Chapter 12

Study Guide - Smart Notes

Tailored notes based on your materials, expanded with key definitions, examples, and context.

Explain blocking and describe how it can help researchers control variation.
Differentiate between sampling and identifying response variables in experiments.
Define confounding variables and identify their impact on experimental results.
Describe various sampling methods and their uses.
Discuss the importance of statistical power and sources of variability.
Evaluate the quality of a survey and identify situations where a sample is useful for drawing population estimates.

Treatment Variable: The variable manipulated as a possible cause; also called the independent variable.
Response Variable: The variable measured as the effect; also called the dependent variable.
Example: In a study on exercise and weight loss, the amount of exercise is the treatment variable, and weight loss is the response variable.

Confounding variables are unknown variables that might affect the response variable.
They affect both the treatment and the response.
If we cannot rule out their presence, we cannot conclude that a treatment variable caused the change in the response variable.
Example: In a study on test preparation courses and SAT scores, student motivation could be a confounding variable if more motivated students are more likely to take the course and also score higher.

Controlled Experiments: Researchers assign subjects to treatment groups, often using random assignment. This helps ensure that differences between groups are due to the treatment.
Observational Studies: Researchers observe subjects in their natural groups without assigning treatments. These studies are more prone to confounding variables.
Example: Studying the effect of smoking on health is often observational, as researchers cannot ethically assign people to smoke.

Statistical power is the probability that a test will correctly reject the null hypothesis when a true effect exists.
It is the probability of detecting differences that really exist between groups.
Power depends on:
- Sample size
- Size of the true difference between groups
- Natural variability within the population
Formula: Power is not a single formula but is related to the significance level (), effect size, and sample size.

Natural variability in subjects
Measurement error
Researchers try to control for variability by holding variables fixed or using techniques like blocking.

Blocking is a technique where researchers group similar subjects into "blocks" and then assign treatments randomly within each block.
Reduces bias and increases statistical power by controlling for known sources of variability.
Example: In a medical study, subjects might be blocked by age group before assigning treatments.

Matched-Pairs Design: Each subject is measured twice (e.g., before and after treatment).
Crossover Design: Subjects receive multiple treatments in random order, with measurements taken after each.
Example: Measuring weight before and after a diet (matched-pairs); patients receiving two drugs in random order (crossover).

Measured by two features:
1. Bias: How far the estimator tends to be from the correct population value.
2. Precision: How variable the estimator is from sample to sample; a small standard deviation indicates high precision.

An estimator can be biased if the sample is not representative of the population.
Example: Surveying only fast food restaurant customers about eating habits introduces bias, as they may not represent the general population.

Surveys where participants choose to respond may not be representative, as those with strong opinions are more likely to participate.
Example: Internet polls often suffer from voluntary response bias.

Random sampling methods help avoid bias:
1. Systematic sampling
2. Stratified sampling
3. Cluster sampling

Individuals are sampled at regular intervals (e.g., every 10th person after a random start).
Useful when a complete list of the population is available.
Example: Selecting every 5th person from a list to participate in a survey.

The population is divided into subgroups (strata) based on a characteristic, and a random sample is taken from each stratum.
Ensures representation from all subgroups.
Example: Sampling students from each grade level in a school.

The population is divided into groups (clusters), some clusters are randomly selected, and all individuals in chosen clusters are surveyed.
Useful when the population is naturally divided into groups.
Example: Surveying all households in randomly selected city blocks.

Sampling Method	Description	Example
Simple Random Sampling	Every individual has an equal chance of selection	Randomly drawing names from a hat
Systematic Sampling	Sample every nth individual after a random start	Every 10th person on a list
Stratified Sampling	Divide population into strata, sample from each	Sampling by age group
Cluster Sampling	Divide into clusters, randomly select clusters, sample all in clusters	Surveying all students in selected classrooms

Designing experiments to test new drugs, educational methods, or consumer products.
Conducting surveys to estimate population parameters such as average income or voting preferences.

Additional info: Some explanations and examples were expanded for clarity and completeness based on standard statistics curriculum.