Identify the experimental units or subjects, the explanatory...

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 “finish” 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.

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 “finish” 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.

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Key Concepts

Experimental Units

The experimental units are the individual objects or subjects on which the experiment is performed. They are the basic units that receive the treatments and provide the data; their variability is a central aspect of experimental design as it affects the inference about the treatments’ effects.

Explanatory Variables

Explanatory variables, often referred to as factors, are the variables that the experimenter manipulates to study their influence on the outcome. They include the different conditions or levels that are systematically varied in the experiment to assess their effect on the response variable.

Treatments

Treatments are the specific combinations of levels of the explanatory variables that are applied to the experimental units. They represent different conditions under which the units are tested, and comparing responses across these treatments helps determine which factors or combinations are most effective.

Response Variables

Response variables are the outcomes or measurements recorded from the experimental units after the treatments have been applied. They reflect the effects of the varied treatments and are used to assess the performance or quality in the context of the study.

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