Lecture Notes on Statistics

Introduction to Statistics

• Definition: Statistics is the science of collecting, analyzing, and interpreting data.
• Common Misconceptions: Statistics can be misrepresented, e.g., exaggerated values in media.
• Importance of Context: Data needs context to be meaningful.

Key Concepts

Conditional Probability

• Example: 4 out of 9 Alabamians with colorectal cancer will die from it.
• Importance: Contextualizes data (e.g., probability changes when conditional on a disease).

Data-Driven Decisions

• Definition: Making decisions based on data.
• Process: Measure variation, understand variation, reduce/adapt to variation.
• Example: Evaluating basketball players' performance by shots made.

Data Collection and Cleaning

• Planning: Essential to plan how data will be collected and cleaned.
• Challenges: Non-response bias, ridiculous or ambiguous responses.

Types of Data

Quantitative vs. Categorical Data

• Quantitative: Numerical data (e.g., height, weight).
  • Continuous: Can take any value (e.g., height in centimeters).
  • Discrete: Specific values (e.g., number of pets).
• Categorical: Puts things into categories (e.g., gender, type of car).
  • Nominal: No inherent order (e.g., types of desserts).
  • Ordinal: Clear order (e.g., class levels like freshman, sophomore).
  • Identifiers: Unique, non-repeating (e.g., social security numbers).

Context in Data

• Who, What, When, Where, Why, How: Essential questions to give context to data.
• Example: Survey data (e.g., who were surveyed, what questions were asked).

Population and Sample

• Population: The entire group of interest (e.g., all students at a university).
• Parameter: Specific characteristic of the population (e.g., average height).
• Sample: Subset of the population used to make inferences.
• Sample Statistics and Population Parameters: Statistics from samples are used to estimate population parameters.
• Representativeness: Ensuring the sample accurately reflects the population.

Randomness in Statistics

• Definition: Random events have uncertain outcomes, though the range of possible outcomes is known.
• Random Sampling: Used to create representative samples.
• Random Number Generation: Used in simulations to predict outcomes (e.g., loot drops in video games).
• Applications: Randomness is crucial in simulations, data collection, and more.

Challenges and Pitfalls

• Messy Data: Inconsistent or ambiguous data can complicate analysis.
• Non-Response Bias: Occurs when certain individuals do not respond to surveys.
• Ambiguous Data: Data that lacks clarity or precision (e.g., shoe sizes).

Final Notes

• Importance of Planning: Thorough planning of data collection methods is crucial.
• Email for Questions: Students are encouraged to ask questions for clarification.