### What is Normal Probability Plot

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.

### Sample Plot The points on this plot form a nearly linear pattern, which indicates that the normal distribution is a good model for this data set.

### How to form Normal Probability Plot

The normal probability plot is formed by:

• Vertical axis: ordered response values;
• Horizontal axis: normal order statistic medians;

The observations are plotted as a function of the corresponding normal order statistic medians which are defined as:

``Ni = G(Ui)``

where Ui are the uniform order statistic medians (defined below) and G is the percent point function of normal distribution.

#### Percent Point Function

The percent point function is the inverse of the cumulative distribution function (probability that x is less than or equal to some value). That is, given a probability, we want the corresponding x of the cumulative distribution function.

#### Uniform Order Statistic Medians

The uniform order statistic medians can be approximated by:

``````Ui = 1 - Un    for i = 1
Ui = (i - 0.3175)/(n + 0.365)    for i = 2, 3, ..., n-1
Ui = 0.5(1/n)    for i = n``````

In addition, a straight line can be fit to the points and added as a reference line. The further the points vary from this line, the greater the indicatioin of departures from normality.

### What Normal Probability Plot can answer?

The normal probability plot is used to answer the following questions:

1. Are the data normally distributed?
2. What is the nature of the departure from normality (data skewed, shorter than expected tails, longer than expected tails)?

• N/A