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Chapter 2: Problem 30

Deal with an experiment to study the effects of financial incentives to quit smoking. 19 Smokers at a company were invited to participate in a smoking cessation program and randomly assigned to one of two groups. Those in the Reward group would get a cash award if they stopped smoking for six months. Those in the Deposit group were asked to deposit some money which they would get back along with a substantial bonus if they stopped smoking. After six months, 156 of the 914 smokers who accepted the invitation to be in the reward-only program stopped smoking, while 78 of the 146 smokers who paid a deposit quit. Set up a two-way table and compare the success rates between participants who entered the two programs.

Short Answer

Expert verified
To calculate the success rates, divide the number of people who quit smoking by the total number of people in each program. The Reward program had a success rate of about 17.07%, and the Deposit program had a success rate of about 53.42%. Therefore, it appears that the Deposit program was more effective.

Step by step solution

01

Set up a two-way table

First, organize the given data into a two-way table. The two columns would represent the two groups: Reward and Deposit. The rows would indicate the number of people who quit smoking and those who didn't quit for each group. Based on the given, the table would look like this:| | Reward | Deposit ||---------|------------|-----------|| Quit | 156 | 78 || Didn't | 914-156 | 146-78 |
02

Calculate the success rates

Next, calculate the success rates for both groups. This is done by dividing the number of people who quit smoking by the total number of people who were in the program for each group. The formulas to calculate the success rates would be as follows:Success rate for Reward group = Number who quit (156) / Total (914)Success rate for Deposit group = Number who quit (78) / Total (146)
03

Compare the success rates

Compare the success rates calculated in step 2 by observing which group has a higher success rate, and discuss the comparison in terms of the effectiveness of each program.

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Key Concepts

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

Two-way Table
A two-way table is an incredibly useful tool for organizing data in statistical analysis. It allows you to display the frequency of different outcomes across two categorical variables. In our exercise, the categories are 'Reward' and 'Deposit' groups, as well as those who 'Quit' and those who 'Didn't Quit'.
This table helps provide a clear visual representation of the data, making it easier to interpret and analyze.
  • Two columns represent the two different groups: Reward and Deposit.
  • Two rows represent outcomes: Quitting smoking and Not Quitting smoking.
By simply organizing data in this format, you can quickly derive insights. For example, you can easily see how many people were successful in quitting smoking, based on which group they were in. Such organization is the first step in any comparative study as it lays the foundation for further statistical analysis.
Success Rates
Understanding success rates is vital when assessing the effectiveness of different programs. In our context, it tells us how well each group performed in helping participants quit smoking. Success rate is calculated by dividing the number of successful outcomes by the total number of participants in each group.

The formula for the success rate for each group is:
  • For the Reward group: \( \text{Success Rate} = \frac{\text{Number who quit}}{\text{Total number in group}} = \frac{156}{914} \)
  • For the Deposit group: \( \text{Success Rate} = \frac{\text{Number who quit}}{\text{Total number in group}} = \frac{78}{146} \)
These calculations give us a percentage that indicates the proportion of participants who managed to quit smoking. Such rates are crucial metrics for gauging the effectiveness and appeal of different programs. When you look at these rates, you can make informed decisions about which method might be more successful in broader applications.
Comparative Study
A comparative study involves analyzing results from different groups to determine which method is more effective. In our specific exercise, the comparison is between the success rates of two groups鈥攖hose who were given a reward upon quitting and those who had to deposit money for a chance to benefit from a bonus.
  • Success rates offer direct insight into which program was more effective.
  • Through comparison, it's possible to evaluate not only effectiveness but also participant preference and motivation.
It is important to remember that comparative studies consider both the statistics and the context. While pure numbers provide a snapshot, understanding why one group was more successful can yield richer insights.
This means considering factors like participant demographics, psychological motivations, and external influences.
The comparative study here can help stakeholders decide on strategies for larger organizations or public health campaigns. It highlights the power of statistical analysis in revealing deeper truths about human behavior and program efficacy.

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