Practice Problems 3

Case Study 1

Consider the following case study:

“Researchers want to find out how a new diet affects weight gain among underweight subjects. This experiment only has two treatment conditions, the new diet and the standard diet. For this study, the researchers recruited 200 subjects which will be grouped into 100 pairs based on shared characteristics such as age, gender, weight, height, lifestyle, and so on. A 20-year-old female within the weight range of 90-110 pounds and the height range of 60-63 inches will be paired with another 20-year-old female that falls into the same weight and height categories. Once all 100 pairs are made, a subject from each pair will be randomly assigned into the treatment group (will be administered the new diet for 2 months) while the other subject from the pair will be assigned to the control group (will be assigned to follow the standard diet for two months). At the end of the time time period of 2 months, researchers will measure the total weight gain for each subject.”

Observed data:

The researchers found that 60 of 100 subjects in the new diet group showed substantial improvement, compared to 43 of 100 subjects in the standard diet group.

(a). Identify the experimental units in this study.
Click for answer Answer: The experimental units in this study are the 200 subjects.


(b). Classify each variable as categorical or quantitative.

Click for answer Answer: The variables are: age (quantitative), gender (categorical), weight (quantitative), height (quantitative), lifestyle (categorical), and total weight gain (quantitative).


(c). Which variable would you regard as explanatory and which as response?

Click for answer Answer: The explanatory variable is the type of diet (new or standard) and the response variable is the total weight gain.


(d). Is this an observational study or an experiment? Justify your answer.

Click for answer Answer: This is an experiment because the researchers are manipulating the explanatory variables (type of diet) to observe the effects on the response variables (total weight gain).


(e). If it is an experiment, is it randomized comparative experiment or a matched pairs experiment?

Click for answer Answer: This is a matched pairs experiment because each subject is paired with another subject who has similar characteristics and one subject from each pair is randomly assigned to the treatment group and the other to the control group. More specifically, this is a \(pretest - posttest\) matched pairs design.


(f). Construct a two-way table based on the results of the experiment.

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Two-way table:

Outcome New Diet Standard Diet Total
Improvement 60 43 103
No Improvement 40 57 97
Total 100 100 200


Case Study 2

Consider the following case study:

“In a psychology class, researchers want to know which method of study yields higher exam scores. The class has 50 students who all agree to participate. Each student will first study for Exam 1 using traditional textbook reading and then take the exam. Afterward, the same students will study for Exam 2 using interactive online modules and take that exam. The order of study techniques is kept the same to eliminate the impact of subject matter difficulty. Exam scores are the outcome of interest.”

(a). Identify the experimental units in this study.
Click for answer Answer: The experimental units are the individual students.


(b). Classify each variable as categorical or quantitative.

Click for answer Answer: “Study technique” is categorical, and “exam score” is quantitative.


(c). Which variable would you regard as explanatory and which as response?

Click for answer Answer: “Study technique” is the explanatory variable, and “exam score” is the response variable.


(d). Is this an observational study or an experiment? Justify your answer.

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Answer: This is an experiment because the researchers are imposing treatments (study techniques) on the subjects to observe the effects on exam scores.


(e). If it is an experiment, is it randomized comparative experiment or a matched pairs experiment?

Click for answer Answer: This is a matched pairs experiment with repeated measures, as each student experiences both treatments and serves as their own control.


(g). Construct a hypothetical two-way table based on the experiment.

Click for answer
Exam Score Range Textbook Study Interactive Online Module
\(90-100\) 12 20
\(80-89\) 15 18
\(70-79\) 10 7
\(60-69\) 8 3
Below 60 5 2
Total \(\mathbf{5 0}\) \(\mathbf{5 0}\)


Case Study 3

“Researchers aim to investigate the effect of a new high-intensity interval training (HIIT) program and a new nutritional supplement on muscle growth and fat loss. The subjects for this experiment include both males and females of varying ages between 18-35, who are recreational gym-goers. Researchers pair 240 subjects into 120 pairs based on similar characteristics such as age, gender, body mass index, and baseline fitness levels. In each pair, one subject will be assigned to follow the new HIIT program along with the nutritional supplement for a period of 3 months. The other subject will follow a standard workout routine without the nutritional supplement. The metrics of interest are muscle mass gained and body fat percentage lost.”

