rate fallacy ensures that a high fraction of statistically significant results—sometimes up to 38% or more, depending on the conditions—are actually false positives.
Issues Magnifying Base Rate Fallacy
This error is magnified by issues like multiple comparisons.
Interpreting Research Results
Understanding the base rate is essential to avoid being misled by low p-values.
Example of Base Rate Fallacy
Even a highly sensitive test (like a mammogram) may yield a positive result where the actual chance of disease is very low (e.g., 9%), due to the low base rate of the disease in the general population being tested.