Hypothesis TestingPart III – Applying the

Concepts

This video is designed to accompany

pages 95-116in

Making Sense of UncertaintyActivities for Teaching Statistical

ReasoningVan-Griner Publishing Company

Multivitamins and Cancer

Multivitamin Use Linked to Lowered Cancer Risk By RONI CARYN RABIN

Published: October 17, 2012

After a series of conflicting reports about whether vitamin pills can stave off chronic disease, researchers announced on Wednesday that a large clinical trial of nearly 15,000 older male doctors followed for more than a decade found that those taking a daily multivitamin experienced 8 percent fewer cancers than the subjects taking dummy pills. The findings were to be presented Wednesday at an American Association for Cancer Research conference on cancer prevention in Anaheim, Calif., and the paper was published online in The Journal of the American Medical Association.

The reduction in total cancers was small but statistically significant, said the study’s lead author, Dr. J . Michael Gaziano, a cardiologist at Brigham and Women’s Hospital and the VA Boston Healthcare System. While the main reason to take a multivitamin is to prevent nutritional deficiencies, Dr. Gaziano said, “it certainly appears there is a modest reduction in the risk of cancer from a typical multivitamin.”

Article Analysis

When you see “statistically significant” or “not statistically significant” you have to:

1. Establish what was being compared.2. Express this comparison appropriately as a

choice between a null and an alternative hypothesis.

3. Determine how the comparison turned out.4. Articulate the risk associated with the decision

made.

Multivitamins and Cancer

1. Number of cancers seen in group taking multivitamins and the number of cancers seen in group taking placebo.

2. In terms of H0 and HA:a) H0: Number of cancers in vitamin group is same as in

placebo group.b) HA: Number of cancers in vitamin group is less than

in placebo group.3. Results were statistically significant so you know that the

decision was to accept HA, that multivitamin usage reduces cancer risk.

4. There is always a chance that this was the wrong decision, that the multivitamins are not effective at reducing cancer risk. We know that in this case the “false positive” risk is less than 5 chances in 100.

Subway versus McDonalds

HEALTH

Teens ate 'too many calories' at Subway and McDonald's, study says By Mary MacVean 5:53 p.m. CDT, May 7, 2013

Adolescents who went to McDonald’s and Subway in Los Angeles bought about the same number of calories at each, despite Subway's reputation as a healthier place to eat, researchers said.

The menus are not the point, lead researcher Dr. Lenard Lesser of the Palo Alto Medical Foundation Research Institute said by phone. “Our study was not based on what people have the ability to pick, our study was based on what adolescents actually selected in a real-world setting.”

The adolescents bought an average of 1,038 calories at McDonald’s and 955 calories at Subway. The calorie difference was not statistically significant, the researchers said. Their work was published Monday in the Journal of Adolescent Health.

Subway Versus McDonald’s1. Calories consumed by teens at Subway and those

consumed by teens at McDonald’s.2. In terms of H0 and HA:

a) H0: Number of calories consumed by teens at Subway is the same as at McDonald’s.

b) HA: Number of calories consumed by teens at Subway is less than at McDonald’s.

3. Results were NOT statistically significant so you know that the decision was to not accept HA, so no evidence that Subway is a practically healthier food choice for teens.

4. There is always a chance that this was the wrong decision, that in the whole population of teens fewer calories are consumed at Subway. We don’t monitor this “False Negative Rate” explicitly, but assume the method of comparison had robust sensitivity.

Mental Illness and Obesity

A Battle Plan to Lose Weight April 15, 2013, 5:15 pm

By CATHERINE SAINT LOUIS People with serious mental illnesses, like schizophrenia, bipolar disorder or major depression, are at least 50 percent more likely to be overweight or obese than the general population. They die earlier, too, with the primary cause heart disease. Yet diet and exercise usually take a back seat to the treatment of their illnesses. The drugs used, like antidepressants and antipsychotics, can increase appetite and weight. “Treatment contributes to the problem of obesity,” said Dr. Thomas R. Insel, the director of the National Institute of Mental Health. “Not every drug does, but that has made the problem of obesity greater in the last decade.” It has been a difficult issue for mental health experts. A 2012 review of health promotion programs for those with serious mental illness by Dartmouth researchers concluded that of 24 well-designed studies, most achieved statistically significant weight loss, but very few achieved “clinically significant weight loss.”

