1. Intro to Stats and Collecting Data

Intro to Stats

1. Intro to Stats and Collecting Data

Intro to Stats

4:04 minutes

Problem 1.R.34

Textbook Question

What is the role of randomization in a designed experiment? If you were conducting a completely randomized design with four treatments and 100 experimental units, describe how you would randomly assign the experimental units to the treatments.

Verified step by step guidance

Understand that randomization in a designed experiment serves to eliminate bias by ensuring that each experimental unit has an equal chance of receiving any treatment. This helps to balance out the effects of confounding variables and allows for valid statistical inference.

Recognize that in a completely randomized design, the assignment of treatments to experimental units is done purely by chance without any restrictions or blocking factors.

Since there are four treatments and 100 experimental units, determine how many units will be assigned to each treatment. If the units are to be evenly distributed, divide 100 by 4 to find the number of units per treatment.

Use a randomization method such as a random number generator, drawing lots, or a computer program to assign each experimental unit to one of the four treatments. For example, you could label treatments as 1, 2, 3, and 4, then generate random numbers to assign each unit accordingly.

Ensure that the random assignment is recorded carefully to maintain the integrity of the experiment and to allow for proper analysis of the treatment effects later.

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Key Concepts

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

Randomization in Experimental Design

Randomization is the process of assigning experimental units to different treatment groups by chance. It helps eliminate bias, balances unknown confounding variables across groups, and ensures that the treatment effects can be attributed to the treatments rather than other factors.

Completely Randomized Design

A completely randomized design is an experimental setup where all experimental units are assigned to treatments entirely at random. This design is simple and effective for controlling variability when experimental units are homogeneous or when blocking is not necessary.

Random Assignment Procedure

Random assignment involves using a random mechanism, such as a random number generator or drawing lots, to allocate each of the 100 experimental units to one of the four treatments. This ensures each unit has an equal chance of receiving any treatment, maintaining the integrity of the experiment.

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"Designing an Experiment Researchers want to know if there is a link between hypertension (high blood pressure) and consumption of salt. Past studies have indicated that the consumption of fruits and vegetables offsets the negative impact of salt consumption. It is also known that there is quite a bit of person-to-person variability in the ability of the body to process and eliminate salt. However, no method exists for identifying individuals who have a higher ability to process salt. The U.S. Department of Agriculture recommends that daily intake of salt should not exceed 2400 milligrams (mg). The researchers want to keep the design simple, so they choose to conduct their study using a completely randomized design.

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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.

a. What type of experimental design is this?"

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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.

e. What role does randomization play in the study? How do the researchers verify that randomization resulted in similar groups prior to the treatment?

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