Question

1. “Type I Error Blues,” by David Stein

The managers huddled to see if they had won or lost.

Did the new process from 2 months before yield data showing a reduction in cost?

Or was it merely a matter of chance…

Too soon to do the data dance?

So they set about the business of crafting a hypothesis test

In order to conclude which process was best.

With the null hypothesis meaning “status quo”, no change evident

They quickly concluded H₀ could not stand, as was their true intent.

Just one month later, they realized their grave mistake!

A Type II error would have been so much safer, for goodness sake.

Alas, their final huddle was a sad one with HR Director Bob.

He told them to go back to training school as each was now in need of a new job.

1. What was the likely managerial mood and outcome on the days immediately following the (erroneous) conclusion to reject this null hypothesis?

2. What would have been the likely managerial mood and outcome on the days immediately following an (erroneous) conclusion not to reject the null hypothesis?

3. In the presence of a Type II Error, what do you suppose would have happened to their cost reduction/process improvement efforts 3-6 months down the road? Please explain in everyday English.

Answer 1

1 & 2 ans. If you think only about business then managerial mood will be unhappy by rejecting the null hypothesis H0 : is the new process from the 2 months before yield data showing reduction in cost. Conversely manager will be happy by not rejecting the same. But you need to understand the statistical interpretation behind it. Here we need to have control about not only probability of making type 1 error but also on probability of making type 2 error. But at first think about the lower confidence interval & upper confidence interval. That will tell you about the extend of manager being happy or unhappy based on the rejecting and not rejecting the null.

3. ans. Now come to the point that there is presence of type 2 error. that is accepting the false null when new process do not provide reduction in cost. We do not have the control in prob of making type 2 error always. So, we write null as "do not reject H0" instead of "accept H0". In this case we should write null hypothesis like H0 : there is no difference between the two process in terms of cost. Then if we reject it then there will be possibility of type 1 error not type 2 error. Type 1 error is easy to determined & always in control.

Though their cost process improvements efforts will be getting a smashed , they will not get enough profit from minimizing cost.

To find it at the time we need to define our null hypothesis properly to get the impact on testing of hypothesis. By seeing the p value we reject/accept our null hypothesis. So probability of making error is very important. Every model should have some error. Otherwise a model cannot be improved further.