Stats 1/17/25

Experiment vs. Observational Study

• Experiment: Researcher controls and manipulates variables, assigns groups randomly to treatments.

  • Example: Randomly split students into groups for tutoring and compare grades.

  • Random assignment prevents confounding variables from influencing results.

  • Confounding variable: Impacts both explanatory and response variables, leading to incorrect conclusions.

  • Importance of identifying confounding variables for accurate results.

Random Assignment and Its Importance

• Random assignment allows for equal representation of confounding variables.

• Ensures that any observed differences in outcomes are due to the treatment being tested.

• Example: Clinical trials often involve a treatment group and a placebo group.

Interactive Example: Ice Cream and Crime Rates

• Observed data may show a correlation between unrelated variables due to confounding factors.

  • Example: Ice cream sales and crime rates in hot weather suggest a common confounding variable (temperature).

  • As temperature rises, both ice cream sales and crime may increase, but one does not cause the other.

Key Definitions

• Random Sampling: Using randomness to select individuals from a population for a study.

• Explanatory Variable vs. Response Variable:

  • Explanatory variable: The independent variable that influences the response.

  • Response variable: The dependent variable being measured.

  • Example: Caloric intake (explanatory) impacts weight change (response).

Observational Studies vs. Experiments

• Observational studies track outcomes without manipulating variables; they can show associations but not causation.

• In experiments, researchers manipulate the independent variable to observe effects on the dependent variable.

• Example: A study following women over years for brain tumors suggests an association with cell phone use but lacks causal evidence.

Case Studies: Rats and Phone Usage

• Rats assigned to different groups based on radio frequency exposure exemplify experimentation.

• Control groups are essential to determine the true impact of an explanatory variable (radio frequency).

Distinguishing Types of Studies

• Cross-sectional studies: Examine a population at a specific point in time.

• Cohort studies: Follow a group over a longer period.

• Case-control studies: Retrospective analysis of outcomes based on past data.

Confounding Variables and Lurking Variables

• Confounding variable: May cause erroneous conclusions about causation due to its influence on both variables.

• Lurking variable: An unaccounted variable that affects results but is not included in the analysis.

  • Example: Health and age could affect flu vaccine effectiveness but weren't controlled in observational studies.

The Placebo Effect

• Placebos can lead to symptom improvement in the treatment group due to psychological factors and expectation management.

Statistical Bias in Sampling

• Statistical bias occurs when the selected sample does not represent the population, causing over or underestimation of results.

• Example: Sampling only from NCAA basketball teams skews the height data upwards.

Practical Application of Sampling

• Simple random sampling ensures each individual in the population has an equal chance of selection, minimizing bias.

• Effective research design includes careful consideration of variables and their potential interactions.