Chapter 1- Statistical and Critical Thinking

Access to Files
- Files available on Canvas
- No need for MyMathLab access to view notes
- Students enrolled in class can print and use the materials

Statistical Bias
- Discussed in relation to data collection from reputable institutions
- Example: Dataset on brain volumes from twins collected by Harvard, Massachusetts General Hospital, Dartmouth College, UC Davis
Potential for Bias
- Options for evaluating bias:
- A: No potential bias (Articles from reputable organizations)
- B: Potential bias if organizations are not reputable
- C: Incentive to produce biased data (e.g., show identical brain volumes)
- D: Potential bias if results are statistically insignificant
- Preferred response: Option A, as the organizations involved are credible

Definitions
- Statistical Significance: Indicates if results are unlikely to occur by chance
- Practical Significance: Indicates if results have real-world relevance or importance
Example Case Study - Weight Loss Program
- Average weight loss: 43 pounds over four subjects
- Chance of achieving these results without the program: 31%
- Evaluation of statistical significance options:
- A: Program is statistically significant; results unlikely by chance (perceived chance rates mentioned)
- B: Program is statistically significant; chances high (incorrect)
- C: Program not statistically significant; results likely by chance (correct answer)
- D: Not significant; results likely occurred by chance (incorrect)
- Conclusion: Only C is correct, as a 31% chance indicates results could occur by chance

Homework Purpose
- Homework serves as practice for quizzes and tests
- Mastery through understanding is more beneficial than just completing for grades

Population vs Sample
- Population: Complete collection of all items
- Sample: Subset of the population representing the larger group
Context of Data
- Importance of understanding the meaning behind data rather than just processing numbers
- Examples include GPAs, weights, etc.

Parameters vs Statistics
- Parameters: Numbers summarizing characteristics of a population
- Statistics: Numbers summarizing characteristics of a sample
Measures of Central Tendency
- Strategies for analyzing data: mean, median, mode, range
- Key takeaway: We cannot see the entire population's data in practice

Quantitative Data: Data associated with numbers
- Examples: GPAs, weights, heights
Qualitative Data: Data associated with non-numeric labels
- Example: Color preferences
Discrete vs Continuous Data
- Discrete: Countable (e.g., number of people)
- Continuous: Measurable (e.g., weight, height)

Nominal Level
- Categories without any meaningful order
Ordinal Level
- Categories with order but no meaningful difference in value
Interval Level
- Ordered categories with meaningful differences, no true zero
Ratio Level
- Has order, meaningful differences, and a true zero point exists

Random Sampling
- Each individual in the population has an equal chance of selection
Systematic Sampling
- Chosen at determined intervals (every nth member)
Convenience Sampling
- Using the most available data, often biased
Stratified vs Cluster Sampling
- Stratified: Population divided into strata/groups, samples taken from each
- Cluster: Entire clusters are sampled, not individuals within those groups

Sampling Error
- Difference between observed and expected results
Nonsampling Error
- Errors due to collection method or bias
Confounding Variables: External factors that may influence study outcomes, muddying the conclusions drawn about cause-and-effect relationships
Note on Data Collection: Ensuring a systematic and unbiased sampling method is critical for valid conclusions and analysis.
Emphasis on frequent review of homework and continuous practice for mastery of material.