Experiments

Response Variable:
- Definition: A response variable measures an outcome or result in a study.
Explanatory Variable:
- Definition: An explanatory variable is a variable believed to explain or cause changes in the response variable.
Subjects:
- Definition: The individuals studied in an experiment are referred to as subjects.
Treatment:
- Definition: A treatment is any specific experimental condition or combination of conditions applied to the subjects.
- Treatment Group: The group receiving the treatment.
- Control Group: The group that does not receive the treatment and is used as a benchmark.
Performance Metric:
- Definition: The response variable is typically a performance metric, such as sales, recovery from illness, or lifespan.
Explanatory Variable in Treatment:
- Definition: The treatment acts as the explanatory variable, measuring how it affects the response variable.

Observational Studies:
- Definition: These studies collect data without any intervention. Researchers observe, record or measure events without imposing treatments on subjects.
- Key Question: Were particular treatments deliberately assigned, or were they self-selected?
Experiments:
- Definition: In contrast, experiments involve researchers intentionally intervening and imposing treatments on subjects to assess the impact on response variables.

Lurking Variable:
- Definition: A lurking variable is one that significantly affects the relationship among the study variables but is not included as an explanatory variable in the study.
- Implication: Lurking variables complicate establishing a cause-and-effect relationship.
Confounded Variables:
- Definition: Two variables are confounded when their individual effects on a response variable cannot be distinguished from one another.
- Importance: Addressing confounding variables is crucial for isolating the effects of multiple explanatory variables on a response variable.

Control:
- Goal: Control the effects of lurking variables on the response by comparing two or more treatments.
Randomization:
- Definition: Employ an impersonal method of chance to assign subjects to different treatments.
Sufficient Sample Size:
- Requirement: Use a large enough sample size in each group to minimize chance variation and improve reliability of results.

Randomized Comparative Experiment:
- Definition: A method where the results of two or more treatments are compared under randomized conditions.
- Core Logic: Assumes that subjects are treated equally, except for the treatments being compared.
Bias:
- Explanation: Any unequal treatment can introduce bias into the experiment.
Observed Effect:
- Definition: An effect observed that has a low probability of occurring due to chance is termed statistically significant.
- Interpretation: Statistically significant results reflect a consistent effect likely to be reproduced in future studies, offering a reliable basis for decision-making.

Observation: In the advertising experiment case, it is claimed that the difference of 200 units in sales attributed to the new advertisement is valid based on the experimental design.

Uniform Starting Conditions:
- Suggestion: To enhance uniformity, add an initial step to ensure both groups start under similar conditions.
- Example: The effect attributed to the new ad is actually influenced by prior exposure to the old ad, thereby inflating the perceived difference in sales.
- Quantitative Adjustment: If the baseline difference before the new ad was already 100 units, this should be subtracted from the difference claimed after treatment.

Field Experiment:
- Definition: An experiment conducted in a real-life setting.
- Example: Selling the same product with different advertising methods or promotions to real customers.
Natural Experiment:
- Definition: An observational study arising from an event or change in a natural setting.
- Examples: Measuring sales impact before and after a tax change or a presidential election.
- Note: This type of experiment is observational because the event occurs beyond the researcher's control, but it allows for assessing causal effects of significant changes.

Placebo Effect:
- Definition: A placebo is a treatment with no active ingredients, and the placebo effect is when subjects respond positively based on the belief in the treatment's efficacy.
- Issue: The placebo effect can confound the actual treatment effect, thus complicating the findings.
Double-Blind Design:
- Definition: In a double-blind experiment, neither subjects nor researchers know which treatment is given, minimizing bias in response assessment.

Issue with Randomization:
- Explanation: Randomly assigning subjects may lead to flaws; hence a matched pairs design offers a solution.
- Definition: Matches subjects closely to control for potential confounding variables.
Treatment Assignment:
- Method: One treatment is assigned to each subject in the matched pair randomly, ensuring precision in results.
- Purpose: This design isolates the treatment effect by comparing outcomes within matched pairs.

Example:
- Comparisons: Difference in response variables can be quantified across matched subjects, e.g., age 42 female vs age 40 female and similarly for males.

Purpose of Blocks:
- Definition: Blocking involves organizing subjects into groups based on shared characteristics that may influence treatment results.
- Control of Variability: This method reduces variation effects by ensuring that certain demographic factors are comparable across treatment groups.
Random Assignment within Blocks:
- Process: Randomly assign treatments within each block to effectively isolate the treatment effect

Randomized vs Block Design:
- Issue with Random Design: Treating all subjects as a single pool ignores significant variables.
- Improved Block Design: Recognizes gender differences, treating male and female subjects separately in a 2 × 3 block design. This ensures that interactions between different treatment factors are systematically studied through the combination of treatments.