1.3 Exploration Do People Use Facial Prototyping? A study in Psychonomic Bulletin and Review (Lea, Thomas, Lamkin, and B

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1.3 Exploration Do People Use Facial Prototyping?
A study in Psychonomic Bulletin and Review (Lea, Thomas, Lamkin,
and Bell, 2007) presented
evidence that “people use facial prototypes when they encounter
different names.”
Participants were given two faces and asked to identify which
one was Tim and which one
was Bob. The researchers wrote that their participants
“overwhelmingly agreed” on which
face belonged to Tim and which face belonged to Bob but did not
provide the exact results
of their study.
STEP 1: Ask a research question. We will gather data from your
class to investigate the
research question of whether students have a tendency to
associate certain facial features with
a name.
STEP 2: Design a study and collect data. Each student in your
class will be shown the
same two pictures of men’s faces used in the research study. You
will be asked to assign the name
Bob to one photo and the name Tim to the other. Each student
will then submit the name that
he or she assigned to the picture on the left . Th en the name
that the researchers identify with
the face on the left will be revealed.
5. How many students put Tim as the name on the left ? How many
students participated in
this study (sample size)? What proportion put Tim’s name on the
left ?
When we conduct analyses with binary variables, we oft en call
one of the outcomes a
“success” and the other a “failure” and then focus the analysis
on the “success” outcome. It is
arbitrary which outcome is defi ned to be a success, but you
need to make sure you do so consistently
throughout the analysis. In this case we’ll call “Tim on left ”
a success because that’s
what previous studies have found to be a popular choice.
STEP 4: Draw inferences. You will use the One Proportion applet
to investigate how
surprising the observed class statistic would be if students
were just randomly selecting which
name to put with which face.
6. Before you use the applet, indicate what you will enter for
the following values:
a. Probability of success:
b. Sample size:
c. Number of repetitions:
7. Conduct this simulation analysis. Make sure the Proportion of
heads button is selected
in the applet and not Number of heads.
a. Indicate how to calculate the approximate p-value (count the
number of simulated
statistics that equal ____ or ___________).
b. Report the approximate p-value.
c. Use the p-value to evaluate the strength of evidence provided
by the sample data against
the null hypothesis, in favor of the alternative that students
really do tend to assign the
name Tim (as the researchers predicted) to the face on the left
.
Th e p-value is the most common way to evaluate strength of
evidence against the null
hypothesis, but now we will explore a common alternative way to
evaluate strength of evidence.
Th e goal of any measure of strength of evidence is to use a
number to assess whether the
observed statistic falls in the tail of the null distribution
(and is therefore surprising when the
null hypothesis is true) or among the typical values we see when
the null hypothesis is true.
8. Check the Summary Stats box in the applet.
a. Report the mean (average) value of the simulated
statistics.
b. Explain why it makes sense that this mean is close to
0.50.
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c. Report the standard deviation (SD) of the simulated
statistics.
d. Report (again) the observed class value of the statistic.
(What proportion of students in
your class put Tim’s name on the left ?)
pˆ =
e. Calculate how many standard deviations the observed class
value of the statistic is from
the hypothesized mean of the null distribution, 0.50. In other
words, subtract the 0.50
from the observed value and then divide by the standard
deviation. In still other words,
calculate:
(observed statistic (pˆ ) − 0.50)SD of null distribution.
Your calculation in #8e is called “standardizing the statistic.”
It is telling us how far
above the mean the observed statistic is in terms of the “how
many standard deviations.”
standardized statistic = z = statistic − mean of null
distribution
standard deviation of null distribution
Once you calculate this value, you interpret it as “how many
standard deviations the
observed statistic falls from the hypothesized parameter
value.”
Th e next question is how to evaluate strength of evidence
against the null hypothesis
based on a standardized value. Here are some guidelines:
Guidelines for evaluating strength of evidence from standardized
values
of statistics
Standardizing gives us a quick, informal way to evaluate the
strength of evidence
against the null hypothesis. For standardized statistics:
Between −1.5 and 1.5 little or no evidence against the null
hypothesis
Below −1.5 or above 1.5 moderate evidence against the null
hypothesis
Below −2 or above 2 strong evidence against the null
hypothesis
Below −3 or above 3 very strong evidence against the null
hypothesis
Th e diagram in Figure 1.13 illustrates the basis for using a
standardized statistic to
assess strength of evidence against the null hypothesis for a
mound-shaped, symmetric
distribution.
FIGURE 1.13 Positions of standardized statistics for a
bell-shaped distribution.
–3 –2 –1.5 0 1.5 2 3
The figure can be summarized by the following key idea.
To standardize a statistic,
compute the distance of
the statistic from the
(hypothesized) mean of
the null distribution and
divide by the standard
deviation of the null
distribution.
Definition
EXPLORATION 1.3: Do People Use Facial Prototyping?
22 CHAPTER 1 Signifi cance: How Strong Is the Evidence?
Observations that fall more than 2 or 3 standard deviations from
the mean can be
considered in the tail of the distribution.
K E Y I D E A
STEP 5: Formulate conclusions.
9. Let’s examine the strength of evidence against the null.
a. Based on the value of the standardized statistic, z, in #8e
and the guidelines shown
above, how much evidence do the class data provide against the
null hypothesis?
b. How closely does your evaluation of strength of evidence
based on the standardized
statistic compare to the strength of evidence based on the
p-value in #7c?
Now, let’s step back a bit further and think about the scope of
inference. We have found
that in most classes, the observed data provide strong evidence
that students do better than
random guessing which face is Tim’s and which is Bob’s. In that
case, do you think that most
students at your school would agree on which face is Tim’s? Do
you think this means that most
people can agree on which face belongs to Tim? Furthermore, does
this mean that all people
do ascribe to the same facial prototyping?
STEP 6: Look back and ahead.
10. Based on the limitations of this study, suggest a new
research question that you would
investigate next.
Extensions
11. In #5 you recorded the proportion of students in your class
who put Tim’s name with the
photo on the left . Imagine that the proportion was actually
larger than that (e.g., if your
class was 60%, imagine it was 70%).
a. How would this have aff ected the p-value:
Larger Same Smaller
b. How would this have aff ected the absolute value of the
standardized statistic:
Larger Same Smaller
c. How would this have aff ected the strength of evidence
against the null hypothesis:
Stronger Same Weaker
12. Suppose that less than half of the students in your class
had put Tim’s name on the left , so
your class result was in the opposite direction of the research
conjecture and the alternative
hypothesis.
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a. What can you say about the standardized value of the
statistic in this case? Explain.
(Hint: You cannot give a value for the standardized statistic,
but you can say something
specifi c about its value.)
b. What can you say about the strength of evidence against the
null hypothesis and in
favor of the alternative hypothesis in this case