Watch this video lesson to learn about the two possible errors that you can make when performing hypothesis testing. You will see how important it is to really understand what these errors mean for your results.
Hypothesis testing is the formal procedure used by statisticians to test whether a certain hypothesis is true or not. It’s a four-step process that involves writing the hypothesis, creating an analysis plan, analyzing the data, and then interpreting the data. These tests are useful because you can use these tests to help you prove your hypotheses. If you have a successful test, then you can publish that information to let people know what you have found.For example, a cleaning company can publish information that proves that their cleaning product kills 99% of all germs if they perform a hypothesis test that has data that proves their hypothesis that their cleaning product kills 99% of germs.While these tests can be very helpful, there is a danger when it comes to interpreting the results.
It is possible to make two different kinds of errors when interpreting the results.
Type I Errors
The first type is called a type I error. This type of error happens when you say that the null hypothesis is false when it is actually true. Our null hypothesis is the hypothesis for our expected outcome. If our null hypothesis is that dogs live longer than cats, it would be like saying dogs don’t live longer than cats, when in fact, they do.
To help you remember this type I error, think of it as having just one wrong. You are wrongly thinking that the null hypothesis is false. In statistics, we label the probability of making this kind of error with this symbol:
It is called alpha. This is a value that you decide on. Usually, it is 0.05, which means that you are okay with a 5% chance of making a type I error.
The lower the alpha number, the lower the risk of you making such an error. The tricky part with setting the alpha number is that if you set it too low, it may mean that you won’t catch the really small differences that may be there.
Type II Errors
The other type of error is called a type II error.
This type of error happens when you say that the null hypothesis is true when it is actually false. For our null hypothesis that dogs live longer than cats, it would be like saying that dogs do live longer than cats, when in fact, they don’t. To help you remember a type II error, think of two wrongs. You are wrongly thinking that the null hypothesis is wrong. The probability of making a type II error is labeled with a beta symbol like this:
This type of error can be decreased by making sure that your sample size, the number of test subjects you have, is large enough so that real differences can be spotted.
So for the dogs and cats, this would mean that you need to gather data about enough dogs and cats to see a real difference between them. If you have information about just one dog and one cat, you can’t say for sure that the statement that dogs live longer than cats is true or not. If the dog lives longer than the cat, then you might make the mistake of saying that dogs do live longer than cats, even though the opposite were true. Your sample size isn’t large enough for you to see a difference.If you take this beta value and you subtract it from 1 (1 – beta), you will get what is called the power of your test.
The higher the power of your test, the less likely you are to make a type II error.
Let’s look at what might happen when either mistake is made.Let’s say that our null hypothesis is that all tap water is safe to drink. If we make a type I error, we would say that the result of our hypothesis test is that all tap water is not safe to drink. Because we’ve made a type I error, the reality is that all tap water is safe to drink. What would this mean for people who believed us? They might begin to filter the tap water or drink only bottled water.
They wouldn’t drink the water coming from the tap. Is this a bad thing? No, because people won’t get hurt.But what if we made a type II error? What if we said that our hypothesis test shows that all tap water is safe to drink? Because we’ve made a type II error, the truth is that not all tap water is safe to drink. What would happen in this case? Well, if people believed us and drank tap water everywhere, then they might get sick from the water because, in reality, it isn’t safe to drink. People might get worms or other diseases.
And in a worst-case scenario, some might even die!As you can see, depending on what your hypothesis is, making a type I or a type II error can be life-threatening. When you are planning out your hypothesis test, it’s important to think about these two types of errors and which one will be best to minimize. For our water hypothesis, it is the type II error that we want to minimize.
Let’s review what we’ve learned.Hypothesis testing is the formal procedure used by statisticians to test whether a certain hypothesis is true or not. Two types of errors can present themselves when interpreting the data. A type I error happens when you say that the null hypothesis is false when it actually is true.
A type II error happens when you say that the null hypothesis is true when it actually is false.Making one or the other type of error can be dangerous, depending on what your hypothesis is. You have to minimize the type of error that is most likely to cause damage. Our null hypothesis is the hypothesis for our expected outcome.Think of a type I error as having one wrong. You are wrongly thinking that the null hypothesis is true.
Your type II error has two wrongs. You are wrongly thinking that the null hypothesis is wrong.
|This hypothesis can usually be proven true or