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The Median Isn't the Message by Stephen Gould, Discover, June 1985.

Examples of good and bad graphical displays from ``The Visual Display Quantitative Information", by Edward R. Tufte, Graphics Press 1983.

``The Evil Twin Strategy for a Football Pool", DeStefano, Doyle, and Snell, American Mathematical Monthly, April 1993.


A judge's charge to a jury might by like the following issued by Judge Weinstein:

``If you entertain a reasonable doubt as to any fact or element necessary to constitute the defendant's guilt, it is your duty to give him the benefit of that doubt and return a verdict of not guilty. Even where the evidence demonstrates a probability of guilt, if it does not establish such guilt beyond a reasonable doubt, you must acquit the accused. This doubt, however, must be a reasonable one; that is one that is founded upon a real tangible substantial basis and not upon mere caprice and conjecture. It must be such doubt as would give rise to a grave uncertainty, raised in your mind by reasons of the unsatisfactory character of the evidence or lack thereof. A reasonable doubt is not a mere possible doubt. It is an actual substantial doubt. It is a doubt that a reasonable man can seriously entertain. What is required is not an absolute or mathematical certainty, but a moral certainty." State v. Cage, 554 So.2d 39, 41 (La. 1989)


Read the obove extract from Judge Weinstein's opinion in Fatico (458 F. Supp. 388, *409).

1. Do you feel a moral certainty that if you roll three dice, you will not roll three 6's?

2. Does it make sense to assign an actual probability to the notion of a reasonable doubt? If so, what probability would you assign?

3. Do you suppose that juries are ever really told what probability to associate to the phrase `reasonable doubt'?

4. What percent of the people on death row do you think are innocent?

5. From a recent chance news discussing the trial of John Bertsch and Jeffrey Hronis accused of a 1985 kidnap, rape and murder case we read:

``The FBI's DNA tests in 1989 showed that the chances of a match were 1 in 12 million for Bertsch and 1 in 8 million for Hronis. In a re-testing in 1992 the FBI came up with 1 in 16,000 for Hronis and 1 in 200 for Bertsch."

Would the 1989 tests have satisfied ``beyond a reasonable doubt"? What about the 1992 tests?


(1) Read the article:

HLA - Paternity - sexual assault New Jersey Law Journal, 11 January 1993, Judith Nallin

This article is in the Chance folder on public and on gopher in the Dartmouth_Course_Fall_93folder in the Chance_Coursefolder. Comment in your journal on your feeling about the use of Bayes theorem in the courts.

(2) A great deal of the statistics you see in newspapers and magazines is presented in graphical form. We have given you examples of good and bad uses of graphics from the book by Tufte. His book is on reserve in Kresge and you can see many more there. Find an example of a graph that you think is interesting either for its good or bad features and include it with comments in your next journal report.


We are enjoying reading your journals. On the whole your comments on the reading and discussions are interesting and thoughtful and the kind that we are looking for. Remember, we have read the articles, so do not need a summary of what is in them. What we want is your opinions, evaluations etc. The answers to the review exercises were quite good but some of you could benefit from a more careful reading of the text.

The only disappointment is the number that have not yet mastered data-desk. As the successful ones commented, it is not easy getting started but when you do it is enjoyable and instructive. If you are having trouble getting started come around and let one of us show you how it works.


As we read the journals we will indicated some of the questions that you have raised and are worthy of further comments either by one of you or by us. Here are a few for starters:

Margo Conti asks why can't you have bias ``by chance" in a controlled experiment? For example, there might be more men then women then should normally happen. If this happens, what do you do about it?

She and others commented on the fact that, while ESP did not show up in our card experiments, it does in other ways. For example, her mother happened to think of a friend that she had not thought of for 15 years and a week later she got a letter from this friend.

Recall that two Princeton economists were praised for using a controlled experiment to measure the effect of a change in minimum wage on the fast food stores in New Jersey and Pennsylvania. Danika Vittitoe wondered if it was reasonable for them to generalize their results to other states and other kinds of businesses.

Scott Reeder commenting on the article about the use of psychics to predict the market: for ``every one that gets it right their are ten others that get it wrong".

Kristine Beneman wondered if the 19%lefties out of 861 children subjected to ultrasound tests as compared to 15%lefties for those who were not subjected to these tests was really a significant difference.

Danielle Brune asked if the stock market is random and was surprised by the number of high verbal SAT scores until noticing how many in the class were English majors.

J. Lavender has difficulty shrugging off the clusters of cancer cases described by Paul Broeder in his book and New Yorker articles.

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