MARE 250 Dr. Jason Turner The Normal Distribution.

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Presentation transcript:

MARE 250 Dr. Jason Turner The Normal Distribution

Define Normal

So, am I Normal? Standardized Normal Distribution –

Properties of Normality

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

Assessing Normality Large samples: Small sample:

Normal Probability Plot: Assessing Normality

Probability Plots - PP

When Using Probability Plots

Guidelines for Probability Plots

Testing for Normality

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

Probability Plots - PP

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