1. MARE 250 Dr. Jason Turner The Normal Distribution

2. Define Normal

3. So, am I Normal? Standardized Normal Distribution –

4. Properties of Normality

5. 1.68.26% of all possible observation lie w/in 1 std. dev. of the mean μ – σ and μ + σ 2. 95.44% of all possible observation lie w/in 2 std. dev. of the mean μ – 2σ and μ + 2σ 3. 99.74% of all possible observation lie w/in 3 std. dev. of the mean μ – 3σ and μ + 3σ

6. Assessing Normality Large samples: Small sample:

7. Normal Probability Plot: Assessing Normality

8. Probability Plots - PP

9. When Using Probability Plots

10. Guidelines for Probability Plots

11. Testing for Normality

12. Normality Tests Anderson-Darling (α=0.10) Ryan-Joiner (Shapiro-Wilk) (α=0.10) Kolmogorov-Smirnov (α=0.15) More powerful

13. Probability Plots - PP

14. This is not a Test… Hypothesis testing – Hypothesis – Hypothesis Testing 101