Type I and II Errors
Heather has analyzed data from her study investigate the relationship between how Make a Type II error, that is, to conclude that there is no effect when there . You can quickly check to see how well you understand type I and type II errors in hypothesis testing when you have access to our short quiz and. I also appreciate the fact that students can retake quizzes etc. if they are The Relationship Between Confidence Intervals & Hypothesis Tests . The probability of making a type II error is labeled with a beta symbol like this.
And we'll do this on some population in question. This will say some hypotheses about a true parameter for this population. And the null hypothesis tends to be kind of what was always assumed or the status quo while the alternative hypothesis, hey, there's news here, there's something alternative here.
And to test it, and we're really testing the null hypothesis. We're gonna decide whether we want to reject or fail to reject the null hypothesis, we take a sample.
We take a sample from this population. Using that sample, we calculate a statistic, we calculate a statistic, that's trying to estimate the parameter in question.
And then using that statistic, we try to come up with the probability of getting that statistic, the probability of getting that statistic that we just calculated from that sample of a certain size, given if we were to assume that our null hypothesis, if our null hypothesis is true.
Type I Error and Type II Error
And if this probability, which is often known as a p-value, is below some threshold that we set ahead of time which is known as the significance level, then we reject the null hypothesis. Let me write this down.
So this right over here, this is our p-value.
This should all be review, we introduced it in other videos. We have seen on other videos if our p-value is less than our significance level, then we reject our null hypothesis, and if our p-value is greater than or equal to our significance level, alpha, then we fail to reject, fail to reject our null hypothesis.
And when we reject our null hypothesis, some people will say that might suggest the alternative hypothesis. But we might be wrong in either of these scenarios and that's where these errors come into play. Let's make a grid to make this clear. By one common convention, if the probability value is below 0.
What are Type I and Type II Errors? - Students 4 Best Evidence
Another convention, although slightly less common, is to reject the null hypothesis if the probability value is below 0. It is also called the significance level. As discussed in the section on significance testingit is better to interpret the probability value as an indication of the weight of evidence against the null hypothesis than as part of a decision rule for making a reject or do-not-reject decision. Therefore, keep in mind that rejecting the null hypothesis is not an all-or-nothing decision.
However, this is not correct. If the null hypothesis is false, then it is impossible to make a Type I error.
The second type of error that can be made in significance testing is failing to reject a false null hypothesis. This kind of error is called a Type II error.
When a statistical test is not significant, it means that the data do not provide strong evidence that the null hypothesis is false. Lack of significance does not support the conclusion that the null hypothesis is true.