Introduction to Statistics with Justin Zeltzer

Overview

• Aim to explain statistics intuitively in under 30 minutes.
• Ideal for beginners or those curious about statistics.
• Examples themed around NBA data.

Types of Data

• Categorical Data: Divided into
  • Nominal: No order (e.g., NBA teams)
  • Ordinal: Has order (e.g., player positions)
• Numerical Data: Divided into
  • Discrete: Distinct values (e.g., missed free throws)
  • Continuous: Infinite possibilities (e.g., height)

Proportions

• Percentages and proportions are similar but expressed differently.
• Example: Steph Curry's three-point percentage.
  • Built from nominal data (made/missed shots) to a numerical summary.

Distributions

• Normal Distribution: Major distribution pattern in statistics.
  • Example: Heights of NBA players.
  • Symmetrical bell curve, with most data around the mean.
• Other Distributions:
  • Uniform Distribution: Equal probability across values.
  • Bimodal Distribution: Two peaks.
  • Skewed Distribution: Asymmetry in data distribution.

Sampling Distributions

• Looking at averages from random samples rather than individual data points.
• Larger sample sizes reduce the variance and make distributions "skinnier."

Sampling and Estimation

• Sample Statistic: An estimate of a population parameter (e.g., Steph Curry’s shooting percentage is a sample estimate of his true ability).
• Confidence Intervals: A range where the true parameter value lies with a certain probability (e.g., 95%).
• Larger samples produce more reliable estimates.

Parameters and Sample Statistics

• Parameters (Greek symbols): True values, unknowable
  • Mu (μ): Mean
  • Sigma (σ): Standard deviation
  • Pi (π): Proportion
  • Rho (ρ): Correlation
  • Beta (β): Gradient
• Sample Statistics (Roman symbols): Estimates derived from data
  • X-bar (x̄): Sample mean
  • S: Sample standard deviation
  • P: Sample proportion
  • R: Sample correlation

Hypothesis Testing

• Null Hypothesis (H₀): Initial assumption (no effect/change).
• Alternate Hypothesis (H₁): What you seek evidence for.
• Use statistical tests to determine if sample data is extreme enough to reject H₀.
• Significance Level: Often set at 5%, the threshold for rejecting H₀.
• Never "prove" anything; only infer based on the evidence.

P-Values

• Measure how extreme the sample data is under the null hypothesis.
• A small p-value (< 0.05) suggests rejecting H₀.
• Larger p-values indicate insufficient evidence to reject H₀.

Issues in Statistical Research

• P-hacking: Manipulating data/tests to find significant results.
• Testing multiple hypotheses increases chances of finding false positives.

Conclusion

• Understanding basic statistics concepts like data types, distributions, sampling, and hypothesis testing is crucial for interpreting statistical results and conducting research.
• Further resources and more detailed explanations available at zstatistics.com.