Experiment Design In‐Class Assignment Revisited as Homework Identifying parts of an experiment Name (legibly written)___________Solutions____________________ In the following description of an experiment, there is information that you have not been given. Your job is to identify the parts of the experiment, and justify your responses. Where you have not been given enough information to answer the question, you can either 1.) make an assumption, which you justify, or 2.) give two scenarios, and tell which one you think would be better. You may want to use the More On Experimental Units handout to help you. Bachman, Herzberg, and Rich conducted a factorial study of fluid flow through thin tubes. They measured the time required for the liquid level in a fluid holding tank to drop from 4 in. to 2 in. for two drain tube diameters and two fluid types. Two different technicians did the measuring. Here is their data: Technician Diameter (in.) Fluid Time (sec) 1 .188 water 21.12, 21.11, 20.80
2 .188 water 21.82, 21.87, 21.78
1 .314 water 6.06, 6.04, 5.92 2 .314 water 6.09, 5.91, 6.01 1 .188 ethylene glycol 51.25, 46.03, 46.09
2 .188 ethylene glycol 45.61, 47.00, 50.71
1 .314 ethylene glycol 7.85, 7.91, 7.97 2 .314 ethylene glycol 7.73, 8.01, 8.32 1. What is the response variable? Time (in seconds) required for the liquid level to drop from 4in to 2in 2. How many factors? 2 factors: I am assuming that the researchers are not interested in the effect of the variable “technician” on the value of the response variable, and I am assuming that “technician” is a blocking variable. There are times, however, when we are interested in the effect of “person” on a response. For example, suppose there was an experiment where one factor was “surgeon,” with levels Dr. Brown, Dr. Jones, Dr. Smith, and another factor was “method of performing surgery”, with levels A, B, C. Suppose the response variable is “ two‐year survival rate.” Over the next year, each of the three heart surgeons in General Hospital performs heart surgery using each of the three methods, and each patient is observed for two years after surgery, whereupon his/her survival status is noted. Such an experiment is ethical if we truly do not know which method is the best and which surgeon is the best. If you are a potential patient, or if you are the person evaluating the performance of the surgeons, you are interested in the effect of surgeon on survival rate. (Yes, there are lots of complications with this experiment that I am not discussing.) 3. What are the factors (and their levels)? Diameter in inches(.188, .314) Liquid ( water, ethylene glycol) 1 4. How many treatments? 4 treatments 5. What are the experimental units? There is not enough information to answer this question. Scenario 1 (Detroit): If the researchers are interested in generalizing to all tubes of this type with the two diameters and if they are interested in generalizing to any water of ethylene glycol speciments, then they need to replicate the tubes and they need to use different water and different ethylene glycol in each run of the experiment. In this case, the experimental units are specific tubes used in conjunction with specific samples of liquid. This scenario is most likely to be the scenario of interest. Scenario 2 (Detroit and NASCAR): If the researchers are interested in future drainings of water and ethylene glycol through these specific tubes, but generalized over any quantity of water or ethylene glycol (not the same water and glycol over and over), then they need to replicate the liquid samples, and the experimental unit is liquid sample. Scenario 3 (NASCAR only): If the researchers are interested in draining the same quantity of water and the same quantity of ethylene glycol over and over using the same tubes—and no, it is not likely that anyone would be interested in this—then they simply replicate the act of draining, and the experimental unit is the act of draining. 6. Are there any controlled variables? Should there be?  “Person draining” should either be a controlled or a blocking varaible. The text said “person measuring” was spread over two people, but it didn’t say anything about “person draining.”  All conditions under which the draining takes place should be controlled—the starting condition of the drains, the exact way the liquid is poured, the temperature, etc… 7. Are there any blocking variables? Should there be?  Technician is a blocking variable. Yes, technician should be a blocking variable (or a controlled variable).  See controlled variables. 8. How many replicates? They used r=3 replicates per treatment. 2