Introduction to Statistics Lecture

Presenter

• Justin Zeltzer from zstatistics.com

Overview

• Challenge: Explain statistics in under half an hour
• Aimed at developing intuition around statistics
• Examples themed around the NBA

Types of Data

Categorical Data

• Nominal Categorical Data: No order to categories (e.g., sports teams)
• Ordinal Categorical Data: Ordered categories (e.g., player positions in basketball: Guard, Forward, Center)

Numerical Data

• Discrete Numerical Data: Countable values (e.g., number of free throws missed)
• Continuous Numerical Data: Any value in a range (e.g., player's height)

Proportions

• Percentages as numerical summaries of nominal data
• Example: Steph Curry's three-point percentage

Distributions

• Probability Density Function: Describes data distribution or probability of selecting a random sample
• Normal Distribution (Bell Curve): Bulk of data is in the middle
• Uniform Distribution: Equal probability across outcomes
• Bimodal Distribution: Two peaks in data
• Skewed Distribution: Tail direction indicates skewness (e.g., left skew)

Sampling Distributions

• Distribution of sample averages
• Larger samples reduce variance of the average

Estimation

• Sample Statistic: An estimate of an unknown parameter (e.g., Steph Curry’s 3-point percentage is an estimate for his true skill level)
• Confidence Intervals: Provide range of where the true parameter may lie

Parameters in Statistics

• Mu (μ): Mean of a numerical variable
• Sigma (σ): Standard deviation
• Pi (π): Proportion of a categorical variable
• Rho (ρ): Correlation between variables
• Beta (β): Gradient in regression

Hypothesis Testing

• Null Hypothesis (H0): Default assumption (e.g., player’s performance is random)
• Alternate Hypothesis (H1): Assumes an effect or difference exists
• Rejection Region: Area beyond which the null hypothesis is rejected
• Level of Significance: Commonly 5%

P-Values

• Measure how extreme the sample is compared to the null hypothesis
• Small p-values suggest rejecting the null hypothesis
• P-Hacking: Testing multiple hypotheses to find significant results by chance

Conclusion

• Introduction to key statistical concepts using basketball examples
• Emphasized intuition-building for understanding statistics

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Extra Section: P-Hacking

• P-Hacking: Misuse of p-values by testing multiple hypotheses and only reporting significant results
• Problems with P-Hacking: Increased likelihood of false positives in research

Additional Resources

• More detailed videos and discussions available on zstatistics.com