1.4 Statistical Decision-Making Process

The statistical decision-making process (SDMP) tries to minimize errors while ensuring that valuable insights are not overlooked. For example, if we wanted to see if customers are interested in purchasing a new product, we would want to make sure we don't simply look for any sign of interest—we would want only those that predict sales. If we thought that every sign of interest was valid, we would have a lot of false positives where we thought someone was interested in purchasing, but they were not. Our sample results would mistakenly lead us to believe sales will be high. In statistics, we call false positives Type I errors.

Type II errors are misses, or false negatives. If we had a Type II error in the above scenario, our sample would lead us to predict that there would not be high sales when sales actually would have been high.

An error rate is the chance or probability of a type of error occurring. While we will explain this in detail in future chapters, we think of the highest Type I error rate we can accept as alpha (α) and the Type II error rate as beta (β).

• Alpha (α) can be thought of as our Type I error rate, or the probability of a result being a false positive (we think our new sales technique works better than the one we've used before, but it really does not work better). 1 - α is the probability of our data not being a false positive and is often called our confidence level.

• Beta (β) can be thought of as our Type II error rate. 1 - β is referred to as power, or the probability we didn't miss something (our new sales technique really does work and we recognize that it does). It can also be thought of as the probability of finding something important if it is there.