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I am learning about Experimental Design and I am confused with an example:

'The following chart displays the burning times of flares of two different type of torch design. The engineers are interested in comparing the mean burning times for the two types of design. Sample torches are tested one-at-a-time and the burning times of flares are recorded.

So The response is the burning time of flares, factor is the type of torch design, factor levels is type or type 2. I am confused for the treatments because there is no combination of the factor levels so is it possible this experimental design has no treatments or is this a case of a single treatment? Any help would be greatly appreciated!

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    $\begingroup$ The word "treatment" is a little vague. I would call "torch type" the treatment, which is a factor with two levels. $\endgroup$ – Noah Mar 7 at 3:18
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    $\begingroup$ Factors: Variable(s) manipulated by researchers in order to observe response(s) Levels: Values of factors Treatments: Combinations of level of factors, applied to experimental units $\endgroup$ – Tom Butcher Mar 7 at 3:24
  • $\begingroup$ Treatments are defined as combinations of level of factors so how would that work? $\endgroup$ – Tom Butcher Mar 7 at 3:24
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    $\begingroup$ There's only one factor so its levels are the treatments. If there was another factor, say the temperature of the environment (which had two levels), the treatments would be the combinations of torch type and temperature. $\endgroup$ – Noah Mar 7 at 3:42
  • $\begingroup$ Are you positive? I have never heard that before. $\endgroup$ – Tom Butcher Mar 7 at 3:51
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There seems to be only two types of Torch design, and no other variables varied in the experiment. As the experimenter decided on which kind of Torch design to use in the experiment (they did not only passively observe design types in use), that factor variable is the experimental treatment.

You seems to be confused by Treatments are defined as combinations of level of factors, which taken literally could be taken to mean there must be at least two factors there! But that does not make very much sense, and is like arguing that "zero is not a number, because number is measuring quantity and with zero there is no quantity", a viewpoint we left in the dustbin of history.

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