List Operations for Paired t Test on TI83/84
Copyright © 2003–2023 by Stan Brown, BrownMath.com
Copyright © 2003–2023 by Stan Brown, BrownMath.com
Summary: In a paired t test, you find the difference between data pairs. That can be tedious, and it’s easy to drop a minus sign. This page shows you how to use TI83/84 list operations to find the differences.
Person  Before  After 

1  78  83 
2  64  66 
3  70  77 
4  71  74 
5  70  75 
6  68  71 
Consider the data at left, which come from the example on Dabes & Janik [full citation at https://BrownMath.com/swt/sources.htm#so_Dabes1999], page 264. Heart rate is recorded for six people before and half an hour after drinking two cups of coffee. H_{1} is μ_{d}>0, and α=.01.
To perform the paired t test, you define the difference
d = After − Before
and then compute the differences. For this particular data set, all the differences are positive. But usually you will have a few negatives among the positives. It’s easy to overlook a minus sign when taking differences for many pairs of numbers, but of course that makes your t test completely bogus. Your TI83/84 can help.
Store the “Before” numbers in L1 and the “After” numbers in L2.  [STAT ] [1 ]; cursor to L1 column heading, press
[CLEAR ] [ENTER ], and enter the “Before” numbers.
Cursor to L2 column heading, press
[CLEAR ] [ENTER ], and enter the “After” numbers.

You want to get the column of differences, After−Before. That’s the same as L2−L1, which is the formula for L3.  Cursor to L3 column heading. Enter the formula,
[2nd 2 makes L2 ] [− ] [2nd 1 makes L1 ] [ENTER ]. 
Notice that any excess numbers in L3, beyond the length of L1 and L2, are automatically removed. (The formula might be L1−L2 or L2−L1, depending on how you defined your d.)
Now you can proceed with the t test, using the data in L3.
Find sample mean and standard deviation.  [STAT ] [► ] [1 ] for 1VarStats , then
[2nd 3 makes L3 ]. 
Since the sample statistics are automatically pasted to the t test screen, you don’t need to copy them. Just enter the μ and the “>” from your H_{1}.  [STAT ] [◄ ] [2 ] for TTest
Enter 0 for μ_{o}. Skip past x̅, s, and n. Enter >μ_{o}, then select CALCULATE or DRAW . 
How would you show your work for this problem? Here’s a sample:
“before” in L1, “after” in L2, L3=L2L1
1VarStats L3
TTest inputs: μ_{o}: 0, x̅: 4.17, s: 1.83, n: 6, μ >μ_{o}
Outputs: t = 5.5624, p = .0013
Now practice with any of the examples in your textbook.
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