Issues In Research Propoals

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Tactics for Multiple Measures

• Treat them as independent variables.
• Hold them constant.
• Use simultaneous repeated measures, for
  example, percent recalled and percent recognized.
• Statistically control for them via ANCOVA
  (Analysis of Covariance).

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Analysis of Covariance

• An ANOVA design with a second variable called a
  covariate. The second variable is probably
  uncontrolled and occurs in different amounts
  across groups.
• Examples SAT scores, self-confidence ratings,
  pre-tests in a pre-test post-test design.

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• For ANCOVA, we find the correlation between the
  covariate and the dependent variable.
• We use the correlation to adjust the original
  scores so that the confounded difference between
  groups is eliminated.

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The CIRP (Cooperative Institutional Research
Program) first-year survey is given to incoming
Grinnell College students during New Student
Days. Among the many questions are Self-report
of SAT or ACT scores. Self-identification of
sex. Self-ratings on 20 items comparing the
student to the average person your age.
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Rate yourself on each of the following traits as
compared with the average person your age. We
want the most accurate estimate of how you see
yourself. Mathematical Ability Highest 10
5 Above average 4 Average 3 Below average
2 Lowest 10 1
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In 1999, 118 men and 137 women provided
self-ratings of math ability. Note that the
rating is a self-efficacy rating, not an
objective analysis. The means and standard
deviations for the response were Gender Mean S
D Men 3.89 .91 Women 3.64 .89
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Notice that the SD is about .90. The difference
between men and women is that the men rate
themselves about .27 SDs higher than the
women. A between subjects ANOVA yields an F test
of 4.79, which is significant at the .05 level (
p .03). What accounts for the difference?
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Suppose that both men and women rate themselves
realistically. That is, they think about their
past accomplishments in math and use those
memories for their ratings. Maybe the difference
in ratings is based on some other
difference. Tactic Look at another measure of
math ability. If the men and women differ on
that measure, statistically correct for the
difference and look again at the ability rating.
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The CIRP asks the students to report test scores
such as SAT and ACT. The SAT is more frequently
reported. In 1999, the following was reported
for the SAT Math Gender Mean SD N Men 678 69
92 Women 653 66 106 Note the loss of
subjects. The following analysis will be on only
these people.
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What if we could statistically equate the men and
women on SAT? Would the difference in self-rated
math ability change? Gender Mean SD N Men 678
69 92 Women 653 66 106
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Recall from Statistics class that two variables
may be correlated, and that the correlation
produces a straight line called the regression
line. In this case, treat SAT as the X variable
and Math Ability as the Y variable. The
correlation between the variables .62 (p lt
.01). The regression equation is Predicted Y
-1.544 .008 (X)
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Predicted Y -1.544 .008 (X) The equation is
a sort of data transformation. We can enter a
value of the SAT and get the predicted Math
ability score. These new scores replace the
original data.
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The Analysis of Covariance first transforms the
data based on the relation with the covariate,
then performs the ANOVA on the new data. This
approach gives us an idea of what differences are
present if the groups had been equal on the
covariate. The new ANOVA results Covariate
(Math SAT) F 118, p lt .05 Gender F lt 1,
ns Result No difference is self-rated math
ability once we correct for SAT scores.
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Objection! The correlation between SAT math and
math ability ratings must be similar for each
group. Show that the correlation is the same for
men as it is for women. For men r .70 For
women r .54 These are not significantly
different at p .05, two-tailed.
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Counter-example Lopatto, et al. (1998) compared
operant stereotypy across two age groups, college
students and older adults. Stereotypy was
measured as repetition of a response on a
computer keyboard task. Subjects were asked about
computer anxiety. Students reported little (Mean
2.6 out of 7) but older adults had some anxiety
(Mean 5 out of 7). Anxiety was probably
related to stereotypy because anxious people tend
to be more stereotypical. However, the underlying
correlation between stereotypy and anxiety was
.41 for older people and 0 for college students.
These were significantly different. ANCOVA was
not employed.
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