## Normal Probability Plot

### 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:

`N`_{i} = G(U_{i})

where U_{i} 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:

`U`_{i} = 1 - U_{n} for i = 1
U_{i} = (i - 0.3175)/(n + 0.365) for i = 2, 3, ..., n-1
U_{i} = 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:

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

### Examples

### References & Resources

- N/A

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