Calculating Correlation Coefficients With the TI-84
Calculating correlation coefficients requires dealing with two lists of numbers. For the sake of
convenience, I will use specific list names: L1, L2, L3, etc., the default list names in the TI-84.
The first consideration is that both lists must have the same number of entries. Otherwise the calculator
refuses to process them.
Entering numbers into the lists is done the same way as detailed in the Procedure for Finding Mean and
Standard Deviation. Specifically, the STAT editor is used. Stat Editor function. Press the STAT button
on the calculator. The ribbon menu across the top of the screen gives choices of EDIT CALC TESTS.
The initial choice is EDIT , and there is a subsidiary menu with choices 1 through 5. The initial choice in
that menu is 1. Edit, which is the desired function. Press the ENTER button, and there is a choice of
three lists showing: L1, L2, L3. Three other lists, L4, L5, and L6 do not show on the screen at this point,
but are available. The right and left arrows in the blue keys, upper right, allow the choice of any of
these 6 lists. It is necessary to remember the labels of whichever lists are to be used. The following will
assume that the data are entered in the lists L1 and L2, although any pair of lists may be used.
As before, it is a good idea to check that the lists have been entered correctly. This is done from the
home screen by entering 2nd L1 or 2nd L2 and scrolling with the direction arrows.
Since the correlation coefficient is calculated from the z-scores, it is necessary to know the mean and
standard deviation. For this, see the Procedure for Finding Mean and Standard Deviation listed on my
web site for Chapter 7. These numbers will disappear in subsequent calculations, so it is necessary to
write them down or store them in memory registers. This procedure will assume that they are written
down. The TI-83 has the ability to do repetitive calculations on entire lists. Denote the means of list L1
and L2 as ÿ1 and ÿ2 and the standard deviations as s1 and s2. Then the z-scores for list L1 can be
calculated and stored to list L3 in a single operation by entering
(L1-ÿ1)/s1 → L3
E.g., if the mean of L1 is 5.6 and the standard deviation is 1.2, then the key presses would be
( 2nd L1 - 5.6)/1.2 → 2nd L3
L3 will now contain all of the z-scores for list L1. These numbers could have been stored in L1 instead of
L3, but that would make it more difficult to go back and check numbers later. The same procedure,
using ÿ2 and s2 can be used to calculate the z-scores for L2 and store them in L4.
At this point L3 and L4 contain the z-scores for L1 and L2. Since the correlation coefficient is
∑
𝑧𝑥 ∗𝑧𝑦
𝑛−1
,
the next step is to multiply the pairs of z-scores in L3 and L4, divide by n-1 and save to L5. If there were
12 entries in each list, then the set of key presses would be
( 2nd L3 * 2nd L4 ) / 11 → 2nd L5
Note that here there are 12 terms, n-1 term is equal to 11, and each product is divided by 11.
The only remaining operation is to sum the values in L5 to get the correlation coefficient. There are
several ways to do this. One is to press 2nd LIST and use the right or left cursor arrows to highlight
MATH, then either press 5 to select SUM( ,or use the down arrow to go to SUM( and press the ENTER
button. The screen will display the prompt sum( which has to be followed by the name of the list to be
summed and a parenthesis. In this case , the buttons 2nd L5 ) would be used. When that is done the
bottom line of the screen will display
sum(L5)
Pressing ENTER tells the computer to calculate and display the sum of L5, which is the correlation
coefficient.
Another way to get the sum of L5 is to use the procedure for calculating the mean and standard
deviation of L5. One of the variables displayed on the screen will be the sum of the list, ∑x, which is the
correlation coefficient.
Practice problems :
L1 = 5.0, 6.4, 7.2, 9.7, 10.5, 11.7, 12.6, 10.9, 6.5, 8.5, 9.2, 9.5
L2 = 123, 131, 117, 132, 125, 128, 115, 135, 121, 119, 126, 128