Download How to find out whether a numerical variable is a Normal (Bell

How to find out whether a numerical variable is a Normal
(Bell-Shaped) Distribution or not
Q: Why do we care? A: If Normal then empirical rule applies! Many stat tests and
procedures assume Normality.
Method A. Summary Measures (Data Analysis / Descriptive Statistics)
- Almost Normal:
Symmetric (Skewness within + 1)
Not flat, not peaked (Kurtosis within + 1)
- Skewed:
Right Skewed (Skewness > 1)
Left Skewed (Skewness < -1)
- Peaked or Flat:
Peaked (Kurtosis > 1 )
Flat (Kurtosis < -1)
Method B. B-n-W (PHStat / Descriptive Statistics/Box-and-Whisker)
This is ideal
- Normal (must be both symmetric and not flat or peaked)
Symmetric: Two Whiskers have same length (box is in the middle) RoT: less than 2x
Median line divides the box in half RoT: less than 2x
Not flat or peaked:
Whiskers is slightly longer than box RoT: about 3 boxes fit
- Skewed:
If it not symmetric, then it’s NOT Normal.
Right Skewed (longer right whisker and wider right box)
Left Skewed (longer left whisker and wider left box)
- Flat if box is too wide (could be symmetric)
If it’s flat, it is not Normal even if it is symmetric
- Peaked if box is too narrow (could be symmetric)
If it’s peaked, it is not Normal even if it is symmetric
Method C. Normal Probability Plot (PHStat/Probability and Prob.
Distributions/Normal Probability Plot)
The Normal Probability Plot
Normal Probability Plot
(continued)
A normal probability plot for data
from a normal distribution will be
approximately linear:
X
(continued)
Left-Skewed
X 90
X 90
60
60
30
30
-2 -1 0
90
60
Right-Skewed
1
2 Z
-2 -1 0
1
2 Z
Nonlinear plots indicate a
deviation from normality
30
-2
-1
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
0
1
2
Z
Chap 6-38
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 6-39