A Chemist plans to investigate the effects of four types of catalyst and three t

Question

A Chemist plans to investigate the effects of four types of catalyst and three types of reagents on the rate of a chemical reaction. Suppose that the amount of each type of catalyst and reagent, if decided to add, is fixed. Also, at most one type of catalyst and one type of reagent can be added simultaneously. Before planning the experiment she seeks your advice on how to run the experiment. She has written to you as follows: “I intend to study the catalysts first and then the reagents. However, I am restricted to fewer than or equal to 50 observations in total. In the first experiment I could use 6 replicates of each catalyst and in the second experiment I could use 8 replicates of each reagent. Then, I have 4*6 + 3*8 = 48 observations from this experimental plan. Alternatively, I could use 7 replicates of each catalyst in the first experiment, and 6 replicates of each reagent in the second experiment. Then, I totally use 4*7 + 3*6 = 46 observations from this experimental plan. Which of the two experimental plans would be best?” You have made an appointment to see her in order to discuss this. Make clear notes on the most important points to discuss with her at your meeting. Explain the statistical motives for discussing these points. You do not need to restrict the discussion to her specific question and you should include a preliminary recommendation of a plan for the experiment
A Chemist plans to investigate the effects of four types of catalyst and three types of reagents on the rate of a chemical reaction. Suppose that the amount of each type of catalyst and reagent, if decided to add, is fixed. Also, at most one type of catalyst and one type of reagent can be added simultaneously. Before planning the experiment she seeks your advice on how to run the experiment. She has written to you as follows: “I intend to study the catalysts first and then the reagents. However, I am restricted to fewer than or equal to 50 observations in total. In the first experiment I could use 6 replicates of each catalyst and in the second experiment I could use 8 replicates of each reagent. Then, I have 4*6 + 3*8 = 48 observations from this experimental plan. Alternatively, I could use 7 replicates of each catalyst in the first experiment, and 6 replicates of each reagent in the second experiment. Then, I totally use 4*7 + 3*6 = 46 observations from this experimental plan. Which of the two experimental plans would be best?” You have made an appointment to see her in order to discuss this. Make clear notes on the most important points to discuss with her at your meeting. Explain the statistical motives for discussing these points. You do not need to restrict the discussion to her specific question and you should include a preliminary recommendation of a plan for the experiment
A Chemist plans to investigate the effects of four types of catalyst and three types of reagents on the rate of a chemical reaction. Suppose that the amount of each type of catalyst and reagent, if decided to add, is fixed. Also, at most one type of catalyst and one type of reagent can be added simultaneously. Before planning the experiment she seeks your advice on how to run the experiment. She has written to you as follows: “I intend to study the catalysts first and then the reagents. However, I am restricted to fewer than or equal to 50 observations in total. In the first experiment I could use 6 replicates of each catalyst and in the second experiment I could use 8 replicates of each reagent. Then, I have 4*6 + 3*8 = 48 observations from this experimental plan. Alternatively, I could use 7 replicates of each catalyst in the first experiment, and 6 replicates of each reagent in the second experiment. Then, I totally use 4*7 + 3*6 = 46 observations from this experimental plan. Which of the two experimental plans would be best?” You have made an appointment to see her in order to discuss this. Make clear notes on the most important points to discuss with her at your meeting. Explain the statistical motives for discussing these points. You do not need to restrict the discussion to her specific question and you should include a preliminary recommendation of a plan for the experiment

Explanation / Answer

We are having 48 observations on one hand and 46 observations on another hand.

Though it is good to go with  anyone ( 48 or 46), it would impact that much in the results.

But since 48 observations make it easy to make the small sample size for statistical carryouts, like to perform ANOVA and other tests if required as per the approch. And with 46 also we can perform ANOVA but making equal sample size is difficult with 46 observations.

With 48 observations there are various options to choose sample size of 4,6,8,12,16 but in 46 it is difficult to have equal sample size.

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