The items were:
You answered the following questions about each item:
Here are some data, in percents. The proportion of males in the
group who did the assignment is 51.8%.
In the following tables: Real=true proportions, Judge=judgments,
Final=judgment after calculation,
Diff=female-male difference, Bayes=calculated by Bayes's theorem,
e.g., p(Y|M) = p(M|Y)*p(Y)|p(M). "|" means "conditional on." Notice
that we can apply Bayes' theorem to calculate many things other than
p(M|Y), which was what you were asked to calculate.
Answer the questions after each data set.
RealY|F RealY|M Diff JudgedY|F JudgedY|M Diff BayesY|F BayesY|M Diff
lovestory 73.6 12.1 61.5 70.9 19.4 51.6 60.0 21.1 38.9
sports 24.5 57.6 -33.0 40.2 79.5 -39.2 27.9 117.9 -90.0
computer 5.7 21.2 -15.6 15.1 34.6 -19.6 7.9 44.5 -36.6
tall67 28.3 93.9 -65.6 30.5 74.8 -44.3 20.7 107.1 -86.3
dress15 64.2 21.2 42.9 76.4 29.3 47.1 68.3 31.7 36.5
What can you best conclude about the accuracy of
perception of the male/female "stereotype" from these data?
Most judgments about gender differences are in the right direction and very roughly
of the right magnitude.
All male/female differences are exaggerated, showing an exaggerated stereotype.
All judged differences are too small, showing a weaker stereotype than is true.
4. Are the judgments of p(y|m) for computer calculated by Bayes more
accurate than the initial direct judgments of p(y|m) at capturing the true p(y|m)?
5. Are the values calculated by Bayes's theorem for computer more
accurate than the direct judgments at capturing the male/female difference?
Should the values calculated by Bayes's theory always be more accurate (in terms of correspondence)?
Yes, because Bayes's theorem is a normative model.
Not always, because they are based on other judgments, which could be better or
worse than the direct judgments.
Here are more data. The column labeled BayesM|Y is what you were
asked for in the very last part of Assignment 1.
RealM|Y RealM|N Diff JudgedM|Y JudgedM|N Diff BayesM|Y BayesM|N Diff
lovestory 9.3 67.4 -58.1 17.4 76.5 -59.1 15.7 57.7 -42.0
sports 59.4 25.9 33.4 73.0 18.0 55.1 52.4 18.9 33.5
computer 70.0 34.2 35.8 71.1 25.1 46.0 54.9 32.4 22.5
tall67 67.4 5.0 62.4 74.3 21.7 52.5 55.5 19.1 36.4
dress15 17.1 57.8 -40.7 21.8 71.6 -49.8 19.7 60.4 -40.8
How do the Bayes values (BayesM|Y and BayesM|N) - not their differences - compare to the real values?
8. all too large
all too small
some of each
What is illustrated by the fact that, for "lovestory", BayesM|Y and
JudgedM|Y are very close but both very far from RealM|Y (and likewise for "sports" M|N)?
9. Bayes' theorem is better than direct judgment at making actual predictions.
Coherence does not imply correspondence.
Correspondence does not imply coherence.
Here are data relative to conditional assessment of the
probability of "yes," which you were asked to calculate in the
first part of the assignment.
TrueY JudgedY CondAssess
lovestory 50.0 45.4 51.1
sports 37.2 61.5 55.3
computer 11.6 23.5 22.6
tall67 53.5 52.6 47.5
dress15 47.7 56.2 58.3
How do the values calculated by conditional assessment (third
column of numbers) compare to the judged values (second column of
numbers) in predicting the true values?
10. CA consistently closer to the real values than are the judged values
CA consistently farther from the real values than are the judged values
CA neither consistently closer nor consistently farther
Should the values calculated by conditional assessment always be more accurate?
Yes, because conditional assessment is based on a normative model.
No, because they are based on other judgments, which could be better or
worse than the direct judgments.
Consider the following graph. The dashed lines are the correct proportions based
on the class's answers.
How would you describe what it shows about conditional assessment?
13. It moderates extreme judgments.
It exaggerates extreme judgments.
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