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**Data Analysis [2-15]**

**Normality Test**

You are often required to check and ensure the data follows a normal distribution prior to many statistical analysis.

This can be done by using:

- (1) Numerical Method or
- (2) Graphical Method

__Example__

*Note: there are 82 observations in this data set. Not all of them are shown in the image above.*

The TICKET data set contains 3 variables:

- Team: Raptors (GO RAPS GO)
- Game: The nth game of the season
- MPrice: Median Ticket Price

An analyst is interested in checking whether the median selling price (i.e. MPrice) follows a normal distribution.

**1. Numerical Method**

The numerical method is based on 4 normality test results.

__Example__

Proc Univariate Data=Ticket normal;

Var Mprice;

Run;

Adding the NORMAL option to Proc Univariate creates an additional table with the list of normality tests in the output:

Note: this is the 4th table in the output.

The numerical method looks at the 4 normality testings:

Since all of the p-values are greater than 0.05, the median ticket price is assumed to be normally distributed.

The numerical method looks at the 4 normality testings:

- Shapiro-Wilk
- Kolmogorov-Smirnov
- Cramer-von Mises
- Anderson-Darling

Since all of the p-values are greater than 0.05, the median ticket price is assumed to be normally distributed.

*Quick Resources to learn about:*

**2. Graphical Method**

The graphical method looks at the stem-and-leaf plot, box plot, and normality probability plots as well as the histogram.

__Example__

Proc Univariate Data=Ticket plots;

Var Mprice;

Histogram;

Run;

The PLOTS option generates 3 plots:

- Stem-and-leaf plot (or a horizontal bar chart)
- Box plot
- Normal probability plot

The HISTOGRAM option plots the histogram as well:

All of the graphs show a distribution that is fairly close to a normal distribution.

*Quick Resources to learn about:*

**Exercise**

Locate the CARS data set from the SASHelp library.

Analyze whether the MSRP follows a normal distribution using both the numerical and graphical methods.

What would be your conclusion and why?

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