Mental Illness and Obesity

1. Weight before and after patients complete fitness program for mentally ill.

2. In terms of H0 and HA:a) H0: Weight before fitness program is no different than

weight after fitness programb) HA: Weight before fitness program is less than weight

after fitness program.3. Results were statistically significant so you know that the

decision was to accept HA, that the fitness programs to lead to weight loss.

4. There is always a chance that this was the wrong decision, that the fitness programs are not effective at reducing weight in the larger population. We know that in this case the “false positive” risk is less than 5 chances in 100.

Presidential Payment

NEWS

How to Tell if College Presidents Are Overpaid By Richard Vedder, Bloomberg NewsBloomberg 11:20 p.m. CDT, May 13, 2013

The Chronicle of Higher Education tells us the median salary of public university presidents rose 4.7 percent in 2011-12 to more than $440,000 a year. This increase vastly outpaced the rate of inflation, as well as the earnings of the typical worker in the U.S. economy. Perhaps, most relevant for this community, it also surpassed the compensation growth for university professors.

There appears to be neither rhyme nor reason for vast differences in presidential pay. David R. Hopkins, the president of Wright State University — an unremarkable commuter school ranked rather poorly in major-magazine rankings — makes far more than the presidents of the much larger, and vastly more prestigious, University of California at Berkeley, University of North Carolina at Chapel Hill, or the University of Wisconsin.

My associate Daniel Garrett analyzed the relationship between presidential compensation and academic performance for 145 schools, using the Forbes magazine rankings of best colleges. (Full disclosure: My Center for College Affordability and Productivity compiles those rankings for Forbes.) Adjusting for enrollment differences, no statistically significant relationship was observed between academic quality and presidential pay.

Presidential Pay and Performance1. Presidential pay at low achieving universities and

Presidential pay at high achieving universities2. In terms of H0 and HA:

a) H0: There is no correlation between Presidential pay and Performance of a University.

b) HA: There is a positive correlation between Presidential pay and the Performance of a University.

3. Results were NOT statistically significant so you know that the decision was to not accept HA, so no evidence that universities that pay their Presidents more get better results in terms of performance.

4. There is always a chance that this was the wrong decision, that in the whole population of universities (not just those 145 studied) there is a correlation that is significant. We don’t monitor this “False Negative Rate” explicitly, but assume the method of comparison had robust sensitivity.

Streaks and Basketball

Winning streaks in sports may be more than just magical thinking, several new studies suggest.

Whether you call them winning streaks, “hot hands” or being “in the zone,” most sports fans believe that players, and teams, tend to go on tears …. But our faith in hot hands is challenged by a rich and well-regarded body of science over the past 30 years, much of it focused on basketball, that tells us our belief is mostly fallacious. In one of the first and best-known of these studies, published in 1985, scientists parsed records from the Philadelphia 76ers, the Boston Celtics and the Cornell University varsity squad and concluded that players statistically were not more likely to hit a second basket after sinking a first.

In the most wide-ranging of the new studies, Gur Yaari, a computational biologist at Yale, and his colleagues gathered enormous amounts of data about an entire season’s worth of free throw shooting in the N.B.A. and 50,000 games bowled in the Professional Bowlers Association. In these big sets of data, which were far larger than those used in, for instance, the 1985 basketball study, success did slightly increase the chances of subsequent success — though generally over a longer time frame than the next shot. Basketball players experienced statistically significant and recognizable hot periods over an entire game or two, during which they would hit more free throws than random chance would suggest.

Streaks and Basketball

1. Streaks of free throw successes versus what player would make at random.

2. In terms of H0 and HA:a) H0: Streaks (“Runs”) are no longer than would be

expected by random chance.b) HA: Streaks (“Runs”) are longer than would be

expected by random chance.3. Results were statistically significant so you know that the

decision was to accept HA, that there is evidence streaks are longer than expected by random chance.

4. There is always a chance that this was the wrong decision, that the streaks are not longer than random chance in the larger population. We know that in this case the “false positive” risk is less than 5 chances in 100.

One-Sentence Reflection

To understand the usage of “statistical significance” in the media, always ask what is being compared, what the null and alternatives are, how the comparison turned out, and what risks were involved in the decision that was made.