## Just for you: FREE 60-day trial to the world’s largest digital library.

The SlideShare family just got bigger. Enjoy access to millions of ebooks, audiobooks, magazines, and more from Scribd.

Cancel anytime.Free with a 14 day trial from Scribd

- 1. Statistics for Non-Statisticians Gerald Belton
- 2. Statistics: A science of collection, presentation, analysis, and interpretation of numerical data.
- 3. The science of statistics is based on probability.
- 4. Discrete distributions describe data that can only take specific values.
- 5. A coin toss is an example of a Bernoulli distribution. 0 0.1 0.2 0.3 0.4 0.5 0.6 Heads Tails Probability Bernoulli Distribution
- 6. A Binomial Distribution results from multiple coin tosses. 0.001 0.0098 0.0439 0.1172 0.2051 0.2461 0.2051 0.1172 0.0439 0.0098 0.001 0 0.05 0.1 0.15 0.2 0.25 0 1 2 3 4 5 6 7 8 9 10 Probability Number of heads Tossing a coin 10 times
- 7. Rolling one die can be described with a Uniform distribution. 0.167 0.167 0.167 0.167 0.167 0.167 0.000 0.050 0.100 0.150 0.200 0.250 1 2 3 4 5 6 Probability Number Rolled Rolling one die 0.028 0.056 0.083 0.111 0.139 0.167 0.139 0.111 0.083 0.056 0.028 0.000 0.050 0.100 0.150 0.200 0.250 2 3 4 5 6 7 8 9 10 11 12 Probability Number Rolled Rolling two dice
- 8. Continuous distributions describe data that can take infinitely many values.
- 9. Rainfall amounts follow an exponential distribution.
- 10. The Normal Distribution is a very special continuous distribution. 1 2𝜋𝜎2 𝑒 − (𝑥−𝜇)2 2𝜎2
- 11. Lots of real-world measures are “sort of” normally distributed.
- 12. Here’s an idealized normal distribution.
- 13. Here’s an idealized normal distribution.
- 14. 68% Here’s an idealized normal distribution. σ
- 15. Here’s an idealized normal distribution. 95% 99.7%
- 16. Central Limit Theorem makes other distributions “act normal.”
- 17. Descriptive statistics tell us about the world.
- 18. Visualizations quickly convey information.
- 19. Census Map of NC
- 20. Florence Nightingale
- 21. Florence Nightingale
- 22. Minard’s Map
- 23. Numerical descriptions provide more detail.
- 24. Location: Mean, Median, Mode
- 25. Spread: Variance, Std Dev
- 26. Five number summary > summary(GaltonFathers$father) Min. 1st Qu. Median Mean 3rd Qu. Max. 62.00 68.00 69.50 69.32 71.00 78.50 >
- 27. We have tools for looking at the relationship between variables.
- 28. Correlation
- 29. Not Causation!
- 30. Spurious Correlation Example
- 31. Statistical Inference uses properties of a sample to explain a population. Population Sample StatisticsParameters Sampling Technique Inference
- 32. Sampling is extremely important.
- 33. Online Survey Example
- 34. Simple Random Sample vs. Stratified Random Sample
- 35. Sample Size vs Precision
- 36. We use data to build models of reality.
- 37. Confidence Intervals, Hypothesis Testing, p- value • Null Hypothesis: What we are hoping to disprove. • Alternative Hypothesis: What we hope to prove. • P-value: The probability of observing results at least as extreme as these, if the null hypothesis is true.
- 38. When we get it wrong α β
- 39. Another way to remember it
- 40. Significance is important, but significant results might not be.
- 41. Significant <> Important
- 42. P-hacking: false significance Goodheart’s Law: when a measure become a target, it is no longer a measure
- 43. Measuring weirdness
- 44. Measuring Weirdness
- 45. Measuring Weirdness in two dimensions
- 46. Probability Descriptive Statistics Inference Questions?
- 47. Contact me: email: gerald.belton@gmail.com website: http://www.geraldbelton.com LinkedIn: https://www.linkedin.com/in/beltongerald/