Just one more production step: is it worthwhile?

The techies (scientists) in the lab have been lobbing you and your management in general to include just one more laboratory step. They think it is a good idea, although you have some doubt because one of them is known to be good friends with the founder of the startup biotechnology company that makes the regent used in the reaction. But if adding this step works as expected, it could help immensely in reducing production costs. The trouble is, the test results just came back and they don't look good. Discussion at the upcoming meeting between the technical staff and management will be spirited, so you have to decide to take a look at the data. Your firm is anticipating government approval from FDA to market a new medical diagnostic test made possible by monoclonal antibody technology, and you are part of the team in charge of production. Naturally, the team has been investigating ways to increase production yields or lower costs.

The proposed improvement is to insert yet another reaction as an intermediate purifying procedure. That is good because it focuses resources down the line on the particular product you want to produce. This is good because it focuses resources down the line on the particular product you want to produce. But it shares the problem of any additional step in the lab: one more manipulation, one more intervention, one more way for something to go wrong. In this particular case, it has been suggested that while small amounts of the reagent may be helpful, trying to purify too well will actually decrease the yield and increase the cost.

The design of the test was to have a series of test production runs, each with different amount of purifier, including one test run with the purification step omitted entirely. The order of the tests was randomized so that at any time trends would not be mistakenly interpreted as being due to purification. Here are the data and the regression results:

ANOVA df SS MS F Significance F Regression 1 471.339 471.339 3.259 0.105 Residual 9 1,301.553 144.615 Total 10 1,772.872 Std Low Up Coefficients Err P 95% 95% Intercept 21.577 6.783 3.181 0.011 6.232 36.922 Purifier 1.147 1.805 0.105 -0.524 4.664 2.070Amount of Observed Amount of Purifier Yield Purifier Observed Yield UI A WN - O 13.39 11.86 37.07 27.93 51.07 35.83 51.69 31.37 28.52 21.26 41.21 Summary Output Regression statistics Multiple R 0.516 R2 0.266 Adjusted R2 0.184 Standard Error 12.026 Observations 11