Download Test for Normal Distribution

Test for Normal Distribution
Test of Normality - 1
Graphical Test
• Histogram
– Check shape: skewness, outliers
• Normal Probability Plot
– Check shape: straight, convex,
S-shaped
Construction of a Normal
Probability Plot
• Alternative estimates of the cumulative relative
frequency of an observation
– pi = (i - 0.5)/ n
– pi = i / (n+1)
– pi = (i - 0.375) / (n+0.25)
• Estimate of the percentile | Normal
– Standardized Q(pi) = NORMSINV(pi)
– Q(pi) = NORMINV(pi, mean, stand. dev.)
Non-Normal Populations
Flat
Data
Skewed
Data
Expected | Normal
Expected | Normal
Test of Normality - 2
Test Statistics
n
• Stand. Dev.
ˆ 
 Y
t 1
t
Y

2
n
 Yt  Y 
1
ˆ
S  

n t 1  

n
• Skewness
 Yt  Y 
1
K  

n t 1  

n
• Kurtosis
4
3
The Jarque-Bera Test
If the population is normal and the data are random,
then:
2 1
2
n
JB =
S +
K-3
6
4
follows approximately c2 with the # 0f degrees of
freedom 2.
Reject H0 if JB > 6