E. The T-Test

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Obesity

According to the Centers for Disease Control, obesity is one of the primary health concerns in the United States today. More people are classified as overweight and obese now than at any point in American history. Recent figures from the Centers for Disease Control estimate that two out of three adults between the ages of 20 and 74 in the United States are overweight or obese.

What's more, obesity has become a much more prevalent health concern over the past three decades, with substantial growth in obesity rates during this time, particularly among children.

  • Since 1991, obesity among adults has increased by nearly 60 percent in the United States.
  • The percentage of children and adolescents who are defined as overweight has more than doubled since the early 1970s.
  • Approximately 13 percent of children and adolescents are now seriously overweight.

(Sources: Centers for Disease Control)

Although obesity itself is a serious health concern, it is related to a number of other significant health risks, including coronary heart disease, stroke, high blood pressure, and diabetes. Overweight and physical inactivity account for more than 300,000 premature deaths each year in the U.S., second only to tobacco-related deaths.

How is Obesity Measured?

The way that obesity is measured currently is through the Body Mass Index (BMI). The BMI is a measure of an adult's weight in relation to his or her height. Specifically, it's equal to weight (measured in kilograms) divided by the square of height (measured in meters).

In formula terms:

By current practice, individuals with BMI of 25 or greater are classified as "overweight" while those with a BMI of 30 or more are classified as "obese."

You can calculate your own Body Mass Index using the following BMI Calculator.

Partly as a result of the rates of obesity and a desire to do something about it, there are seemingly thousands of diets available. Some emphasize changes in nutrition programs, eliminating carbohydrates and increasing protein intake, for example. Others promote changes in meal sizes, encouraging smaller portions of familiar foods, while some suggest selective fasting or juice-fasting days.

One of the most intriguing ones, the Furstenberg diet, promises that it can help dieters lose significant weight in 40 days. The Furstenberg diet, developed by Reverend Bartholomew Furstenberg of Stockton, California, places its emphasis on eating unpleasant foods, such as foods that taste bad or foods that are on the verge of spoiling. By taking away the pleasurable aspect of eating, the diet is designed to reinforce negative ideas about food, which will then make dieters less likely to eat. "By changing the way that people think about food," says Rev. Furstenberg, "this diet not only helps people lose weight, but helps them keep it off. The Furstenberg diet can whip any other diet out there."

Ads fill the magazines with reports of how much weight people have lost through Rev. Furstenberg's plan. Riders on the New York City subway system can practically recite the text of his advertisements from memory.

And in perhaps the most influential endorsement of all, Weight Loss Weekly recently named the Furstenberg Diet as the "Best Diet of 2002."

Yet amidst the hype for the diet, there are reports that the diet is less effective than its advertisements claim. Some dieticians have reported seeing increasing numbers of people who have not lost any weight through the Furstenberg plan, despite rigidly following the diet's guidelines. To evaluate just how effective the diet is, Hollywood Upstairs Medical School (HUMS) recently decided to take Rev. Furstenberg at his word and see whether, in fact, people on the diet are able to lose weight. They developed a study to compare the Furstenberg diet with a Health Through High-Fiber diet to see whether the Furstenberg dieters lost more.

To conduct their study, HUMS recruited a group of individuals in a manner that does not violate the conditions of independence. Some 428 people signed up for the study.

To start the evaluation, each of the people in the study had an interview in which detailed information was collected about their previous experiences with other diets, their eating and exercise habits, and basic characteristics such as age, gender, race, and occupation.

As part of the interview process, the doctor collecting the information handed the future dieter a coin and asked them to flip it. Those whose coins landed as "heads" were assigned to Rev. Furstenberg's diet, while those whose coins landed as "tails" were given the Health Through High-Fiber diet. Through the coin flips, 214 were in the Furstenberg Diet Group, while 214 were in the Health Through High-Fiber Diet group.

At the end of the interview, each of the dieters stepped onto a scale. Their weight was recorded and they were sent on their way.

The two groups compare in at the outset with the following weight: Furstenberg group: mean=199 pounds, SD=29 pounds. Health Through High-Fiber Diet group: mean=195 pounds, SD=31 pounds.

You can examine the records from the initial weigh-in for these two groups by clicking here.

Question

Is there a statistically significant difference in the distribution of weight between the people in the Furstenberg group and Health Through High-Fiber Diet group?

Question

Another way of asking whether the diet worked is to ask whether those dieters in the Furstenberg group lost more weight than those in the Health Through High Fiber group. State the null hypothesis and alternative hypothesis you want to examine here.

As they left the hospital, they were told to hold to the diets and come back in 40 days.

Some time later, brought them back together to measure their weight. Results looked like this:

Furstenberg group: mean=170 pounds, SD=26 pounds. Health Through High-Fiber Diet group: mean=187 pounds, SD=29 pounds.

You can examine the "after" weigh-in for these two groups by clicking here.

Questions

The big question here is did the diet work? But before getting to that question, answer a couple of others along the way.

What is the independent variable (or primary independent variable) you are examining here? What is the dependent variable in this research study?

In evaluating the results of the experiment, another diet expert, Rudy Stengelmaier, argues that the experiment is flawed because the two groups differ in their ages. The group that participated in Dr. F's diet were younger and, therefore, more likely to lose weight. In consulting the interview records from the hospital, you find that the average age of the Furstenberg group is 43, while the average age of the Health Through High-Fiber Diet group is 48. How would you respond? What other data would you need to evaluate whether this difference is statistically significant?

Another (and arguably better) way to address Dr. Stengelmaier's criticism would focus on the way that this research design was constructed. What features of the design speak to Dr. Stengelmaier's critique? Why is this research design well-suited to dismiss Sengelmaier's criticism?

Finally, what do you conclude about the effectiveness of the Furstenberg Diet as compared to the Health Through High Fiber Diet?