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 TI-83/84 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. H1 is μd>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 TI-83/84 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 1-VarStats, 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 H1. | [STAT] [◄] [2] for T-Test
Enter 0 for μo. Skip past x̅, s, and n. Enter >μo, 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=L2-L1
1-VarStats L3
T-Test inputs: μo: 0, x̅: 4.17, s: 1.83, n: 6, μ >μo
Outputs: t = 5.5624, p = .0013
Now practice with any of the examples in your textbook.
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