The Paired t-Test (A.K.A. Dependent Samples t-Test, or t-Test for Correlated Groups) - PowerPoint PPT Presentation

Loading...

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



Loading


The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
About This Presentation
Title:

The Paired t-Test (A.K.A. Dependent Samples t-Test, or t-Test for Correlated Groups)

Description:

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 – PowerPoint PPT presentation

Number of Views:100
Avg rating:3.0/5.0
Slides: 23
Provided by: Jillian61
Learn more at: http://psychologyaustralia.homestead.com
Category:

less

Write a Comment
User Comments (0)
Transcript and Presenter's Notes

Title: The Paired t-Test (A.K.A. Dependent Samples t-Test, or t-Test for Correlated Groups)


1
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

2
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.

3
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)

4
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
5
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?

6
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.

7
Example 4.1 (cont.)
, df n-1
8
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
    ).

9
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.

10
Example 4.1 (cont.)
-4.78, df 4
11
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.

12
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.

13
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).

14
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)

15
Example 4.1 Using SPSS (cont.)
  • In our example, the variables are setup as
    follows in the SPSS variable view

16
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

17
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).

18
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

19
Example 4.1 Using SPSS (cont.)
  • After running the syntax, the following appears
    in the SPSS output viewer

20
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.

21
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).

22
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
About PowerShow.com