2 Methods for Describing Sets of Data

Where We’ve Been

  • Examined the difference between inferential and descriptive statistics

  • Described the key elements of a statistical problem

  • Learned about the two types of data: quantitative and qualitative

  • Discussed the role of statistical thinking in managerial decision making

Where We’re Going

  • Describe qualitative data with graphs (2.1)

  • Describe quantitative data with graphs (2.2)

  • Describe quantitative data with numerical measures (2.32.7)

  • Describe the relationship between two quantitative variables with a graph (2.8)

  • Detect descriptive methods that distort the  truth (2.9)

Statistics in Action Body Image Dissatisfaction: Real or Imagined?

“Everything has beauty, but not everyone sees it” —ancient Chinese sage Confucius

“Body dissatisfaction can produce extreme body-­shaping behaviors, such as eating disorders. Women and girls can’t help being exposed to ultra-thin models in advertising whose body size is unrealistic and unhealthy. There is good evidence already that exposure to these unhealthy models leads a large proportion of women to feel dissatisfied with their own bodies.” —Helga Dittmar, University of Sussex researcher

“Action figures (like G.I. Joe) present subtle messages of unrealistic role models of well-sculpted, heavily muscled, ‘perfect’ bodies that little boys see as their role models.” —Sondra Kronberg, director of Eating Disorder Associates Treatment & Referral Centers

“By age 13, 53% of American girls are unhappy with their bodies; that figure grows to 78% by the time girls reach 17. In another study on fifth graders, 10-year-old girls and boys told researchers they were dissatisfied with their own bodies after watching a music video by Britney Spears or a clip from the TV show Friends. And adolescent girls who viewed commercials depicting unrealistically thin models felt ‘less confident, more angry, and more dissatisfied with their weight and appearance.’” —statistics posted by the National Institute on Media and the Family

Are you dissatisfied with your physical appearance? Do you have a negative image of your own body? In today’s media-driven society, many of us would answer yes to these questions (as the statistics in the previous quote show). Much research has been conducted on the body images of normal adolescents and adults. However, there is a lack of information on how patients with a body image disorder evaluate their own appearance, health, and fitness. To fill this gap, researchers from the Department of Psychiatry and Human Behavior at Brown University conducted and published a study in Body Image: An International Journal of Research, January 2010.

Data were collected on 92 patients diagnosed with body dysmorphic disorder (BDD). This disorder “is characterized by a distressing or impairing preoccupation with an imagined or slight defect in appearance that causes clinically significant distress or functional impairment.” (Patients were also diagnosed with additional mental disorders, such as major depression or social phobia, called a comorbid disorder.) Each patient completed the Multidimensional Body-Self Relations Questionnaire (MBSRQ). The questionnaire elicits responses that assess how satisfied one is with his/her appearance, health, fitness, and weight. In this Statistics in Action, our focus is on the appearance evaluations (e.g., “How satisfied are you with your physical attractiveness and looks?”) of the BDD patients. The scores for each of seven appearance items (questions) were recorded on 5-point Likert scales, where the possible responses are 1=definitelydissatisfied, 2=somewhatdissatisfied, 3=neutral, 4=somewhat satisfied, and 5=definitely satisfied. These scores were summed and a total appearance score (ranging from 7 to 35 points) was recorded for each patient.

The data for the study (simulated on the basis of summary statistics presented in the journal article) are provided in the BDD file. For each of the 92 patients in the experiment, the following variables were measured:

  1. Total Appearance Score (points)

  2. Gender (M or F)

  3. Comorbid Disorder (Major Depression, Social Phobia, Obsessive Compulsive, or Anorexia/Bulimia Nervosa)

  4. Dissatisfied with Looks (Yes or No)

For this application, we are interested in evaluating the data collected on the BDD patients. Specifically, we want to know if (1) BDD females tend to be more dissatisfied with their looks than BDD males, (2) certain comorbid disorders lead to a higher level of dissatisfaction with body appearance, and (3) BDD patients have lower appearance scores than normal people. We apply the graphical and numerical descriptive techniques of this chapter to the BDD data to answer these questions in the following Statistics in Action Revisited sections:

Statistics in Action Revisited

  • Interpreting Pie Charts for the Body Image Data (p. 35)

  • Interpreting Histograms for the Body Image Data (p. 48)

  • Interpreting Descriptive Statistics for the Body Image Data (p. 75)

  • Detecting Outliers in the Body Image Data (p. 90)

Data Set: BDD

Teaching Tip

Explain to the students that descriptive techniques will also be useful in inferential statistics, for generating the sample statistics necessary to make inferences and also for generating the graphs necessary to check assumptions that will be made.

Suppose you wish to evaluate the mathematical capabilities of a class of 1,000 first-year college students, based on their quantitative Scholastic Aptitude Test (SAT) scores. How would you describe these 1,000 measurements? Characteristics of interest include the typical, or most frequent, SAT score; the variability in the scores; the highest and lowest scores; the “shape” of the data; and whether the data set contains any unusual scores. Extracting this information isn’t easy. The 1,000 scores provide too many bits of information for our minds to comprehend. Clearly, we need some method for summarizing and characterizing the information in such a data set. Methods for describing data sets are also essential for statistical inference. Most populations make for large data sets. Consequently, we need methods for describing a data set that let us make inferences about a population on the basis of information contained in a sample.

Two methods for describing data are presented in this chapter, one graphical and the other numerical. Both play an important role in statistics. Section 2.1 presents both graphical and numerical methods for describing qualitative data. Graphical methods for describing quantitative data are illustrated in Sections 2.2, 2.8, and 2.9; numerical descriptive methods for quantitative data are presented in Sections 2.32.7. We end the chapter with a section on the misuse of descriptive techniques.

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