Normality Check on the TI-83/84 or TI-89
How Can You Tell Whether a Distribution is Normal?

Summary:  By plotting data on your TI calculator, you can easily see how close they are to a normal distribution. The special quantile plot or normal probability plot asks what the distribution would look like if it were normal, and plots that against the actual distribution. The closer the points seem to be to a straight line, the more nearly normal the original distribution.

See also:  In addition to the test shown here, you can test the skewness and kurtosis of your data. The closer the skewness is to 0 and the kurtosis to 3, the closer you are to a normal distribution.

The Example

Consider these vehicle weights (in pounds):

2500, 3250, 4000, 3500, 2900, 4500, 3800, 3000, 5000, 2200

How would you construct a plot to decide whether these vehicle weights seem to be normally distributed? In principle you could compute the mean and standard deviation of the sample, then compute the z score of each data point, then compute the fraction of a normal distribution that falls below that z score. You would then plot points, where the x value of each point was the actual measurement and the y value was that “quantile”. If the plot is approximately a straight line, you conclude that the distribution is approximately normal.

Fortunately, you don’t have to go through all that pain. The TI-83/84 or TI-89 can do all the work for you.

TI-83 or TI-84 Procedure

Turn off other plots.	[Y=] Move cursor to each highlighted = sign or Plot number and press [ENTER] to deactivate.
Enter the numbers.	[STAT] [1] selects the list-edit screen.   Move cursor onto the label L1 at top of first column, then [CLEAR] [ENTER] erases the list. Enter the above values; there is no need to sort them first.
Set up the quantile plot.	[2nd Y= makes STAT PLOT] [1] [ENTER] turns Plot 1 on.   [▼] [► 5 times] [ENTER] selects the normal probability plot. (This is the last of the six plot types.)   [▼] [2nd 1 makes L1] says data are in list 1.   [▼] [ENTER] says data will plot on the x axis and quantiles will plot on the other axis (y).
Plot the points.	[ZOOM] [9] automatically adjusts the window frame to fit the data, but does not adjust the grid spacing.
(optional) Adjust grid.	[WINDOW] Set Xscl=200 (choose number based on your data) Set Yscl=1 (always for a quantile plot) [GRAPH] to redisplay it.

As you can see, the points lie approximately on a straight line. From this you conclude that the distribution is approximately normal.

It is not always so obvious whether the points lie on a straight line. Later in this note, a TI-83/84 program is given that helps you determine that and also does all the graphing for you.

TI-89 Procedure

For TI-89 users, the procedure is similar:

• Enter the numbers in a list.
• Press [F2] [3] [F2] [4] to turn off all other plots.
• Press [F2] [2] and the “Norm Prob Plot” dialog box appears. The preselected plot number is the first one that isn’t already defined, but you can change it. Enter your list name in the first box, make sure that “Data Axis” is set to x, and press [ENTER].
• Press [F2] [1] [F5] to display the plot. The result should be similar to the illustration above.
• (If you wish, press green [WINDOW] and adjust the grid.)

TI-83/84 Program NORMCHEK

I’ve written a program that automates the process of making the normal probability plot. Also, because it can be hard to look at a plot and decide whether the points lie close to a straight line, the program computes how close to a line they do lie.

Getting the Program

There are three methods to get the program into your calculator:

• If you have the TI-Connect or TI-Graph Link software and a cable, download NORMCHEK.ZIP (5 KB), unzip it, and transfer file NORMCHEK.8xp to your calculator. (If nothing happens when you double-click the NORMCHEK.ZIP file, you need a ZIP program; I recommend WinZip.)
• If a classmate already has the program on her calculator, you can transfer it to yours by using the short cable with headphone-style plugs that comes with all TI calculators. On your calculator, press [2nd x,T,θ,n makes LINK] [►] [ENTER], and then on hers press [2nd x,T,θ,n makes LINK] [3], select the program, then press [►] [ENTER]. (It’s okay if you don’t have the same exact model, as long as each one is a TI-83 or TI-84.)
• If you don’t have the software and cable, and you can’t get the program from a classmate, you can key it in. For the complete source code of the program, download the NORMCHEK.ZIP file as above, and then double-click on NORMCHEK_SourceCode.htm within the ZIP file.

Using the Program

Put the data in any statistics list, then press [PROG], scroll down to NORMCHEK, and press [ENTER]. Caution: The program uses LD and LF for temporary calculations, so you’ll lose any data you have in them. Regular lists L1–L6 are not affected.

The program will make the plot and display the sample size n and correlation coefficient r, as shown at right. r is a measure of how close the points lie to a straight line, with 1 being perfectly linear and 0 being completely non-linear. A good rule of thumb is that r≥0.8 usually means the plot is linear and the original points are normally distributed.

For our example, the program computed a correlation coefficient of 0.9936. If it weren’t already obvious from the plot, this would tell us that there is a linear association between the points and the z scores, and therefore the original data are approximately normal.