91Ó°ÊÓ

Scientists are working to train dogs to smell cancer, including early stage cancer that might not be detected with other means. In previous studies, dogs have been able to distinguish the smell of bladder cancer, lung cancer, and breast cancer. Now, it appears that a dog in Japan has been trained to smell bowel cancer. \({ }^{12}\) Researchers collected breath and stool samples from patients with bowel cancer as well as from healthy people. The dog was given five samples in each test, one from a patient with cancer and four from healthy volunteers. The dog correctly selected the cancer sample in 33 out of 36 breath tests and in 37 out of 38 stool tests. (a) The cases in this study are the individual tests. What are the variables? (b) Make a two-way table displaying the results of the study. Include the totals. (c) What proportion of the breath samples did the dog get correct? What proportion of the stool samples did the dog get correct? (d) Of all the tests the \(\operatorname{dog}\) got correct, what proportion were stool tests?

Step by step solution

01

Identifying the variables

In this study, the variables refer to the entities that can take different values. Here, the variables would be the type of test (breath or stool), the health status of the patients (healthy or with cancer), and the outcome of the dog's test (correct or incorrect).

02

Creating a two-way table

A two-way table would show the relationship between the variable of the dog's test (correct or incorrect) and the health status of the patients (healthy or with cancer) for both the types of tests (breath and stool). So, the rows of the table can be the outcome of the test (correct or incorrect), and the columns can be the patient type (healthy or with cancer):| | Cancer patient | Healthy volunteer | Total ||------------|---------------|-------------------|-------|| Correct | 33 | 3 | 36 || Incorrect | 3 | 1 | 4 || Total | 36 | 4 | 40 |Stool Test:| | Cancer patient | Healthy volunteer | Total ||------------|---------------|-------------------|-------|| Correct | 37 | 1 | 38 || Incorrect | 1 | 0 | 1 || Total | 38 | 1 | 39 |

03

Calculating proportions

For breath test, the proportion of samples the dog got correct will be the number of correct outcomes divided by the total number of samples, i.e., \(33/36\). Similarly, for stool test, it will be \(37/38\). To find out the proportion of all the tests the dogs got correct that were stool tests, divide the number of correct stool tests by the total number of correct tests: \(37/(33+37)\).

04

Interpreting results

Calculate the values obtained in Step 3 and interpret the results. The proportion of breath and stool samples the dog got correct give the success rate of the dog’s sniffing ability for each type of test. The proportion of all the tests the dogs got correct that were stool tests indicates what proportion of the dog's correct identifications were for stool tests.

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Key Concepts

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

Variables in Research Studies

Understanding the variables in a research study is crucial to grasping the framework of the research's investigation. In the context of biomedical research, variables are attributes or characteristics that can vary among subjects or across time. These can be quantitative, like age or blood pressure, or qualitative, like the presence or absence of a disease.

For example, in the study about dogs detecting cancer, the primary variables include the type of sample (breath or stool), the health status (whether the subject has cancer or not), and the outcome of the dog's test (correct identification or not). Each of these variables is integral to the research design and further analysis. Recognizing these variables helps researchers to systematically collect data, define the scope of the study, and analyze the results using statistical methods.

Two-Way Table

A two-way table is a powerful tool used for organizing data and summarizing the relationships between two categorical variables. The table helps in visualizing how different variables interact with each other, making it simpler to identify patterns and relationships.

In our case study, the two-way table displayed the dog's ability to correctly identify cancer samples against breath and stool tests. The rows labeled 'Correct' and 'Incorrect' represent the outcomes, while the columns are divided into 'Cancer patient' and 'Healthy volunteer', reflecting the health status of the subjects. By laying out the results in this manner, the two-way table made it easier to compare the dog's performance across different test types and to comprehend the success rate associated with each variable.

Proportion Calculation

Proportion calculation is a statistical method that expresses the part of a whole as a fraction or a percentage. It is often used to understand the prevalence or success rate in studies.

In the dog cancer detection study, calculating the proportion involves dividing the number of correct identifications by the total number of samples. Through this process, we can obtain the success rate of the dog’s ability to identify cancer. For example, if the dog correctly identified 33 out of 36 breath samples, the proportion of success for breath samples is calculated as \(\frac{33}{36}\). Similarly, the proportion for stool samples is obtained by \(\frac{37}{38}\). These calculations give us insight into the reliability and efficiency of cancer detection by the trained dog.