NSCORES of C Put Into C

NSCORES of C put into C

Calculates and stores normal scores. This command is used mainly to produce normal probability plots and perform various tests.

Here is an example of normal scores:

NSCORES C1 C2

PRINT C1-C2

C1 C2

1.1 0.0

0.1 -----> -1.18

2.3 1.18

1.8 0.50

0.9 -0.50

Loosely speaking, -1.18 is the smallest value you would expect to get if you took a sample of size 5 from a standard normal (i.e., the expected value of the first order statistic), and -0.50 is the second smallest value you would expect to get (i.e., the expected value of the second order statistic), and so on.

You can do a simple normal probability plot by entering:

NSCORES C1 C2

PLOT C2*C1

Computational Details

Minitab does not calculate the expected values of the order statistics exactly, but uses percentage points as an approximation. Thus, if there are n data values, Minitab puts f-1[(i - 3/8)/(n + 1/4)] next to the ith smallest data value, where f(x) is the distribution function of the standard normal. The following approximation is used:

If several observations are equal, they are all given the same normal score. This is calculated using the average of their ranks.

The command %NORMPLOT provides additional information. The output from %NORMPLOT includes a normal probability plot, relevant statistics about the data, and test statistics useful for testing a hypothesis of normality.

The normal probability plot is a graphical technique for assessing whether or not a data set is approximately normally distributed.

The data are plotted against a theoretical normal distribution in such a way that the points should form an approximate straight line. Departures from this straight line indicate departures from normality. (Egr. Stat. Handbook)

Sample Plot

NScr MTB 1