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The practice of quantitative research not only involves statistical calculations and formulas but also involves the understanding of statistical techniques related to real-world applications. You might not become a quantitative researcher nor use statistical methods in your profession but as a consumer, citizen, and scholar-practitioner, it will be important for you to become a critical consumer of research, which will empower you to read, interpret, and evaluate the strength of claims made in scholarly material and daily news.

For this Assignment, you will critically evaluate a scholarly article related to repeated measures ANOVA.

To prepare

Review the Article Critique Assignment Guide in the Walden Library, listed in the Week 2 Learning Resources.

Search the Walden Library for a quantitative article that applies repeated measures ANOVA.

By Day 7

The Assignment

Write a 2- to 3-page critique of the research you found in the Walden Library that includes responses to the following prompts:

Why did the authors select repeated measures ANOVA in the research?

Do you think this test was the most appropriate choice? Why or why not?

Did the authors display the results in a figure or table?

Does the results table stand alone? In other words, are you able to interpret the study from it? Why or why not?

Introduction to Analysis of Variance with Repeated Measures: Week 7
Introduction to Analysis of Variance with Repeated Measures:
Week 7
Program Transcript
DR. ANNIE PEZALLA: By now, you’re most likely comfortable with the concept of
one-way and multi-way ANOVA. Yet you’ve only been exposed to variables that
are independent. You’re now equipped to answer a lot of different questions, but
what if you want to do more? What if you wanted to test for a difference in means
across time?
Let’s turn again to the example of the statistics professor and his anxious
students. This professor may wish to examine his students anxiety about him as
their statistics professor over time at the beginning, the middle, and the end of
the course. The hope of course, is that this anxiety will go down over time.
Will the information in each wave of data collection be independent of the other
waves? No, it won’t because the same people are being assessed each time.
Could you run multiple paired sample t-tests? You could, but that would not only
be inefficient, it would introduce the possibility of error. Therefore, you need a
statistical test that will take this time-based dependency into consideration.
The repeated measures ANOVA allows you to compare three or more means on
dependent data without using multiple t-tests. It does this by conceptualizing the
independent variable as time, with each level of independent variable
representing a specific time point. So for those statistics professor who wants to
test his students anxiety toward him across the beginning, middle, and end of the
course, what would the levels be within the independent variable? They’d be the
beginning, the middle, and the end of the course.
This week after you watch Doctor Jones demonstrate this test within SPSS, you’ll
practice using the repeated measures ANOVA yourself. Then you’ll critique an
article that uses this method.
Introduction to Analysis of Variance with Repeated Measures:
Week 7
FOOTAGE:
simonkr/Creatas Video/Getty Images
AzmanL/Creatas Video/Getty Images
1
Introduction to Analysis of Variance with Repeated Measures: Week 7
David Baumber/Vetta/Getty Images
2
Analysis of Variance with Repeated Measures: Week 7
Analysis of Variance with Repeated Measures: Week 7
Program Transcript
[MUSIC PLAYING]
MATTHEW JONES: This week we’re going to be doing an ANOVA with repeated
measures. This is very similar to a one-way ANOVA except that the data are
paired. That is, the same unit has been measured over time.
In the example for this week, we’re going to be measuring students at three
different time periods and we’re measuring their anxiety about the teacher. They
were measured at the beginning of the course, the mid-point of the course, and
the end-point of the course. Essentially we want to know did their anxiety about
the teacher increase or decrease?
We could do several paired sample t-tests, but this would not only be unwieldy
but it would introduce a great deal of error. The ANOVA, like the one-way
ANOVA, uses a factor, except in this case time becomes our factor. To perform a
repeated measures ANOVA in SPSS, we click on Analyze, and then general in
You will see this box here appears to be quite different than what we’ve looked at
before. Factor one will always come up as a default, and so I just like to name it
whatever factor it is I’m looking at. So since I’m looking at anxiety about the
teacher, I’m just going to call it teacher. SPSS requests the number of levels.
So this variable, or the student I should say, has been measured three times.
Again, at the beginning, the mid-point, and the end. So there is a teacher one,
teacher two, and teacher three variables. So I’ll click three. Number of levels,
three. And I have to be sure and click Add. If I don’t click Add, this defined box
won’t highlight. It won’t let me go any further. So click Add and there we go. It’s
highlighted, It turns a nice bright blue. I can click Define.
Then you’ll see these question marks with one, two, and three. So SPSS is
asking you, what variables do you want to move over? And again, this is a within
subjects. So we’re only looking at within subjects. So the students measured at
three different time periods about teacher anxiety. So here we have teacher at
time point one, so we just need to move that over. Find our teacher at a time
point two, move that over. And find our teacher at time point three and move that
over as well.
So I’m also going to click on Contrasts. Under Contrasts, I’m going to click on
Simple. Move my reference category to the first. Click Continue. And plots, move
teacher over to the horizontal axis. Click Add. Click Continue.
1
Analysis of Variance with Repeated Measures: Week 7
