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Chapter 14: Problem 5

The article "Dieters Should Use a Bigger Fork" (Food Network Magazine, January/February 2012) described an experiment conducted by researchers at the University of Utah. The article reported that when people were randomly assigned to either eat with a small fork or to eat with a large fork, the mean amount of food consumed was significantly less for the group that ate with the large fork. a. What are the two treatments in this experiment? b. In the context of this experiment, explain what it means to say that the mean amount of food consumed was significantly less for the group that ate with the large fork.

Short Answer

Expert verified
a. The two treatments in this experiment are 'eating with a small fork' and 'eating with a large fork'. b. In this context, the mean amount of food consumed being significantly less for the group that ate with the large fork means that, on average, people who ate with a large fork consumed less food and this difference is statistically significant indicating a likely effect of fork size.

Step by step solution

01

Identify the Treatments

In this experiment, the treatments refer to the different conditions that participants are subjected to for the purpose of the study. From the given problem, the two treatments are 'eating with a small fork' and 'eating with a large fork'.
02

Interpret the Research Outcome

When the article states that the mean amount of food consumed was significantly less for the group that ate with the large fork, this means that on average, those who ate with a large fork ate less food than those who ate with a small fork. The word 'significantly' in this context implies that this result is not just a random variation, but is a statistically significant outcome that suggests a real effect of the fork size on the amount of food consumed.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Random Assignment
Random assignment is a fundamental aspect of conducting a statistical experiment. In this study, participants were randomly assigned to eat with either a small or large fork. This process ensures that each participant has an equal chance of receiving either treatment.

By doing so, researchers minimize the effects of confounding variables鈥攆actors other than the fork size that could affect the amount of food consumed.
  • Equalizing Groups: Random assignment helps create similar groups, ensuring differences in outcomes are likely due to the treatment itself.
  • Reducing Bias: It prevents systematic differences between those using the small fork and those using the large fork.
  • Improving Validity: This random process enhances the internal validity of the experiment, making the results more reliable.
Random assignment is thus crucial for inferring causality from the data collected in such experiments.
Statistical Significance
Statistical significance refers to the likelihood that a result is not due to chance. In the context of this study, when it is said that the mean amount of food consumed was significantly less for the group using the large fork, it suggests a true effect of fork size on food consumption.

To determine statistical significance, researchers typically use hypothesis testing. Here鈥檚 what it involves:
  • Null Hypothesis: Assumes there is no difference in food consumption between the two groups.
  • Alternative Hypothesis: Suggests a difference exists鈥攈ere, that fork size influences consumption.
  • Significance Level: A threshold (e.g., 0.05) below which the null hypothesis is rejected.
  • P-value: Indicates the probability of observing the difference if the null hypothesis is true. A small p-value signifies a result unlikely due to random chance.
In conclusion, the significant difference observed implies the effect of fork size is viable, not a fluke.
Treatment Effect
The treatment effect is the impact that utilizing different treatments has on the outcome of an experiment. In this case, the primary treatment was fork size鈥攕mall versus large.

The treatment effect can be understood as the direct consequence of which fork size was employed. The key elements include:
  • Measurable Change: Represents the change in the amount of food consumed due to the fork size.
  • Comparison Between Groups: In this study, it's seen as the difference in food intake between the large fork and small fork groups.
  • Practical Implications: Such findings can influence recommendations on eating habits and tool usage.
Ultimately, analyzing the treatment effect helps determine if the intervention (using a larger fork) achieves the intended outcome of reducing food consumption.
Mean Comparison
Mean comparison is a statistical technique used to evaluate differences between the average outcomes of different groups. It is essential in determining if treatments lead to different effects.

In this study, the mean amount of food consumed was calculated and compared between participants using small and large forks. Here鈥檚 how mean comparison works:
  • Calculating Means: Compute the average consumption for both groups individually.
  • Assessing Differences: Check the gap between these means to see if it's substantial.
  • Using Statistical Tests: Techniques such as t-tests can affirm if observed differences are statistically significant.
By comparing these means, researchers can deduce if the fork size truly influences food intake, lending credibility to the hypothesis.

