送交者: lala 于 February 14, 2002 21:27:37:
Descriptive Methods for Assessing Normality
Question Given a random variable x. How can we know that the obtained data set of x is from an approximately normal distribution?
Several descriptive methods can be used to check for normality. We have the following four methods:
1. Histogram or stem-and-leaf method.
If the data are approximately normal, the shape of the histogram or stem-and-leaf display will
be similar to the normal curve.
2. The Empirical Method.
Compute the intervals m ± s, m ± 2s, and m ± 3s, and determine the percentage of mesurements falling in each where m and s are the sample mean and sample standard deviation, respectively,
of the data set. If the data are approximately normal, the percentages will be approximately
equal to 68%, 95%, and 100%, respectively.
3. The IQR Method.
Find IQR (Interquartitle Range) and s (sample standard deviation) for the data set. If the
data are approximately normal, then
IQR/s = 1.34 roughly.
4. The Normal Probability Plot Method.
Construct a normal probability plot for the data set. If the data are approximately normal,
the points will fall (approximately) on a straight line. Usually the normal probability plot
is constructed for normalized data set z = (x - m)/s.