And then finally under Options– whenever you’re doing a comparison of means
test, it’s always helpful to display the means. So I’m going to move that over. And
move over Descriptive Statistics. Estimates of Effect Size. And I want to compare
main effects. I’m just going to go ahead and drop down menu, click on Bonferroni
and click Continue. And OK.
And here you’ll see my output. Here I have the descriptive statistics, so teacher
at time– so there’s a mean anxiety level. It’s rather high. It decreases at time two
and it decreases at time three. Now, as far as our overall tests, we get a couple
of tests.
So the multivariate test is a different approach to the interpretation of a within
subjects or repeated measures ANOVA, so we’re going to go ahead and we’re
not going to interpret that today because that deals with more of a multivariate
analysis approach to it. We’re going to move down to the test of sphericity and
this is an assumption of one-way repeated measures ANOVA.
So much like you can think of a Levene’s test for equality of variances was an
assumption for an ANOVA or a t-test, this is similar in some respects. So if this
test is statistically significant– we can get a chi-square along with this– if this is
statistically significant, then we violated this assumption of sphericity. And these
epsilons here, they’ll be the closer they are to one, the less likely these values,
the less likely we’ve violated that assumption. The significance is well above 0.05
and so we can go ahead and assume sphericity.
OK, well why do we care about that? Well beyond the aspect that it is an
assumption, it really sort of drives what value we interpret down here. So we can
see, since we’re assuming sphericity, we can interpret this sphericity assumed. If
that test had been statistically significant, then we violated the assumption, but
that doesn’t mean all is lost.
We can still move forward and comment on some of the output as we have some
corrected values for that. And that’s, you know, the Greenhouse-Geisser is one
of those. Here we see it really doesn’t make much of a difference across the
board, but let’s go ahead and interpret this sphericity assumed.
So we see it is statistically significant. So much like the omnibus test in an
independent one-way ANOVA, we know there’s a difference in a mean. At least
one of the means is different from one of the other means. And really what we
need to do is look at our post hoc tests, our pairwise comparisons, to really see
where that difference is.
So as I’m scrolling down here, I can see these comparisons. So I can see the
difference between one and two, there’s a difference of 1.210 and it’s statistically
significant. And difference between time point one and three is 1.428 and is
statistically different. The difference between two and one is statistically different.
2
Analysis of Variance with Repeated Measures: Week 7
But the difference between three and two is not statistically significant. So we see
there’s a difference of 0.218.
And, in fact, if we scroll back up to our descriptive statistics, that’s why it’s always
handy to request those, we see that, indeed, between time point two and three, it
did go down. Anxiety about the teacher did go down, but boy, not by much. So
what we can say with some degree of confidence is that anxiety about the
teacher, it does go down.
But it’s statistically significant between time point one and two, and one and
three, but not statistically significant between the midpoint of the course and the
conclusion of course. Even though it does go down, it’s not a statistically
significant result. And again, we have some more multivariate tests that we’re not
going to comment on today. It’s a different interpretation of the output of the test.
But looking at our profile plot, again, a picture is worth a thousand words. And
you can see that that anxiety about the teacher really dramatically dropped from
day one in class to the midpoint and still continued to drop towards the end of the
course, but the slope wasn’t as steep.
[MUSIC PLAYING]
Analysis of Variance with Repeated Measures: Week 7
FOOTAGE:
simonkr/Creatas Video/Getty Images
AzmanL/Creatas Video/Getty Images
David Baumber/Vetta/Getty Images
3
Some common features and some differences between the parametric ANOVA for repeated measures
and the Friedman ANOVA for ranked data
Authors:
WILLI HAGER
Source:
Psychology Science, Vol 49, Iss 3, Pp 209-222 (2007)
Publisher Information:
Pabst Science Publishers, 2007.
Publication Year:
2007
Collection:
LCC:Psychology
LCC:Philosophy. Psychology. Religion
DOAJ:Psychology
DOAJ:Social Sciences
Subject Terms:
Parametric ANOVA for repeated measures and ANOVA for ranks after Friedman
para-metric tests and effect sizes for ranked data
Psychology
BF1-990
Philosophy. Psychology. Religion
Social Sciences
Description:
Some relationships between the parametric ANOVA of repeated measures and its nonparametric
counterpart, the ANOVA for ranks after Friedman, are discussed. The main reason for some marked
differences between both procedures arises from the fact that the mean correlation between the
experi-mental conditions, i.e. rB, can vary between the limits Ã¢â‚¬â€œ1 Ã¢â€°Â¤ rB Ã¢â€°Â¤ +1 for the parametric ANOVA and
usually is greater than zero – only if this is the case, precision is enhanced. In contrast, this correlation
always is negative for the Friedman ANOVA and only depends on the number K of experimental conditions: rR,B = Ã¢â‚¬â€œ1/(K Ã¢â‚¬â€œ 1). – In addition, it is stressed that the nonparametric rank tests can be replaced by
their parametric counterparts without risking divergent decisions about the statistical hypotheses being
tested. The necessary formulae and the respective effect sizes are presented.
Document Type:
article
File Description:
electronic resource
Language:
ENGLISH
ISSN:
1614-9947
Relation:
https://doaj.org/toc/1614-9947
Access URL:
https://doaj.org/article/eb4ec0a7f8a84506a85a4e4b98f4cdc1
Accession Number:
edsdoj.b4ec0a7f8a84506a85a4e4b98f4cdc1
Database:
Directory of Open Access Journals
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