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Chapter 4: Problem 55

Identify the experimental units or subjects, the explanatory variables (factors), the treatments, and the response variables. A maker of fabric for clothing is set- ting up a new line to 鈥渇inish鈥� the raw fabric. The line will use either metal rollers or natural-bristle rollers to raise the surface of the fabric; a dyeing-cycle time of either 30 or 40 minutes; and a temperature of either \(150^{\circ}\) or \(175^{\circ}\) Celsius. An experiment will compare all combinations of these choices. Three specimens of fabric will be subjected to each treatment and scored for quality.

Short Answer

Expert verified
Experimental units: fabric specimens; Explanatory variables: type of rollers, dyeing-cycle time, temperature; Treatments: combinations of factors; Response variable: quality score.

Step by step solution

01

Identifying Experimental Units

The experimental units in this study are the individual fabric specimens. These are the actual items that will be subjected to different treatments in the experiment.
02

Determining Explanatory Variables

Explanatory variables, also known as factors, are the conditions that are manipulated in the experiment. In this experiment, there are three factors: the type of rollers (metal or natural-bristle), the dyeing-cycle time (30 or 40 minutes), and the temperature (150掳C or 175掳C).
03

Describing Treatments

Treatments are the specific combinations of the levels of each factor that will be used in the experiment. Here, treatments are the combinations of the type of roller, dyeing-cycle time, and temperature. For example, one treatment could be using metal rollers, with a dyeing-cycle time of 30 minutes, at a temperature of 150掳C.
04

Identifying Response Variables

The response variable is what is measured to assess the effect of the treatments. In this experiment, the response variable is the quality score assigned to each fabric specimen after being subjected to the treatments.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Explanatory Variables
In experimental design, explanatory variables are factors that we manipulate to see how they affect an outcome. For this particular experiment involving a new line for fabric "finishing," we identify three explanatory variables:
  • The type of rollers: can be metal or natural-bristle.
  • The dyeing-cycle time: options are 30 or 40 minutes.
  • The temperature: set at either 150掳C or 175掳C.
These variables are crucial because by systematically altering them, researchers can observe changes and draw conclusions about the optimal conditions for the fabric finishing process.
This feature highlights the importance of careful selection and control of factors in a well-designed experiment.
Response Variables
Response variables are central to understanding the results of an experiment. They are what you measure to evaluate the effect of the different treatments you apply. In our fabric finishing experiment, the response variable is the quality score given to each fabric specimen.
The quality score provides a quantifiable measure that reflects the success or failure of each treatment combination.
  • Scores give insight into the fabric's appearance, texture, or durability after treatment.
  • By analyzing these scores, researchers can discern which combinations of rollers, dyeing times, and temperatures lead to the best outcomes.
Understanding response variables helps in gauging how well the treatments meet the desired experimental objectives.
Treatments
Treatments in an experiment involve implementing combinations of different levels of explanatory variables. In this fabric study, each treatment consists of:
  • A specific type of roller (metal or natural-bristle).
  • A particular dyeing-cycle time (30 or 40 minutes).
  • A set temperature (150掳C or 175掳C).
Each unique combination constitutes a different treatment. For instance, using metal rollers with a dyeing-cycle time of 30 minutes at 150掳C is one distinct treatment.
By using all possible combinations of explanatory variables, researchers can explore a wide range of scenarios to determine which treatment is most effective for fabric quality improvement.
Experimental Units
The concept of experimental units is essential for conducting fair and unbiased experiments. These units are the smallest divisions of the experimental material, to which treatments are applied independently. In this fabric experiment, the experimental units are the individual fabric specimens.
Each fabric piece will undergo precisely one treatment using a specific combination of variables. This setup ensures that the effects observed can be attributed to the treatments administered, rather than variations in the fabric specimens themselves.
  • By ensuring each treatment is applied to multiple experimental units, researchers can mitigate random errors.
  • This practice improves the reliability and validity of the results.
Knowing the experimental units helps in the planning and execution of a methodologically sound experiment.

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