91Ó°ÊÓ

Identify (i) the cases, (ii) the variables and their types, and (iii) the main research question of the studies described below. (a) While obesity is measured based on body fat percentage (more than \(35 \%\) body fat for women and more than \(25 \%\) for men), precisely measuring body fat percentage is difficult. Body mass index (BMI), calculated as the ratio weight/height \(^{2},\) is often used as an alternative indicator for obesity. A common criticism of BMI is that it assumes the same relative body fat percentage regardless of age, sex, or ethnicity. In order to determine how useful BMI is for predicting body fat percentage across age, sex and ethnic groups, researchers studied 202 black and 504 white adults who resided in or near New York City, were ages \(20-94\) years old, had BMIs of \(18-35 \mathrm{~kg} / \mathrm{m}^{2}\), and who volunteered to be a part of the study. Participants reported their age, sex, and ethnicity and were measured for weight and height. Body fat percentage was measured by submerging the participants in water. (b) In a study of the relationship between socio-economic class and unethical behavior, 129 University of California undergraduates at Berkeley were asked to identify themselves as having low or high social-class by comparing themselves to others with the most (least) money, most (least) education, and most (least) respected jobs. They were also presented with a jar of individually wrapped candies and informed that they were for children in a nearby laboratory, but that they could take some if they wanted. Participants completed unrelated tasks and then reported the number of candies they had taken. It was found that those in the upper-class rank condition took more candy than did those in the lower-rank condition. \(^{52}\)

Step by step solution

01

Identify the Cases for Study (a)

The cases in study (a) are the individual participants who were involved in the research. Specifically, there are 202 black adults and 504 white adults residing in or near New York City, aged between 20 and 94 years old, who volunteered for the study.

02

Identify Variables and Their Types for Study (a)

The variables in study (a) include: 1. Age (Numerical - continuous variable) 2. Sex (Categorical - nominal variable) 3. Ethnicity (Categorical - nominal variable) 4. Body fat percentage (Numerical - continuous variable) 5. BMI (Numerical - continuous variable)

03

Determine the Main Research Question for Study (a)

The main research question for study (a) is: How useful is BMI in predicting body fat percentage across different age, sex, and ethnic groups?

04

Identify the Cases for Study (b)

In study (b), the cases are the 129 undergraduate students from the University of California, Berkeley, who participated in the research.

05

Identify Variables and Their Types for Study (b)

The variables in study (b) include: 1. Socio-economic class (Categorical - nominal variable, low or high social class) 2. Number of candies taken (Numerical - discrete variable)

06

Determine the Main Research Question for Study (b)

The main research question for study (b) is: Is there a relationship between perceived socio-economic class and unethical behavior, measured by the number of candies taken?

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Key Concepts

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

Body Mass Index (BMI)

Body Mass Index, commonly known as BMI, is a widely used method to estimate healthy body weight based on an individual's height. The calculation involves dividing a person's weight in kilograms by the square of their height in meters: \[BMI = \frac{weight (kg)}{height (m)^2}\]This formula provides a number, often interpreted to indicate whether a person has a healthy body weight, is underweight, overweight, or obese.
Although BMI is often employed as an indicator of body fat, it has limitations. It does not distinguish between muscle and fat mass, nor does it account for variations due to age, sex, or ethnicity. These factors can affect how body fat is distributed and may result in discrepancies when using BMI alone as a measure of health.
Despite its limitations, BMI remains popular due to its simplicity and the ease with which it can be calculated.

Socio-economic Class

Socio-economic class refers to a division of people based on their economic status and social standing. This classification can be influenced by factors such as income level, education, occupation, and wealth.
In research, socio-economic class is crucial as it often correlates with various lifestyle choices, access to resources, and social behaviors. For instance, in the study described above, participants self-classified into low or high socio-economic classes.

• High social-class individuals typically have more access to education, health services, and high-paying jobs.
• Low social-class individuals might have limited access to these resources.

Understanding socio-economic class can help researchers analyze patterns in behavior, privileges, and disadvantages across different groups within society. In the given study, a comparison between socio-economic statuses was used to examine ethical behaviors.

Research Methodology

Research methodology is a systematic plan for conducting research. It involves outlining how data will be gathered, analyzed, and interpreted to address the research questions. Choosing the right methodology is crucial to obtaining reliable and valid results.
For instance, in study (a), the researchers used BMI as a tool to explore its effectiveness in predicting body fat percentage among varied demographics. They collected primary data by measuring participants' weight and height as well as body fat percentage through water displacement. This illustrates an experimental approach with direct data collection.
In study (b), a survey method was employed where participants self-assessed their socio-economic class and were observed for their behavior concerning the candies. This was a practical way of exploring perceptions of socio-economic status and associated behaviors without directly intervening.

Numerical and Categorical Variables

Variables in research are essential elements that are measured or manipulated to examine relationships, differences, and trends.
Numerical variables are quantifiable elements that involve numbers. They can be continuous, like age and body fat percentage in study (a), varying over an infinite range, or discrete, like the number of candies taken in study (b), which are countable whole numbers.
Categorical variables, on the other hand, describe characteristics that can be divided into groups. These include

• Nominal variables, which have non-ordered categories, such as sex and ethnicity in study (a).
• Ordinal variables, which have ordered categories but no fixed interval between them, like perceived socio-economic class in study (b).

Understanding the types of variables is vital for determining how data should be collected and analyzed. This understanding helps in selecting the appropriate statistical tests for interpretation.