The items were:

love | prefer love stories to action/adventure movies |

sports | choose to watch football, basketball, or hockey on TV |

program | have programmed a computer |

tall | am 67 inches tall or more (5 feet, 7 inches) |

dress | spend 15 minutes or more getting dressed each day |

You answered the following questions about each item:

me | whether the statement is true for you |

p(y) | your judged probability of yes for a student in the class |

p(y|m) | judged probability of yes for a male student |

p(y|f) | judged probability of yes for a female student |

p(m|y) | judged probability of being male given yes |

p(m|n) | judged probability of being male given no |

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?

1.

2.

3.

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)?

6.

7.

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.

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.

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.

Should the values calculated by conditional assessment always be more accurate?

11.

12.

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.

IMPORTANT!!!

Enter your full upenn email address:

Comments: