Student Handout with Possible Answers Topic: Inference Lesson 2: Activity 2
Types of Errors[1]
In hypothesis testing we need to pick either H0 or Ha. Obviously we would like to make the correct decision, but we can sometimes make the wrong decision. How would you describe each of the following errors in words (in terms of the decision we made about the “fairness” of the process of balancing a Euro) for each one of these situations?
1) We select Ha but it is the wrong decision because H0 is true.
We concluded that balancing a Euro is an unfair process when it actually is a fair process, i.e. there is an equal chance of getting a head or a tail when a Euro is balanced.
2) We select H0 but it is the wrong decision because H0 is not true.
We concluded that balancing Euro is a fair process when it actually is an unfair process, i.e. we don’t expect heads or tails to come up equally when we balance a Euro repeatedly.
We call these situations a type I error and type II error respectively. Of course we would like to keep the chances of making a mistake very small. We usually express our decision in terms of the null hypothesis, H0. (We either reject or fail to reject H0.) In the same way, we usually focus on the probability of making type I error (rejecting the null hypothesis when it is true). This is because the null hypothesis reflects a 'status quo' or neutrality situation, and if we reject it we are making a statement saying that something is better or preferred, or worse, or different, depending on the situation.
Consider the following two hypotheses that could be used to examine the quality control process in a parachute factory.
H0: The parachutes being produced will open.
HA: The parachutes being produced will not open.
Describe what a type I error would be given these hypotheses. What are the practical implications of making a type I error?
We conclude that the parachutes will not open when they actually will open. This means that if the factory rejected that batch of parachutes, they will be discarding viable products and this will result in a loss for the company.
Describe what a type II error would be given these hypotheses. What are the practical implications of making a type II error?
We conclude that the parachutes will open when they will actually fail to open. This means that if the factory passed that batch of parachutes, they will be risking the lives of the people using those parachutes. The consequences are severe and life-threatening if a parachute does not open when it is supposed to.
In this situation, unlike the coin example, making one type of error is much more costly than making the other. This occurs in other situations as well. For instance, when two medicines are being compared in a pharmaceutical study a ' type I error' would mean that one medicine is concluded to be better when they have actually similar effectiveness. Type I error is usually considered a serious error and we like to have some control over it.
Reference
Seier, E., & Robe, C. (2002). Ducks and green – an introduction to the ideas of hypothesis testing. Teaching Statistics, 24(3), 82-86.
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[1] Please note the possible student answers may not, in some cases, be IDEAL student answers.