2. Describing Data with Tables and Graphs

Visualizing Qualitative vs. Quantitative Data

2. Describing Data with Tables and Graphs

Visualizing Qualitative vs. Quantitative Data

3:15 minutes

Problem 7.1.37c

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.

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

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Identify the variables that the researchers measured to assess the outcomes of the patients. These are the response variables because they represent the outcomes influenced by the treatment (therapeutic hypothermia).

The first response variable is the survival status of the patients. This variable indicates whether a patient survived or not, which is a categorical outcome.

The second response variable is the length of stay in the intensive care unit (ICU). This variable measures the number of days a patient stayed in the ICU, which is a numerical measurement.

The third response variable is the time spent on a ventilator. This variable records the number of hours a patient was on mechanical ventilation, which is also a numerical measurement.

Classify each response variable as qualitative or quantitative: Survival status is qualitative (categorical), while length of stay in ICU and time on ventilator are quantitative (numerical) variables.

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Key Concepts

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

Response Variables

Response variables, also called dependent variables, are the outcomes measured in a study to assess the effect of an intervention or exposure. They represent what researchers want to explain or predict, such as survival status or length of hospital stay. Identifying these variables is crucial for analyzing the study results.

Qualitative vs. Quantitative Variables

Qualitative variables describe categories or qualities and are often non-numeric, like survival status (alive or dead). Quantitative variables are numeric and measure amounts or counts, such as length of stay or hours on a ventilator. Distinguishing between these types guides appropriate statistical analysis.

Prospective Cohort Study Design

A prospective cohort study follows a group over time to observe outcomes after an exposure or treatment, here therapeutic hypothermia. Understanding this design helps interpret how response variables are measured and compared to a historical control group, ensuring clarity about causality and temporal relationships.

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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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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.

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

"Putting It Together: Online Homework Keeping students engaged in the learning process greatly increases their chance of success in a course. Traditional lecture-based math instruction has given way to a more student-engaged approach where students interact with the teacher in class and receive immediate feedback to their responses. The teacher presence allows students, when incorrect in a response, to be guided through a solution and then immediately be given a similar problem to attempt. A researcher conducted a study to investigate whether an online homework system using an attempt—feedback— reattempt approach improved student learning over traditional pencil-and-paper homework. The online homework system was designed to increase student engagement outside class, something commonly missing in traditional pencil-and-paper assignments, ultimately leading to increased learning.The study was conducted using two first-semester calculus classes taught by the researcher in a single semester. One class was assigned traditional homework and the other was assigned online homework that used the attempt—feedback—reattempt approach. The summaries are based on data from the study.

g. What type of graph is displayed?"

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Textbook Question

Putting It Together: Drug Side Effects In placebo-controlled clinical trials for the drug Viagra, 734 subjects received Viagra and 725 subjects received a placebo (subjects did not know which treatment they received). The table below summarizes reports of various side effects that were reported.

a. Is the variable “adverse effect” qualitative or quantitative?

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Multiple Choice

Which type of graph is most appropriate for visualizing changes in $quantitative$ data over $time$ ?

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Multiple Choice

Which of the following is an example of quantitative data collected from a group of students?

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