You are the chief researcher for a pharmaceutical company. You have been assigned to write a research proposal on an experimental cancer drug that shows promise to treat some aggressive and lethal forms of cancer. The Board of Directors for the company has no idea what Type 1 and Type 2 errors are.
Develop a brief report on Type 1 and Type 2 errors specific to this study. Include the following:
- Concerns and consequences if Type 1 and Type 2 errors are committed.
- Ethical implications
- What does this mean for patients?
Type 1 and Type 2 errors revolve around the rejection or failure to reject the null hypothesis. As a review, when we reject the null hypothesis, what we are essentially saying is that there is a difference in the two groups we are comparing.
The null hypothesis states that there is no difference, so when we reject this and in a sense are saying there is a difference in the groups. We have rejected the null hypothesis and failed to reject the alternate hypothesis, which states there is a difference between the groups we are comparing. We are stating that the treatment we administered to the treatment group appears to have had an effect.
When we fail to reject the null hypothesis, what we are doing in a sense is stating that we think the null hypothesis is true. In effect, we are saying that there is no difference between the two groups we are comparing. In other words, the treatment we administered to the treatment group had no effect.
A Type 1 error occurs when we reject a null hypothesis that was true. A Type 2 error occurs when we fail to reject a null hypothesis that we should have rejected. In other words, we accepted a false null hypothesis.
Let’s explore these in greater depth. Since there are complexities in the language surrounding Type 1 and 2 errors, it may be helpful to walk through each of these and use some examples.
A Type 1 error occurs when we reject a null hypothesis that was actually true. So basically, we get rid of a null hypothesis that we should not have rejected. The null hypothesis says that there is no difference between the groups, or the treatment had no effect. When we perform a Type 1 error, we are saying that the null hypothesis was not true when in fact it was. We are saying that the treatment had an effect when in fact it did not have any effect.
Let’s discuss a medical example of a Type 1 error. Let’s assume we are testing a new medication. The medication did not have any effect, but we commit a Type 1 error and state that it did have an effect. We essentially state that worthless medication is effective. Let’s say this was a new drug for cancer. We say it is effective when in fact it is not. People who have cancer begin treatment with the drug to no effect. We may wish to say that is ok as the drug did not harm them. However, what may have happened is that a cancer patient may have wasted valuable time on an ineffective treatment. That is the potential damage of a Type 1 error in our example.
Let’s use the same example but commit a Type 2 error. A Type 2 error occurs when we do not reject a null hypothesis that we should have rejected. In other words, we say that the treatment had no effect, when in fact it did have an effect. In our example, we say that the medication had no effect when in fact it did have an effect. If we are again examining a new cancer drug, we are saying the drug was not effective. When we commit a Type 2 error in this example, the danger lies in that we may have rejected an effective treatment for cancer.
The potential to perform a Type 1 or a Type 2 error is inversely related. We set our “rejection levels” using statistical methods. This is beyond the scope of this course but suffice to say when we increase the risk of a Type 1 error, we decrease the risk of a Type 2 error and the inverse is also true. When we determine our rejection levels, we have to balance out the risks and determine what are acceptable levels of rejecting or not rejecting our null hypothesis.
In an ideal world, we reject all false null hypotheses and fail to reject all true null hypotheses. Of course, we are not operating in an ideal world. In our example, we have to set our rejection zones such that we try to decrease the worst of Type 1 or Type 2 errors. In our situation, both are not ideal, but we may want to set our statistics such that we decrease the risk for Type 1 errors. It would probably be less damaging to individuals if we missed out on a potential new cancer drug vs. having someone complete treatment with a cancer drug that was not effective.
Some ethical issues are also introduced when setting our rejection levels with Type 1 and Type 2 errors. In our example, or an individual a Type 1 error may prove worse than a Type 2 error, but if we are examining what is best for society as a whole, we may be better off decreasing the risk for a Type 2 error. Either type of error has practical as well as ethical implications
0 comments