Using sample data to make decisions about your process carries with it the risk of making an erroneous decision. We will explore the concept of producer’s risk in the context of doing hypothesis testing.
Overview: What is producer’s risk?
Producer’s risk is also known as a Type 1, or alpha risk. It is the type of risk you have of being wrong when concluding something false about your process. This concept of risk is part of the decision-making process of hypothesis testing.
Hypothesis testing requires you to state two hypothetical conditions. The first, called the null hypothesis, states there has been no statistically significant change in your process or the part you just inspected is good. The second hypothesis, called the alternate hypothesis, states there was a meaningful change in your process, or that your inspected part is defective and should be rejected.
Once you have done the proper calculations for your hypothesis test, you must decide whether to reject the null and accept the alternate, concluding there was change or the part should be rejected. Or, you can decide not to reject the null and conclude there was no change or the part is good to ship to the customer.
With producer’s risk, you run the risk and consequences of acting when you shouldn’t have. When interpreting the results of your hypothesis test, you conclude the new marketing program was effective and did increase sales. Unfortunately, the truth was, it didn’t increase sales. You now have the cost associated with rolling out the new marketing program when it wasn’t effective. In another case, you concluded the part was defective and rejected it when it was actually good. You, the producer, now absorb the cost of rejecting a good part.
The good news is you can set your producer’s risk beforehand based on your risk profile. Since there is a direct cost from your bad decision, you want to minimize your risk and subsequent cost. The producer’s (or alpha) risk is typically set at 5%. This is the assumed risk you are willing to take for rejecting the null and claiming change when you shouldn’t have.
An industry example of producer’s risk
During consumer testing of a new beverage, a company’s statistician did a hypothesis test to determine whether the new beverage was preferred by customers more than the current product being sold. This was done early in the consumer testing, when there was limited data. As a result, the statistician concluded the new beverage was preferred more than the current drink and recommended the old drink be phased out and the new beverage be rapidly marketed, manufactured, and distributed.
As more consumer data came in, though, it became obvious that consumers were not switching to the new product. Unfortunately, because of lagging sales, the new product had to be discontinued, costing the company millions in wasted advertising and scrapped or heavily discounted product. It was the producer who took the risk and absorbed the producer’s error.
Frequently Asked Questions (FAQ) about producer’s risk
1. What is producer’s risk?
This is rejecting the null hypothesis when you shouldn’t have. It is erroneously determining there was change in the process when there wasn’t. The doctor claiming her patient had cancer when she didn’t is a producer’s risk or error.
2. How is producer’s risk related to the concept of confidence level?
Confidence level is calculated as 1.0 minus alpha or producer’s risk. Assuming you set your producer’s risk at 5%, your confidence level would be 1 – 0.05, or 95%. This means you are confident that if you took 100 samples and calculated a confidence interval for each sample, 95 of those 100 intervals would contain the true population parameter you are interested in.
3. How is producer’s risk different from consumer’s risk?
Consumer’s risk is failing to reject the null hypothesis when you should have rejected it. That is, thinking the inspected part was good when it wasn’t, so you shipped it to the customer. They have a risk of getting a bad part you thought was good. Producer’s risk is rejecting the null hypothesis and claiming change when there was none. Or rejecting a good part and scrapping it.