Lecture Notes: Introduction to Statistics

Understanding Statistics

• Statistics often misrepresented in media.
• Example: Misleading statistics about colorectal cancer.
• Importance of context in statistics.
• Conditional probability adds complexity.

The Role of Context in Statistics

• Statistics without context are just numbers.
• Understanding world through statistical reasoning.
• Basketball example for statistical inference.

Measuring and Understanding Variation

• Measure variation between data points (e.g., basketball shots).
• Control for differences (e.g., same conditions for comparison).
• Decision-making based on data (data-driven decisions).

Importance of Data Context

• Data can be anything: numbers, characters, images.
• Different data types: numeric vs. categorical.
• Context needed to interpret data correctly (e.g., gender as a category).

Data Collection and Analysis

• Data collection is complex and requires planning.
• Need to clean and prepare data before analysis.
• Types of bias: Non-response bias and ridiculous responses.
• Importance of precise data collection.

Key Concepts in Data and Statistics

• Population: Group you want to understand.
• Parameter: Specific thing you want to know about the population.
• Sample: Subset from the population.
• Statistics: Estimates from the sample.
• Inferential Statistics: Making inferences about a population using sample data.
• Representative Samples: Accurate reflection of the population.

Data Types and Variables

• Categorical Data: Qualitative, puts into categories.
  • Ordinal: Has order (e.g., freshman, sophomore).
  • Nominal: No order (e.g., favorite color).
  • Identifiers: Unique and never repeat (e.g., order numbers).
• Quantitative Data: Numerical, can be discrete or continuous.
  • Discrete: Whole numbers (e.g., number of pets).
  • Continuous: Any value on number line (e.g., height).

Randomness in Statistics

• Randomness: Outcome is unpredictable, even if likely outcomes are known.
• Used in data collection, simulations, and gaming.
• Simulations can predict outcomes based on random samples.
• Complex simulations may not perfectly mimic reality.

Conclusion

• Simulating and understanding statistical realities often involves complex modeling.
• Questions or further clarifications can be directed via email.