2. Describing Data with Tables and Graphs

Visualizing Qualitative vs. Quantitative Data

2. Describing Data with Tables and Graphs

Visualizing Qualitative vs. Quantitative Data

2:09 minutes

Problem 11.2.6b

Textbook Question

Platelet-Rich Plasma In a prospective cohort study, 20 patients with alopecia (hair loss) had platelet-rich plasma (PRP) injected in their scalps. After three months, the mean difference in hair density (after - before) was 170.70 hairs per square centimeter with a standard deviation of 37.81hairs/cm2. Source: Gkini MA, Kouskoukis AE, Tripsianis G, Rigopoulos D, Kouskoukis K., “Study of Platelet-Rich Plasma Injections in the Treatment of Androgenetic Alopecia through a One-Year Period”. J Cutan Aesthet Surg, 2014; 7:213–219.
b. What is the variable of interest in this study? Is it qualitative or quantitative?

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Identify the variable that the study is measuring or observing. In this case, it is the change in hair density after the treatment, which is the difference in the number of hairs per square centimeter before and after the PRP injection.

Determine the nature of this variable. Since hair density is measured as a count of hairs per unit area, it is a numerical measurement.

Recall that variables can be classified as qualitative (categorical) or quantitative (numerical). Qualitative variables describe categories or groups, while quantitative variables represent measurable quantities.

Since the variable here is the difference in hair density, which is a measurable numerical value, it is a quantitative variable.

Summarize: The variable of interest is the difference in hair density (after - before) measured in hairs per square centimeter, and it is a quantitative variable.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Variable of Interest

The variable of interest is the specific characteristic or measurement that the study aims to observe or analyze. In this case, it is the change in hair density after treatment, which reflects the effect of platelet-rich plasma injections on hair growth.

Qualitative vs. Quantitative Variables

Variables can be qualitative (categorical) or quantitative (numerical). Qualitative variables describe categories or qualities, while quantitative variables represent measurable amounts or counts, such as hair density measured in hairs per square centimeter.

Measurement of Change (Difference Scores)

The study measures the difference in hair density before and after treatment, which is a quantitative variable representing change. This approach helps assess the treatment effect by comparing paired measurements within the same subjects.

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Textbook Question

Gas Hike The average per gallon price for regular unleaded gasoline in the United States rose from \$1.46 in 2001 to \$2.77 in 2018.

Source: U.S. Energy Information Administration

b. Construct a misleading graphic that makes it appear the average price roughly quadrupled between 2001 and 2018.

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Textbook Question

Ideal Family Size The following USA Today–type graphic illustrates the ideal family size (total children) based on a survey of adult Americans.

a. What type of graphic is being displayed?

b. Describe any problems with the graphic.

c. Construct a graphic that is not misleading and makes the data stand out.

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Textbook Question

Retain Your Knowledge: Decision Making and Hunger Does hunger improve strategic decision making? That is, if you are hungry are you more likely to make a favorable decision when the outcome of your decision is uncertain (as in business decisions)? To test this theory, researchers randomly divided 30 normal weight individuals into two groups. All subjects were asked to refrain from eating or drinking (except water) from 11 P.M. on the day prior to their 9 A.M. meeting. At 9 A.M., the subjects were randomly assigned to one of two groups. The subjects in Group 1 were fed breakfast while the subjects in Group 2 were not fed. All subjects were administered a computerized version of an exam that assesses complex decision making under uncertain conditions. The assessment consisted of subjects choosing cards from four decks marked A, B, C, and D. Cards in decks A and B had a point value of 100 while cards in decks C and D had point values of 50. However, deck A had penalty cards that deducted points between 150 and 300; deck B had one penalty card of 1250; deck C had penalty cards between 25 and 75 points; deck D had a single penalty card of 250 points. So, decks A and B had stiffer penalties over the long haul than decks C and D and in the long haul, decks C and D resolted in more points than decks A and B. In total, the subjects would select 100 cards. However, the response variable was the number of cards selected from decks C and D out of the last 60 cards selected. The thinking here is that after 40 card selections, the subjects would be aware of the advantage of decks C and D. The researchers administered a Barret Impulsivity Scale to be sure the two groups did not differ in terms of impolsivity (e.g., “I do things without thinking”). There was no difference in impulsivity, age, or body mass index between the two groups. Before the exam, subjects were asked to report their level of hunger and it was found that Group 2 was significantly more hungry than Group 1. After analysis of the data, it was determined that the mean number of advantageous cards (decks C and D) selected by the subjects in Group 2 was 33.36 cards while the mean was 25.86 for the subjects in Group 1. The researchers concluded that hunger improves advantageous decision making.

c. What is the response variable? Is it qualitative or quantitative? If quantitative, is it discrete or continuous?

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Textbook Question

f. What are the statistics in the study?

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Textbook Question

b. Identify the experimental units.

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Textbook Question

Cardiac Arrest Researchers conducted a prospective cohort study in which male patients who had an out-of-hospital cardiac arrest were submitted to therapeutic hypothermia (intravenous infusion of cold saline followed by surface cooling with the goal of maintaining body temperature of 33 degrees Celsius for 24 hours. Note that normal body temperature is 37 degrees Celsius). The survival status, length of stay in the intensive care unit (ICU), and time spent on a ventilator were measured. Each of these variables was compared to a historical cohort of patients who were treated prior to the availability of therapeutic hypothermia. Of the 52 hypothermia patients, 37 survived; of the 74 patients in the control group, 43 survived. The median length of stay among survivors for the hypothermia patients was 14 days versus 21 days for the control group. The time on the ventilator among survivors for the hypothermia group was 219 hours versus 328 hours for the control group.

b. What is the explanatory variable in the study? Is it qualitative or quantitative?

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Textbook Question

High Heels The graphic to the right is a USA Today—type graph displaying women’s preference for shoes. a. Which type of shoe is preferred the most? The least? b. How is the graph misleading?

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Textbook Question

c. What are the three response variables in the study? For each, state whether the variable is qualitative or quantitative.

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