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.
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Problem 3.5.21e
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?
Verified step by step guidance1
Understand that randomization in this study means assigning subjects to either the fed group (Group 1) or the hungry group (Group 2) purely by chance, without any systematic bias. This helps ensure that any differences observed in decision making are due to the treatment (feeding or not feeding) rather than other factors.
Recognize that the purpose of randomization is to create groups that are comparable in all respects except for the treatment. This helps control for confounding variables that could influence the outcome, such as age, impulsivity, or body mass index (BMI).
To verify that randomization was successful, the researchers compare the groups on key characteristics measured before the treatment. In this study, they checked for differences in impulsivity (using the Barret Impulsivity Scale), age, and BMI between the two groups.
If statistical tests show no significant differences in these baseline characteristics, it suggests that randomization produced similar groups, meaning the groups are balanced and comparable before the treatment was applied.
This verification step is crucial because it supports the validity of the conclusion that any observed differences in decision making (number of advantageous cards selected) are likely due to the effect of hunger rather than pre-existing differences between the groups.
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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 participants to different groups purely by chance, minimizing selection bias. It ensures that each group is comparable and that confounding variables are evenly distributed, allowing for a fair test of the treatment effect. In this study, randomization helps isolate the effect of hunger on decision making by creating similar groups before feeding.
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Baseline Comparability and Control Variables
Baseline comparability means that groups are similar in key characteristics before treatment begins, ensuring differences in outcomes are due to the treatment. Researchers verify this by comparing variables like impulsivity, age, and body mass index between groups. Demonstrating no significant differences confirms that randomization was effective.
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Role of Control and Treatment Groups
Control and treatment groups allow researchers to compare outcomes with and without the intervention—in this case, feeding breakfast. The control group (no breakfast) and treatment group (fed breakfast) help determine if hunger influences decision making. Differences in results between these groups can be attributed to the treatment effect.
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