Observed data:

After the completion of 3 months, the researchers found that 82 of the 120 subjects in the HIIT program showed statistically significant improvements in muscle mass and fat loss, compared to 54 of the 120 subjects in the standard workout group.

(a). Identify the experimental units in this study.

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Answer:

The experimental units in this study are the individual subjects participating in the experiment.


(b). Classify each variable as categorical or quantitative.

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Answer:

  • Age: Quantitative
  • Gender: Categorical
  • Body Mass Index: Quantitative
  • Baseline Fitness Level: Quantitative
  • Type of workout program (HIIT or standard): Categorical
  • Nutritional supplement (Yes or No): Categorical
  • Muscle mass gained: Quantitative
  • Body fat percentage lost: Quantitative


(c). Which variables would you regard as explanatory and which as response?

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Answer:

  • Explanatory variables: Type of workout program (HIIT or standard), Nutritional supplement (Yes or No)
  • Response variables: Muscle mass gained, Body fat percentage lost


(d). Is this an observational study or an experiment? Justify your answer.

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Answer:

This is an experiment. Researchers are actively manipulating the conditions (workout program and nutritional supplement) to which subjects are exposed and are measuring the outcome (muscle mass gained and body fat percentage lost).


(e). If it is an experiment, is it a randomized comparative experiment or a matched pairs experiment?

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Answer:

This is a matched pairs experiment. Subjects are paired based on similar characteristics, and within each pair, one subject is assigned to the treatment group and the other to the control group.


(f). Construct a two-way table based on the results of the experiment.

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Answer:

\(\begin{array}{l}\text { HIIT Program with } \\\text { Supplement }\end{array}\) \(\begin{array}{l}\text { Standard Workout without } \\\text { Supplement }\end{array}\) Total
\(\begin{array}{l}\text { Significant } \\\text { Improvement }\end{array}\) 82 54 136
\(\begin{array}{l}\text { No Significant } \\\text { Improvement }\end{array}\) 38 66 104
Total 120 120 240


Case Study 4

Consider the following case study:

“Swimming with dolphins can certainly be fun, but is it also therapeutic for patients suffering from clinical depression? To investigate this possibility, researchers recruited 30 subjects aged 18-65 with a clinical diagnosis of mild to moderate depression. Subjects were required to discontinue use of any antidepressant drugs or psychotherapy four weeks prior to the experiment, and throughout the experiment. These 30 subjects went to an island off the coast of Honduras, where they were randomly assigned to one of two treatment groups. Both groups engaged in the same amount of swimming and snorkeling each day, but one group (the animal care program) did so in the presence of bottlenose dolphins and the other group (outdoor nature program) did not. At the end of two weeks, each subjects’ level of depression was evaluated, as it had been at the beginning of the study, and it was determined whether they showed substantial improvement (reducing their level of depression) by the end of the study (Antonioli and Reveley, 2005).”

Observed data

The researchers found that 10 of 15 subjects in the dolphin therapy group showed substantial improvement, compared to 3 of 15 subjects in the control group.

(a). Identify the experimental units in this study.

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Answer: The experimental units in this study are the 30 subjects.


(b). Classify each variable as categorical or quantitative.

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Answer: The variables in this study can be classified as follows: Categorical: Treatment Group (Dolphin and Control) Quantitative: Age, Level of Depression (Beginning and End of Study)


(c). Which variable would you regard as explanatory and which as response?

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Answer: The explanatory variable would be the Treatment Group and the response variable would be the Level of Depression.


(d). Is this an observational study or an experiment? Justify your answer.

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Answer: This is an experiment because the researchers randomly assigned the subjects to the two treatment groups, and then observed the effect of the treatment (presence of dolphins) on the response variable (level of depression).


(e). Construct a two-way table based on the results of the experiment.

Click for answer

Answer:

Two-way table:

Dolphin Therapy Improved Not Improved Total
Group 10 5 15
Control Group 3 12 15
Total 13 17 30