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PPT – The Paired t-Test (A.K.A. Dependent Samples t-Test, or t-Test for Correlated Groups) PowerPoint presentation | free to download - id: 423d80-YmRmO

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The Paired t-Test(A.K.A. Dependent Samples

t-Test, or t-Test for Correlated Groups)

- Advanced Research Methods in Psychology
- - lecture
- Matthew Rockloff

When to use the paired t-test

- In many research designs, it is helpful to

measure the same people more than once. - A common example is testing for performance

improvements (or decrements) over time. - However, in any circumstance where multiple

measurements are made on the same person (or

experimental unit), it may be useful to observe

if there are mean differences between these

measurements. - The paired t-test will show whether the

differences observed in the 2 measures will be

found reliably in repeated samples.

Example 4.1

- In this example, we will look at the throwing

distance for junior varsity javelin toss (in

meters). - Five players are selected at random from the

entire league. - We are interested in the following research

question - Do players improve on their distance between the

pre and post season? - The average throwing distance, in both pre and

post season, is recorded in columns 1 and 2

(see next slide) for each of 5 people (P1-P5)

Example 4.1 (cont.)

Column 1 Column 2 Column 3

Column 4

X1 Pre-season X2 Post-season

P1 1 2 1 4

P2 2 4.5 0 0.25

P3 2 3 0 1

P4 2 4.5 0 0.25

P5 3 6 1 4

2 4

0.4 1.9

Example 4.1 (cont.)

- Unlike the independent samples t-test, on each

row the numbers in columns 2 and 3 come from the

same people. - Person 1, for example, threw an average of 1

meter pre-season, but improved to an average of 2

meters in the post-season (after all competition

was completed). - It appears that this player may have improved

through practice. - How can we find if the league has improved

overall from the pre to the post season?

Example 4.1 (cont.)

- The paired t-test will allow us to see if the

improvement that we see in this sample is

reliable. - If we selected another 5 players at random from

the league, would we still see an improvement? - Without having to go through the trouble and

expense of repeated sampling (called

replication), we can estimate whether the

difference in the 2 means is so large in

magnitude that we would likely find the same

result if we chose another 5 persons.

Example 4.1 (cont.)

, df n-1

Example 4.1 (cont.)

- This paired t needs a couple more values that

we have not yet computed. - First, we need to find the Standard Deviation of

X1 and X2, called Sx1 and Sx2. - These are simply the square-root of the variances

( and

).

Example 4.1 (cont.)

- Second, we need to find the correlation between

the pre and post-season distances ( ), or

likewise columns 2 and 3. - Another section will illustrate how to compute a

correlation. - This computation is somewhat long, so well avoid

it for now. - Ill just tell you the correlation is

rx1x20.9177. - Any scientific or statistical calculator can get

you this answer.

Example 4.1 (cont.)

-4.78, df 4

Example 4.1 (cont.)

- Finally, this computed t statistic must be

compared with the critical value of the

t-distribution. - The critical value of the t is the highest

magnitude we should expect to find if there is

really no difference between the population means

of X1 and X2, or in other words, no difference

between performance in the pre and post season in

the league. - Since we expect there should be improvement in

throwing distance, this is a 1-tailed test.

Example 4.1 (cont.)

- The C.V. t(4), a.05 2.132, therefore we reject

the null hypothesis because the absolute value of

our t at 4.78 is greater than the critical

value. - This is a 1-tailed t-test, so we must verify this

conclusion by noting that the mean of the post

season at 4 meters, is greater than the mean of

the pre-season throw average of 2 meters.

Example 4.1 (cont.)

- Our research conclusion states the facts in

simple terms - Throwing distances increased significantly from

the pre-season (M 2) to the post-season (M

4), t(4) 4.78, p lt .05 (one-tailed).

Example 4.1 Using SPSS

- First, we must setup the variables in SPSS.
- Although not strictly necessary, it is good

practice to give a unique code to each

participant (personid). - Unlike the independent samples t-test, the paired

t-test has separate entries for 2 dependent

variables, rather than an independent and

dependent - DependentVariable1 preseas (for Pre-season

scores) - DependentVariable2 postseas (for Post-season

scores)

Example 4.1 Using SPSS (cont.)

- In our example, the variables are setup as

follows in the SPSS variable view

Example 4.1 Using SPSS (cont.)

- It is no longer necessary to provide codes (or

values) for the independent variable, simply

because one does not exist! We can proceed to

typing in the data in the SPSS data view

Example 4.1 Using SPSS (cont.)

- Notice, this is where the personid variables

has helped. - If we had incorrectly tried to analyze this

problem as an independent samples t-test, then we

would have coded for 10 people under personid. - Of course, since we have only 5 people in this

example, this would have been incorrect. - The personid variable thus allows a simple check

for whether we have typed-in the data correctly. - The number of rows in SPSS should always equal

the number of subjects (or likewise,

experimental units).

Example 4.1 Using SPSS (cont.)

- Next, we need the SPSS syntax to run a paired

t-test. The code is as follows - t-test pairs DependentVariable1

DependentVariable2. - In our example, the following code is written

Example 4.1 Using SPSS (cont.)

- After running the syntax, the following appears

in the SPSS output viewer

Example 4.1 Using SPSS (cont.)

- You should focus your attention first of the mean

values for the pre and the post season

performance. - As before, the means (Pre-season2 and

Post-season4) give us our conclusion. - Namely, we conclude that performance increased

from the pre to the post season. - The statistics tell us that our conclusion is

true not only for this sample of 5 persons, but

also for other samples of 5 persons in the league.

Example 4.1 Conclusion

- Our test is 1-tailed, so we must divide the

2-tailed probability provided by SPSS in half

(p.009/2 .0045). - When expressed to 2 significant digits, this

value will round to .00 and as a result the

lowest value that can be represented in APA style

is plt.01. - In short, we can now write our conclusion as

follows - Throwing distances increased significantly from

the pre-season (M 2) to the post-season (M

4), t(4) 4.78, p lt .01 (one-tailed).

The Paired t-Test(A.K.A. Dependent Samples

t-Test, or t-Test for Correlated Groups)

Thus concludes

- Advanced Research Methods in Psychology
- - Week 3 lecture
- Matthew Rockloff