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Most popular questions from this chapter

The paper "Fudging the Numbers: Distributing Chocolate Influences Student Evaluations of an Undergraduate Course" (Teaching of Psychology [2007]: \(245-247\) ) describes an experiment in which 98 students at the University of Illinois were assigned at random to one of two groups. All students took a class from the same instructor in the same semester. Students were required to report to an assigned room at a set time to fill out a course evaluation. One group of students reported to a room where they were offered a small bar of chocolate as they entered. The other group reported to a different room where they were not offered chocolate. Summary statistics for the overall course evaluation score are given in the accompanying table. \begin{tabular}{lccc} Group & \(n\) & \(\bar{x}\) & \(s\) \\ Chocolate & 49 & 4.07 & 0.88 \\ No Chocolate & 49 & 3.85 & 0.89 \\ \hline \end{tabular} a. Use the given information to construct and interpret a \(95 \%\) confidence interval for the mean difference in overall course evaluation score. b. Does the confidence interval from Part (a) support the statement made in the title of the paper? Explain.

14.25 Can moving their hands help children learn math? This question was investigated in the paper "Gesturing Gives Children New Ideas About Math" (Psychological Science [2009]\(: 267-272\) ). Eighty-five children in the third and fourth grades who did not answer any questions correctly on a test with six problems of the form \(3+2+8=+8\) were participants in an experiment. The children were randomly assigned to either a no-gesture group or a gesture group. All the children were given a lesson on how to solve problems of this form using the strategy of trying to make both sides of the equation equal. Children in the gesture group were also taught to point to the first two numbers on the left side of the equation with the index and middle finger of one hand and then to point at the blank on the right side of the equation. This gesture was supposed to emphasize that grouping is involved in solving the problem. The children then practiced additional problems of this type. All children were then given a test with six problems to solve, and the number of correct answers was recorded for each child. Summary statistics follow.

The paper "Supervised Exercise Versus Non-Supervised Exercise for Reducing Weight in Obese Adults" (The Journal of Sports Medicine and Physical Fitness [2009]: \(85-90\) ) describes an experiment in which participants were randomly assigned either to a supervised exercise program or a control group. Those in the control group were told only that they should take measures to lose weight. Those in the supervised exercise group were told they should take measures to lose weight as well, but they also participated in regular supervised exercise sessions. The researchers reported that after 4 months, the mean decrease in body fat was significantly higher for the supervised exercise group than for the control group. In the context of this experiment, explain what it means to say that the exercise group mean was significantly higher than the control group mean.

The article "Why We Fall for This" (AARP Magazine, May/June 2011 ) describes an experiment investigating the effect of money on emotions. In this experiment, students at University of Minnesota were randomly assigned to one of two groups. One group counted a stack of dollar bills. The other group counted a stack of blank pieces of paper. After counting, each student placed a finger in very hot water and then reported a discomfort level. It was reported that the mean discomfort level was significantly lower for the group that had counted money. In the context of this experiment, explain what it means to say that the money group mean was significantly lower than the blank- paper group mean.

The paper "If It's Hard to Read, It's Hard to Do" (Psychological Science [2008]: \(986-988\) ) described an interesting study of how people perceive the effort required to do certain tasks. Each of 20 students was randomly assigned to one of two groups. One group was given instructions for an exercise routine that were printed in an easy-to-read font (Arial). The other group received the same set of instructions but printed in a font that is considered difficult to read the time (in minutes) they thought it would take to complete the exercise routine. Summary statistics follow. The authors of the paper used these data to carry out a twosample \(t\) test and concluded at the 0.10 significance level that the mean estimated time to complete the exercise routine is significantly lower when the instructions are printed in an easy-to-read font than when printed in a font that is difficult to read. Discuss the appropriateness of using a twosample \(t\) test in this situation.
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