## Type 1 errors

### Outcomes and the Type I and Type II Errors Introduction to Statistics

Beta is commonly set at 0. Happily, the AP Statistics curriculum requires students to understand only the concept of power and what affects it; they are not expected to compute the power of a test of significance against a particular alternate hypothesis.

Read "The insignificance of statistical significance testing" by Johnson and Douglas to have an overview of the issue. In statistics , a null hypothesis is a statement that one seeks to nullify that is, to conclude is incorrect with evidence to the contrary. If the emergency crew thinks the victim is dead, they will not treat him.

Null Hypothesis: The decision is not to reject H 0 when, in fact, H 0 is false incorrect decision known as a Type II error. The outcomes are summarized in the following table:.

## Power in Tests of Significance

When they are done, they should compute what proportion of their simulations resulted in a rejection of the null hypothesis. The value of alpha, which is related to the level of significance that we selected has a direct bearing on type I errors.

And because it's so unlikely to get a statistic like that assuming that the null hypothesis is true, we decide to reject the null hypothesis.

In this case, the criteria of the upper left box are met that there is no sample size or power calculation and therefore the lack of a statistically significant difference may be due to inadequate power or a true lack of difference, but we cannot exclude inadequate power.

### The Difference Between Type I and Type II Errors

Post as a guest Name. What Does Power Mean? The results of such testing determine whether a particular set of results agrees reasonably or does not agree with the speculated hypothesis. Handbook of Parametric and Nonparametric Statistical Procedures. These bags represent populations with different proportions; label them by the proportion of blue chips in the bag: Mitroff, I.

In an ideal world, we would always reject the null hypothesis when it is false, and we would not reject the null hypothesis when it is indeed true. Suddenly my recommendation did not look very credible! The drug is falsely claimed to have a positive effect on a disease.

Figure 2 is an example of what the plot might look like.

## What Is Power?

Mathematically, power is 1 — beta. There is an important principle here: Statistically there would be only 5 numbers in the final hypothesis test, but we achieved greater power to detect an isolated "hot spot" by taking 25 physical samples.

The researcher thinks the blood cultures do contain traces of pathogen X , when in fact, they do not. In a statistical test, the hypothesis that there is no significant difference between specified populations, any observed difference being due to chance. Raiffa, H.

### What Is Power? Statistics Teacher

But if the null hypothesis is true, then, in reality, the drug does not combat the disease at all. Figure 2. Statisticians want to test the claim.